Mathematics Books

Book SynopsisThe mathematical and statistical tools needed in the rapidly growing quantitative finance field With the rapid growth in quantitative finance, practitioners must achieve a high level of proficiency in math and statistics. Mathematical Methods and Statistical Tools for Finance, part of the Frank J.Table of ContentsPreface xi About the Authors xvii CHAPTER 1 Basic Concepts: Sets, Functions, and Variables 1 Introduction 2 Sets and Set Operations 2 Distances and Quantities 6 Functions 10 Variables 10 Key Points 11 CHAPTER 2 Differential Calculus 13 Introduction 14 Limits 15 Continuity 17 Total Variation 19 The Notion of Differentiation 19 Commonly Used Rules for Computing Derivatives 21 Higher-Order Derivatives 26 Taylor Series Expansion 34 Calculus in More Than One Variable 40 Key Points 41 CHAPTER 3 Integral Calculus 43 Introduction 44 Riemann Integrals 44 Lebesgue-Stieltjes Integrals 47 Indefinite and Improper Integrals 48 The Fundamental Theorem of Calculus 51 Integral Transforms 52 Calculus in More Than One Variable 57 Key Points 57 CHAPTER 4 Matrix Algebra 59 Introduction 60 Vectors and Matrices Defined 61 Square Matrices 63 Determinants 66 Systems of Linear Equations 68 Linear Independence and Rank 69 Hankel Matrix 70 Vector and Matrix Operations 72 Finance Application 78 Eigenvalues and Eigenvectors 81 Diagonalization and Similarity 82 Singular Value Decomposition 83 Key Points 83 CHAPTER 5 Probability: Basic Concepts 85 Introduction 86 Representing Uncertainty with Mathematics 87 Probability in a Nutshell 89 Outcomes and Events 91 Probability 92 Measure 93 Random Variables 93 Integrals 94 Distributions and Distribution Functions 96 Random Vectors 97 Stochastic Processes 100 Probabilistic Representation of Financial Markets 102 Information Structures 103 Filtration 104 Key Points 106 CHAPTER 6 Probability: Random Variables and Expectations 107 Introduction 109 Conditional Probability and Conditional Expectation 110 Moments and Correlation 112 Copula Functions 114 Sequences of Random Variables 116 Independent and Identically Distributed Sequences 117 Sum of Variables 118 Gaussian Variables 120 Appproximating the Tails of a Probability Distribution: Cornish-Fisher Expansion and Hermite Polynomials 123 The Regression Function 129 Fat Tails and Stable Laws 131 Key Points 144 CHAPTER 7 Optimization 147 Introduction 148 Maxima and Minima 149 Lagrange Multipliers 151 Numerical Algorithms 156 Calculus of Variations and Optimal Control Theory 161 Stochastic Programming 163 Application to Bond Portfolio: Liability-Funding Strategies 164 Key Points 178 CHAPTER 8 Difference Equations 181 Introduction 182 The Lag Operator L 183 Homogeneous Difference Equations 183 Recursive Calculation of Values of Difference Equations 192 Nonhomogeneous Difference Equations 195 Systems of Linear Difference Equations 201 Systems of Homogeneous Linear Difference Equations 202 Key Points 209 CHAPTER 9 Differential Equations 211 Introduction 212 Differential Equations Defined 213 Ordinary Differential Equations 213 Systems of Ordinary Differential Equations 216 Closed-Form Solutions of Ordinary Differential Equations 218 Numerical Solutions of Ordinary Differential Equations 222 Nonlinear Dynamics and Chaos 228 Partial Differential Equations 231 Key Points 237 CHAPTER 10 Stochastic Integrals 239 Introduction 240 The Intuition behind Stochastic Integrals 243 Brownian Motion Defined 248 Properties of Brownian Motion 254 Stochastic Integrals Defined 255 Some Properties of Itoˆ Stochastic Integrals 259 Martingale Measures and the Girsanov Theorem 260 Key Points 266 CHAPTER 11 Stochastic Differential Equations 267 Introduction 268 The Intuition behind Stochastic Differential Equations 269 Itoˆ Processes 272 Stochastic Differential Equations 273 Generalization to Several Dimensions 276 Solution of Stochastic Differential Equations 278 Derivation of Itoˆ ’s Lemma 282 Derivation of the Black-Scholes Option Pricing Formula 284 Key Points 291 Index 293

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Book SynopsisPraise for the Second Edition An essential desktop reference book . . . it should definitely be on your bookshelf.Technometrics A thoroughly updated book, Methods and Applications of Linear Models: Regression and the Analysis of Variance, Third Edition features innovative approaches to understanding and working with models and theory of linear regression. The Third Edition provides readers with the necessary theoretical concepts, which are presented using intuitive ideas rather than complicated proofs, to describe the inference that is appropriate for the methods being discussed. The book presents a unique discussion that combines coverage of mathematical theory of linear models with analysis of variance models, providing readers with a comprehensive understanding of both the theoretical and technical aspects of linear models. With a new focus on fixed effects models, Methods and Applications of Linear Models: Regression and Table of ContentsPreface to the Third Edition xvii Preface to the Second Edition xix Preface to the First Edition xxi PART I REGRESSION 1 1 Introduction to Linear Models 3 1.1 Background Information, 3 1.2 Mathematical and Statistical Models, 5 1.3 Definition of the Linear Model, 8 1.4 Examples of Regression Models, 13 1.5 Concluding Comments, 21 Exercises, 21 2 Regression on Functions of One Variable 23 2.1 The Simple Linear Regression Model, 23 2.2 Parameter Estimation, 25 2.3 Properties of the Estimators and Test Statistics, 34 2.4 The Analysis of Simple Linear Regression Models, 39 2.5 Examining the Data and the Model, 50 2.6 Polynomial Regression Models, 63 Exercises, 72 3 Transforming the Data 81 3.1 The Need for Transformations, 81 3.2 Weighted Least Squares, 82 3.3 Variance Stabilizing Transformations, 85 3.4 Transformations to Achieve a Linear Model, 86 3.5 Analysis of the Transformed Model, 92 Exercises, 95 4 Regression on Functions of Several Variables 99 4.1 The Multiple Linear Regression Model, 99 4.2 Preliminary Data Analysis, 100 4.3 Analysis of the Multiple Linear Regression Model, 103 4.4 Partial Correlation and Added-Variable Plots, 113 4.5 Variable Selection, 119 4.6 Model Specification, 130 Exercises, 137 5 Collinearity in Multiple Linear Regression 142 5.1 The Collinearity Problem, 142 5.2 An Example with Collinearity, 150 5.3 Collinearity Diagnostics, 156 5.4 Remedial Solutions: Biased Estimators, 166 Exercises, 178 6 Influential Observations in Multiple Linear Regression 182 6.1 The Influential Data Problem, 182 6.2 The Hat Matrix, 183 6.3 The Effects of Deleting Observations, 188 6.4 Numerical Measures of Influence, 192 6.5 The Dilemma Data, 197 6.6 Plots for Identifying Unusual Cases, 201 6.7 Robust/Resistant Methods in Regression Analysis, 209 Exercises, 213 7 Polynomial Models and Qualitative Predictors 216 7.1 Polynomial Models, 216 7.2 The Analysis of Response Surfaces, 220 7.3 Models with Qualitative Predictors, 225 Exercises, 247 8 Additional Topics 254 8.1 Nonlinear Regression Models, 254 8.2 Nonparametric Model-Fitting Methods, 260 8.3 Generalized Linear Models, 265 8.4 Random Input Variables, 274 8.5 Errors in the Inputs, 276 8.6 Calibration, 277 Exercises, 278 PART II THE ANALYSIS OF VARIANCE 283 9 Classification Models I: Introduction 285 9.1 Background Information, 285 9.2 The One-Way Classification Model, 286 9.3 The Two-Way Classification Model: Balanced Data, 304 9.4 The Two-Way Classification Model: Unbalanced Data, 322 9.5 The Two-Way Classification Model: No Interaction, 334 9.6 Concluding Comments, 347 Exercises, 347 10 The Mathematical Theory of Linear Models 359 10.1 The Distribution of Linear and Quadratic Forms, 359 10.2 Estimation and Inference for Linear Models, 368 10.3 Tests of Linear Hypotheses on β, 380 10.4 Confidence Regions and Intervals, 392 Exercises, 395 11 Classification Models II: Multiple Crossed and Nested Factors 405 11.1 The Three-Factor Cross-Classified Model, 406 11.2 A General Structure for Balanced, Factorial Models, 412 11.3 The Twofold Nested Model, 417 11.4 A General Structure for Balanced, Nested Models, 426 11.5 A Three-Factor, Nested-Factorial Model, 429 11.6 A General Structure for Balanced, Nested-Factorial Models, 434 Exercises, 438 12 Mixed Models I: The AOV Method with Balanced Data 443 12.1 Introduction, 443 12.2 Examples of the Analysis of Mixed Models, 444 12.3 The General Analysis for Balanced, Mixed Models, 464 12.4 Additional Examples, 479 12.5 Alternative Developments of Mixed Models, 487 Exercises, 493 13 Mixed Models II: The AVE Method with Balanced Data 499 13.1 Introduction, 499 13.2 The Two-Way Cross-Classification Model, 500 13.3 The Three-Factor, Cross-Classification Model, 511 13.4 Nested Models, 515 13.5 Nested-Factorial Models, 518 13.6 A General Description of the AVE Table, 524 13.7 Additional Examples, 531 13.8 The Computational Procedure for the AVE Method, 537 Exercises, 537 14 Mixed Models III: Unbalanced Data 543 14.1 Introduction, 543 14.2 Parameter Estimation: Likelihood Methods, 545 14.3 ML and REML Estimates with Balanced Data, 554 14.4 The EM Algorithm for REML Estimation, 558 14.5 Diagnostic Analysis with the EM Algorithm, 572 14.6 Models with Covariates, 581 14.7 Summary, 585 Exercises, 585 15 Simultaneous Inference: Tests and Confidence Intervals 591 15.1 Simultaneous Tests, 591 15.2 Simultaneous Confidence Intervals, 610 Exercises, 612 Appendix A Mathematics 615 A.I Matrix Algebra, 615 A.I.1 Notation, 615 A.I.2 The Rank of a Matrix, 616 A.I.3 The Trace of a Matrix, 617 A.I.4 Eigenvalues and Eigenvectors, 617 A.I.5 Quadratic Forms and Definite Matrices, 618 A.I.6 Special Matrices, 619 A.I.7 The Diagonalization of Matrices, 620 A.I.8 Kronecker Products of Matrices, 620 A.I.9 Factorization of Matrices, 621 A.I.10 Matrix Inversion, 622 A.I.11 The Solution of Linear Equations, 624 A.I.12 Generalized Inverses, 627 A.I.13 Cauchy–Schwartz Inequalities, 630 A.II Optimization, 630 A.II.1 The Differentiation of Matrices and Determinants, 630 A.II.2 The Differentiation of a Function with Respect to a Vector, 631 A.II.3 The Optimization of a Function, 632 Appendix B Statistics 634 B.I Distributions, 634 B.I.1 The Normal Distribution, 634 B.I.2 The χ2-Distribution, 637 B.I.3 The t-Distribution, 638 B.I.4 The F-distribution, 639 B.II The Distribution of Quadratic Forms, 639 B.III Estimation, 642 B.III.1 Maximum Likelihood Estimation, 642 B.III.2 Constrained Maximum Likelihood Estimation, 642 B.III.3 Complete, Sufficient Statistics, 643 B.IV Tests of Hypotheses and Confidence Regions, 643 B.IV.1 Tests of Hypotheses, 643 B.IV.2 Confidence Intervals and Regions, 644 Appendix C Data Tables 645 C.I Downloading Data Files from FTP Server, 645 C.II Listing of Data Set Files, 645 Appendix D Statistical Tables 660 References 669 Index 677

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Book SynopsisCausality in a Social World introduces innovative new statistical research and strategies for investigating moderated intervention effects, mediated intervention effects, and spill-over effects using experimental or quasi-experimental data.Table of ContentsPreface xv Part I Overview 1 1 Introduction 3 1.1 Concepts of moderation, mediation, and spill-over 3 1.2 Weighting methods for causal inference 10 1.3 Objectives and organization of the book 11 1.4 How is this book situated among other publications on related topics? 12 2 Review of causal inference concepts and methods 18 2.1 Causal inference theory 18 2.2 Applications to Lord’s paradox and Simpson’s paradox 27 2.3 Identification and estimation 34 3 Review of causal inference designs and analytic methods 40 3.1 Experimental designs 40 3.2 Quasiexperimental designs 44 3.3 Statistical adjustment methods 46 3.4 Propensity score 55 4 Adjustment for selection bias through weighting 76 4.1 Weighted estimation of population parameters in survey sampling 77 4.2 Weighting adjustment for selection bias in causal inference 80 4.3 MMWS 86 5 Evaluations of multivalued treatments 100 5.1 Defining the causal effects of multivalued treatments 100 5.2 Existing designs and analytic methods for evaluating multivalued treatments 102 5.3 MMWS for evaluating multivalued treatments 112 5.4 Summary 123 Part II Moderation 127 6 Moderated treatment effects: concepts and existing analytic methods 129 6.1 What is moderation? 129 6.2 Experimental designs and analytic methods for investigating explicit moderators 136 6.3 Existing research designs and analytic methods for investigating implicit moderators 142 7 Marginal mean weighting through stratification for investigating moderated treatment effects 159 7.1 Existing methods for moderation analyses with quasiexperimental data 159 7.2 MMWS estimation of treatment effects moderated by individual or contextual characteristics 168 7.3 MMWS estimation of the joint effects of concurrent treatments 174 8 Cumulative effects of time-varying treatments 185 8.1 Causal effects of treatment sequences 186 8.2 Existing strategies for evaluating time-varying treatments 190 8.3 MMWS for evaluating 2-year treatment sequences 195 8.4 MMWS for evaluating multiyear sequences of multivalued treatments 204 8.5 Conclusion 207 Part III Mediation 211 9 Concepts of mediated treatment effects and experimental designs for investigating causal mechanisms 213 9.1 Introduction 214 9.2 Path coefficients 215 9.3 Potential outcomes and potential mediators 216 9.4 Causal effects with counterfactual mediators 219 9.5 Population causal parameters 222 9.6 Experimental designs for studying causal mediation 225 10 Existing analytic methods for investigating causal mediation mechanisms 238 10.1 Path analysis and SEM 239 10.2 Modified regression approach 246 10.3 Marginal structural models 250 10.4 Conditional structural models 252 10.5 Alternative weighting methods 254 10.6 Resampling approach 256 10.7 IV method 257 10.8 Principal stratification 259 10.9 Sensitivity analysis 261 10.10 Conclusion 265 11 Investigations of a simple mediation mechanism 273 11.1 Application example: national evaluation of welfare-to-work strategies 274 11.2 RMPW rationale 277 11.3 Parametric RMPW procedure 287 11.4 Nonparametric RMPW procedure 290 11.5 Simulation results 292 11.6 Discussion 295 12 RMPW extensions to alternative designs and measurement 301 12.1 RMPW extensions to mediators and outcomes of alternative distributions 301 12.2 RMPW extensions to alternative research designs 306 12.3 Alternative decomposition of the treatment effect 321 13 RMPW extensions to studies of complex mediation mechanisms 325 13.1 RMPW extensions to moderated mediation 325 13.2 RMPW extensions to concurrent mediators 328 13.3 RMPW extensions to consecutive mediators 340 13.4 Discussion 355 Part IV Spill-over 363 14 Spill-over of treatment effects: concepts and methods 365 14.1 Spill-over: A nuisance, a trifle, or a focus? 365 14.2 Stable versus unstable potential outcome values: An example from agriculture 367 14.3 Consequences for causal inference when spill-over is overlooked 369 14.4 Modified framework of causal inference 371 14.5 Identification: Challenges and solutions 376 14.6 Analytic strategies for experimental and quasiexperimental data 384 14.7 Summary 387 15 Mediation through spill-over 391 15.1 Definition of mediated effects through spill-over in a cluster randomized trial 393 15.2 Identification and estimation of the spill-over effect in a cluster randomized design 395 15.3 Definition of mediated effects through spill-over in a multisite trial 402 15.4 Identification and estimation of spill-over effects in a multisite trial 406 15.5 Consequences of omitting spill-over effects in causal mediation analyses 412 15.6 Quasiexperimental application 416 15.7 Summary 419 Index 423

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Book SynopsisData Mining Algorithms is a practical, technically-oriented guide to data mining algorithms that covers the most important algorithms for building classification, regression, and clustering models, as well as techniques used for attribute selection and transformation, model quality evaluation, and creating model ensembles. The author presents many of the important topics and methodologies widely used in data mining, whilst demonstrating the internal operation and usage of data mining algorithms using examples in R.Table of ContentsAcknowledgements xix Preface xxi References xxxi Part I Preliminaries 1 1 Tasks 3 1.1 Introduction 3 1.2 Inductive learning tasks 5 1.3 Classification 9 1.4 Regression 14 1.5 Clustering 16 1.6 Practical issues 19 1.7 Conclusion 20 1.8 Further readings 21 References 22 2 Basic statistics 23 2.1 Introduction 23 2.2 Notational conventions 24 2.3 Basic statistics as modeling 24 2.4 Distribution description 25 2.5 Relationship detection 47 2.6 Visualization 62 2.7 Conclusion 65 2.8 Further readings 66 References 67 Part II Classification 69 3 Decision trees 71 3.1 Introduction 71 3.2 Decision tree model 72 3.3 Growing 76 3.4 Pruning 90 3.5 Prediction 103 3.6 Weighted instances 105 3.7 Missing value handling 106 3.8 Conclusion 114 3.9 Further readings 114 References 116 4 Naïve Bayes classifier 118 4.1 Introduction 118 4.2 Bayes rule 118 4.3 Classification by Bayesian inference 120 4.4 Practical issues 125 4.5 Conclusion 131 4.6 Further readings 131 References 132 5 Linear classification 134 5.1 Introduction 134 5.2 Linear representation 136 5.3 Parameter estimation 145 5.4 Discrete attributes 154 5.5 Conclusion 155 5.6 Further readings 156 References 157 6 Misclassification costs 159 6.1 Introduction 159 6.2 Cost representation 161 6.3 Incorporating misclassification costs 164 6.4 Effects of cost incorporation 176 6.5 Experimental procedure 180 6.6 Conclusion 184 6.7 Further readings 185 References 187 7 Classification model evaluation 189 7.1 Introduction 189 7.2 Performance measures 190 7.3 Evaluation procedures 213 7.4 Conclusion 231 7.5 Further readings 232 References 233 Part III Regression 235 8 Linear regression 237 8.1 Introduction 237 8.2 Linear representation 238 8.3 Parameter estimation 242 8.4 Discrete attributes 250 8.5 Advantages of linear models 251 8.6 Beyond linearity 252 8.7 Conclusion 258 8.8 Further readings 258 References 259 9 Regression trees 261 9.1 Introduction 261 9.2 Regression tree model 262 9.3 Growing 263 9.4 Pruning 274 9.5 Prediction 277 9.6 Weighted instances 278 9.7 Missing value handling 279 9.8 Piecewise linear regression 284 9.9 Conclusion 292 9.10 Further readings 292 References 293 10 Regression model evaluation 295 10.1 Introduction 295 10.2 Performance measures 296 10.3 Evaluation procedures 303 10.4 Conclusion 309 10.5 Further readings 309 References 310 Part IV Clustering 311 11 (Dis)similarity measures 313 11.1 Introduction 313 11.2 Measuring dissimilarity and similarity 313 11.3 Difference-based dissimilarity 314 11.4 Correlation-based similarity 321 11.5 Missing attribute values 324 11.6 Conclusion 325 11.7 Further readings 325 References 326 12 k-Centers clustering 328 12.1 Introduction 328 12.2 Algorithm scheme 330 12.3 k-Means 334 12.4 Beyond means 338 12.5 Beyond (fixed) k 342 12.6 Explicit cluster modeling 343 12.7 Conclusion 345 12.8 Further readings 345 References 347 13 Hierarchical clustering 349 13.1 Introduction 349 13.2 Cluster hierarchies 351 13.3 Agglomerative clustering 353 13.4 Divisive clustering 361 13.5 Hierarchical clustering visualization 364 13.6 Hierarchical clustering prediction 366 13.7 Conclusion 369 13.8 Further readings 370 References 371 14 Clustering model evaluation 373 14.1 Introduction 373 14.2 Per-cluster quality measures 376 14.3 Overall quality measures 385 14.4 External quality measures 393 14.5 Using quality measures 397 14.6 Conclusion 398 14.7 Further readings 398 References 399 Part V Getting Better Models 401 15 Model ensembles 403 15.1 Introduction 403 15.2 Model committees 404 15.3 Base models 406 15.4 Model aggregation 420 15.5 Specific ensemble modeling algorithms 431 15.6 Quality of ensemble predictions 448 15.7 Conclusion 449 15.8 Further readings 450 References 451 16 Kernel methods 454 16.1 Introduction 454 16.2 Support vector machines 457 16.3 Support vector regression 473 16.4 Kernel trick 482 16.5 Kernel functions 484 16.6 Kernel prediction 487 16.7 Kernel-based algorithms 489 16.8 Conclusion 494 16.9 Further readings 495 References 496 17 Attribute transformation 498 17.1 Introduction 498 17.2 Attribute transformation task 499 17.3 Simple transformations 504 17.4 Multiclass encoding 510 17.5 Conclusion 521 17.6 Further readings 521 References 522 18 Discretization 524 18.1 Introduction 524 18.2 Discretization task 525 18.3 Unsupervised discretization 530 18.4 Supervised discretization 533 18.5 Effects of discretization 551 18.6 Conclusion 553 18.7 Further readings 553 References 556 19 Attribute selection 558 19.1 Introduction 558 19.2 Attribute selection task 559 19.3 Attribute subset search 562 19.4 Attribute selection filters 568 19.5 Attribute selection wrappers 588 19.6 Effects of attribute selection 593 19.7 Conclusion 598 19.8 Further readings 599 References 600 20 Case studies 602 20.1 Introduction 602 20.2 Census income 605 20.3 Communities and crime 631 20.4 Cover type 640 20.5 Conclusion 654 20.6 Further readings 655 References 655 Closing 657 A Notation 659 A.1 Attribute values 659 A.2 Data subsets 659 A.3 Probabilities 660 B R packages 661 B.1 CRAN packages 661 B.2 DMR packages 662 B.3 Installing packages 663 References 664 C Datasets 666 Index 667

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Book Synopsisguidance in all subject areas Editor:Tony Greenfield, Industrial Statistics Research Unit (ISRU), University of Newcastle-upon-Tyne, UK Research Methods for Postgraduates brings together guidance for postgraduate students on how to organise, plan and do research from an interdisciplinary perspective.Table of ContentsAbout the Author ix List of Contributors xi Preface to the Third Edition xiii Preface to the Second Edition xix Preface to the First Edition xxi Part I First Steps 1 1 A View of Research 3Tony Greenfield 2 The Research Journey: Four Steps to Success 7Tom Bourner and Sue Greener 3 Managing Your Doctorate 13Stan Taylor 4 Documenting Your Work 34Vivien Martin 5 Ethics of Research 46Tony Greenfield 6 Plagiarism 56Tony Greenfield 7 Critically Reviewing Your Own Research 60Tom Bourner and Juliet Millican Part II Support 69 8 Research Proposals for Funding 71Lowry McComb 9 Who Can Help? 81Shirley Coleman 10 Information and Library Services 86Claire Abson and Alastair Allan 11 Research Methods for Advanced Web Searching 94Alastair Allan 12 Searching in Unfamiliar Fields 113Tom Bourner and Sue Greener 13 Sources of Population Statistics 121Keith Dugmore 14 An Introduction to Bibliometrics 130Silvia Salini 15 Choosing and Using Software for Statistics 144Felix Grant 16 Computer Support for Data Analysis 152Clifford E. Lunneborg Part III Measurement and Experimentation 157 17 Instrumentation in Experimentation 159Anand D. Pandyan, Frederike van Wijck and Garth R. Johnson 18 Randomised Trials 171Douglas G. Altman 19 Laboratory and Industrial Experiments 180Tony Greenfield 20 Experiments in Biological Sciences 193Roger Payne 21 Survey Research 202David de Vaus 22 Theory and Practice of Qualitative Research 214Irena Ograjenšek 23 Kansei Engineering 231Lluis Marco-Almagro 24 Principles of Sampling 244Peter Lynn 25 Sampling in Human Studies 255Peter Lynn 26 Interviewing 264Mark Hughes 27 Measurement Error 275Roland Caulcutt Part IV Data Analysis 287 28 Elementary Statistics 289David J. Hand 29 Further Statistical Methods 299David J. Hand 30 Spreadsheets: A Few Tips 307Tony Greenfield and Andrea Benn Part V Special Tools 323 31 The Value of Mathematical Models 325Andrew Metcalfe 32 Deterministic Models 342Andrew Metcalfe 33 Stochastic Models and Simulation 357David Green and Andrew Metcalfe 34 Optimisation 372Aiden Fisher and Andrew Metcalfe Part VI Presentation 387 35 Writing the Thesis 389Tony Greenfield 36 The Logic of a Research Report 400Tom Bourner and Linda Heath 37 Presenting Data 412Sue Greener 38 Presenting and Sharing Your Research 419Sue Greener 39 Reporting Research 429Iveta Simera and Douglas G. Altman 40 Social Media – How to Make ItWork for You as a Post-Graduate 440Suzanne Fraser-Martin and Catherine Fraser-Martin Part VII Next Steps 455 41 Protection and Exploitation of Intellectual Property 457Patrick Andrews 42 Career Opportunities 470Sara Shinton Index 479

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Book SynopsisFeaturing practical approaches to various reliability theory applications, this book the first of three in a series helps readers to understand and properly utilize statistical methods and optimal resource allocation to solve everyday engineering problems.Table of ContentsPreface xiii Acronyms and Notations xv 1 What Is Reliability? 1 1.1 Reliability as a Property of Technical Objects, 1 1.2 Other “Ilities”, 2 1.3 Hierarchical Levels of Analyzed Objects, 5 1.4 How Can Reliability Be Measured?, 5 1.5 Software Reliability, 7 1.5.1 Case Study: Avalanche of Software Failures, 8 2 Unrecoverable Objects 9 2.1 Unit, 9 2.1.1 Probability of Failure-Free Operation, 9 2.1.2 Mean Time to Failure, 10 2.2 Series Systems, 11 2.2.1 Probability of Failure-Free Operation, 11 2.2.2 Mean Time to Failure, 13 2.3 Parallel System, 14 2.3.1 Probability of Failure-Free Operation, 14 2.3.2 Mean Time to Failure, 18 2.4 Structure of Type “k-out-of-n”, 20 2.5 Realistic Models of Loaded Redundancy, 22 2.5.1 Unreliable Switching Process, 23 2.5.2 Non-Instant Switching, 23 2.5.3 Unreliable Switch, 24 2.5.4 Switch Serving as Interface, 25 2.5.5 Incomplete Monitoring of the Operating Unit, 26 2.5.6 Periodical Monitoring of the Operating Unit, 28 2.6 Reducible Structures, 28 2.6.1 Parallel-Series and Series-Parallel Structures, 28 2.6.2 General Case of Reducible Structures, 29 2.7 Standby Redundancy, 30 2.7.1 Simple Redundant Group, 30 2.7.2 Standby Redundancy of Type “k-out-of-n”, 33 2.8 Realistic Models of Unloaded Redundancy, 34 2.8.1 Unreliable Switching Process, 34 2.8.2 Non-Instant Switching, 35 2.8.3 Unreliable Switch, 35 2.8.4 Switch Serving as Interface, 37 2.8.5 Incomplete Monitoring of the Operating Unit, 38 3 Recoverable Systems: Markov Models 40 3.1 Unit, 40 3.1.1 Markov Model, 41 3.2 Series System, 47 3.2.1 Turning Off System During Recovery, 47 3.2.2 System in Operating State During Recovery: Unrestricted Repair, 49 3.2.3 System in Operating State During Recovery: Restricted Repair, 51 3.3 Dubbed System, 53 3.3.1 General Description, 53 3.3.2 Nonstationary Availability Coefficient, 54 3.3.3 Stationary Availability Coefficient, 58 3.3.4 Probability of Failure-Free Operation, 59 3.3.5 Stationary Coefficient of Interval Availability, 62 3.3.6 Mean Time to Failure, 63 3.3.7 Mean Time Between Failures, 63 3.3.8 Mean Recovery Time, 65 3.4 Parallel Systems, 65 3.5 Structures of Type “m-out-of-n”, 66 4 Recoverable Systems: Heuristic Models 72 4.1 Preliminary Notes, 72 4.2 Poisson Process, 75 4.3 Procedures over Poisson Processes, 78 4.3.1 Thinning Procedure, 78 4.3.2 Superposition Procedure, 80 4.4 Asymptotic Thinning Procedure over Stochastic Point Process, 80 4.5 Asymptotic Superposition of Stochastic Point Processes, 82 4.6 Intersection of Flows of Narrow Impulses, 84 4.7 Heuristic Method for Reliability Analysis of Series Recoverable Systems, 87 4.8 Heuristic Method for Reliability Analysis of Parallel Recoverable Systems, 87 4.8.1 Influence of Unreliable Switching Procedure, 88 4.8.2 Influence of Switch’s Unreliability, 89 4.8.3 Periodical Monitoring of the Operating Unit, 90 4.8.4 Partial Monitoring of the Operating Unit, 91 4.9 Brief Historical Overview and Related Sources, 93 5 Time Redundancy 95 5.1 System with Possibility of Restarting Operation, 95 5.2 Systems with “Admissibly Short Failures”, 98 5.3 Systems with Time Accumulation, 99 5.4 Case Study: Gas Pipeline with an Underground Storage, 100 5.5 Brief Historical Overview and Related Sources, 102 6 “Aging” Units and Systems of “Aging” Units 103 6.1 Chebyshev Bound, 103 6.2 “Aging” Unit, 104 6.3 Bounds for Probability of Failure-Free Operations, 105 6.4 Series System Consisting of “Aging” Units, 108 6.4.1 Preliminary Lemma, 108 6.5 Series System, 110 6.5.1 Probability of Failure-Free Operation, 110 6.5.2 Mean Time to Failure of a Series System, 112 6.6 Parallel System, 114 6.6.1 Probability of Failure-Free Operation, 114 6.6.2 Mean Time to Failure, 117 6.7 Bounds for the Coefficient of Operational Availability, 119 6.8 Brief Historical Overview and Related Sources, 121 7 Two-Pole Networks 123 7.1 General Comments, 123 7.1.1 Method of Direct Enumeration, 125 7.2 Method of Boolean Function Decomposition, 127 7.3 Method of Paths and Cuts, 130 7.3.1 Esary–Proschan Bounds, 130 7.3.2 “Improvements” of Esary–Proschan Bounds, 133 7.3.3 Litvak–Ushakov Bounds, 135 7.3.4 Comparison of the Two Methods, 139 7.4 Brief Historical Overview and Related Sources, 140 8 Performance Effectiveness 143 8.1 Effectiveness Concepts, 143 8.2 General Idea of Effectiveness Evaluation, 145 8.2.1 Conditional Case Study: Airport Traffic Control System, 147 8.3 Additive Type of System Units’ Outcomes, 150 8.4 Case Study: ICBM Control System, 151 8.5 Systems with Intersecting Zones of Action, 153 8.6 Practical Recommendation, 158 8.7 Brief Historical Overview and Related Sources, 160 9 System Survivability 162 9.1 Illustrative Example, 166 9.2 Brief Historical Overview and Related Sources, 167 10 Multistate Systems 169 10.1 Preliminary Notes, 169 10.2 Generating Function, 169 10.3 Universal Generating Function, 172 10.4 Multistate Series System, 174 10.4.1 Series Connection of Piping Runs, 174 10.4.2 Series Connection of Resistors, 177 10.4.3 Series Connections of Capacitors, 179 10.5 Multistate Parallel System, 181 10.5.1 Parallel Connection of Piping Runs, 181 10.5.2 Parallel Connection of Resistors, 182 10.5.3 Parallel Connections of Capacitors, 182 10.6 Reducible Systems, 183 10.7 Conclusion, 190 10.8 Brief Historical Overview and Related Sources, 190 Appendix A Main Distributions Related to Reliability Theory 195 A.1 Discrete Distributions, 195 A.1.1 Degenerate Distribution, 195 A.1.2 Bernoulli Distribution, 196 A.1.3 Binomial Distribution, 197 A.1.4 Poisson Distribution, 198 A.1.5 Geometric Distribution, 200 A.2 Continuous Distributions, 201 A.2.1 Intensity Function, 201 A.2.2 Continuous Uniform Distribution, 202 A.2.3 Exponential Distribution, 203 A.2.4 Erlang Distribution, 204 A.2.5 Hyperexponential Distribution, 205 A.2.6 Normal Distribution, 207 A.2.7Weibull–Gnedenko Distribution, 207 Appendix B Laplace Transformation 209 Appendix C Markov Processes 214 C.1 General Markov Process, 214 C.1.1 Nonstationary Availability Coefficient, 216 C.1.2 Probability of Failure-Free Operation, 218 C.1.3 Stationary Availability Coefficient, 220 C.1.4 Mean Time to Failure and Mean Time Between Failures, 221 C.1.5 Mean Recovery Time, 222 C.2 Birth–Death Process, 223 Appendix D General Bibliography 227 Index 231

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Book SynopsisOne of the first books to provide in-depth and systematic application of finite element methods to the field, Stochastic Structural Dynamics presents and illustrates direct integration methods for analyzing the statistics of the response of structures to stochastic loads.Table of ContentsDedication xi Preface xiii Acknowledgements xv 1. Introduction 1 1.1 Displacement Formulation Based Finite Element Method 2 1.2 Element Equations of Motion for Temporally and Spatially Stochastic Systems 13 1.3 Hybrid Stress Based Element Equations of Motion 14 1.4 Incremental Variational Principle and Mixed Formulation Based Nonlinear Element Matrices 18 1.5 Constitutive Relations and Updating of Configurations and Stresses 36 1.6 Concluding Remarks 48 References 49 2. Spectral Analysis and Response Statistics of Linear Structural Systems 53 2.1 Spectral Analysis 53 2.2 Evolutionary Spectral Analysis 56 2.3 Evolutionary Spectra of Engineering Structures 60 2.4 Modal Analysis and Time-Dependent Response Statistics 76 2.5 Response Statistics of Engineering Structures 79 References 94 3. Direct Integration Methods for Linear Structural Systems 97 3.1 Stochastic Central Difference Method 97 3.2 Stochastic Central Difference Method with Time Co-ordinate Transformation 100 3.3 Applications 102 3.4 Extended Stochastic Central Difference Method and Narrow-band Force Vector 114 3.5 Stochastic Newmark Family of Algorithms 122 References 128 4. Modal Analysis and Response Statistics of Quasi-linear Structural Systems 131 4.1 Modal Analysis of Temporally Stochastic Quasi-linear Systems 131 4.2 Response Analysis Based on Melosh-Zienkiewicz-Cheung Bending Plate Finite Element 141 4.3 Response Analysis Based on High Precision Triangular Plate Finite Element 156 4.4 Concluding Remarks 166 References 166 5. Direct Integration Methods for Response Statistics of Quasi-linear Structural Systems 169 5.1 Stochastic Central Difference Method for Quasi-linear Structural Systems 169 5.2 Recursive Covariance Matrix of Displacements of Cantilever Pipe Containing Turbulent Fluid 174 5.3 Quasi-linear Systems under Narrow-band Random Excitations 184 5.4 Concluding Remarks 188 References 190 6. Direct Integration Methods for Temporally Stochastic Nonlinear Structural Systems 191 6.1 Statistical Linearization Techniques 191 6.2 Symplectic Algorithms of Newmark Family of Integration Schemes 194 6.3 Stochastic Central Difference Method with Time Co-ordinate Transformation and Adaptive Time Schemes 199 6.4 Outline of steps in computer program 211 6.5 Large Deformations of Plate and Shell Structures 213 6.6 Concluding Remarks 224 References 226 7. Direct Integration Methods for Temporally and Spatially Stochastic Nonlinear Structural Systems 231 7.1 Perturbation Approximation Techniques and Stochastic Finite Element Methods 232 7.2 Stochastic Central Difference Methods for Temporally and Spatially Stochastic Nonlinear Systems 241 7.3 Finite Deformations of Spherical Shells with Large Spatially Stochastic Parameters 251 7.4 Closing Remarks 255 References 257 Appendices 1A Mass and Stiffness Matrices of Higher Order Tapered Beam Element 261 1B Consistent Stiffness Matrix of Lower Order Triangular Shell Element 267 1B.1 Inverse of Element Generalized Stiffness Matrix 267 1B.2 Element Leverage Matrices 268 1B.3 Element Component Stiffness Matrix Associated with Torsion 271 References 276 1C Consistent Mass Matrix of Lower Order Triangular Shell Element 277 Reference 280 2A Eigenvalue Solution 281 References 282 2B Derivation of Evolutionary Spectral Densities and Variances of Displacements 283 2B.1 Evolutionary Spectral Densities Due to Exponentially Decaying Random Excitations 283 2B.2 Evolutionary Spectral Densities Due to Uniformly Modulated Random Excitations 286 2B.3 Variances of Displacements 288 References 297 2C Time-dependent Covariances of Displacements 299 2D Covariances of Displacements and Velocities 311 2E Time-dependent Covariances of Velocities 317 2F Cylindrical Shell Element Matrices 323 3A Deterministic Newmark Family of Algorithms 327 Reference 331 Index 333

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Book SynopsisExplores regular structures in graphs and contingency tables by spectral theory and statistical methods This book bridges the gap between graph theory and statistics by giving answers to the demanding questions which arise when statisticians are confronted with large weighted graphs or rectangular arrays. Classical and modern statistical methods applicable to biological, social, communication networks, or microarrays are presented together with the theoretical background and proofs. This book is suitable for a one-semester course for graduate students in data mining, multivariate statistics, or applied graph theory; but by skipping the proofs, the algorithms can also be used by specialists who just want to retrieve information from their data when analysing communication, social, or biological networks. Spectral Clustering and Biclustering: Provides a unified treatment for edge-weighted graphs and contingency tables via methods of mulTable of ContentsPreface xi Acknowledgements xiii List of abbreviations xv Introduction xix References xxii 1 Multivariate analysis techniques for representing graphs and contingency tables 1 1.1 Quadratic placement problems for weighted graphs and hypergraphs 1 1.1.1 Representation of edge-weighted graphs 2 1.1.2 Representation of hypergraphs 5 1.1.3 Examples for spectra and representation of simple graphs 8 1.2 SVD of contingency tables and correspondence matrices 12 1.3 Normalized Laplacian and modularity spectra 16 1.4 Representation of joint distributions 21 1.4.1 General setup 21 1.4.2 Integral operators between L2 spaces 22 1.4.3 When the kernel is the joint distribution itself 23 1.4.4 Maximal correlation and optimal representations 25 1.5 Treating nonlinearities via reproducing kernel Hilbert spaces 28 1.5.1 Notion of the reproducing kernel 29 1.5.2 RKHS corresponding to a kernel 32 1.5.3 Two examples of an RKHS 33 1.5.4 Kernel – based on a sample – and the empirical feature map 37 References 40 2 Multiway cuts and spectra 44 2.1 Estimating multiway cuts via spectral relaxation 44 2.1.1 Maximum, minimum, and ratio cuts of edge-weighted graphs 45 2.1.2 Multiway cuts of hypergraphs 54 2.2 Normalized cuts 57 2.3 The isoperimetric number and sparse cuts 64 2.4 The Newman–Girvan modularity 76 2.4.1 Maximizing the balanced Newman–Girvan modularity 78 2.4.2 Maximizing the normalized Newman–Girvan modularity 81 2.4.3 Anti-community structure and some examples 84 2.5 Normalized bicuts of contingency tables 88 References 91 3 Large networks, perturbation of block structures 96 3.1 Symmetric block structures burdened with random noise 96 3.1.1 General blown-up structures 99 3.1.2 Blown-up multipartite structures 109 3.1.3 Weak links between disjoint components 112 3.1.4 Recognizing the structure 114 3.1.5 Random power law graphs and the extended planted partition model 121 3.2 Noisy contingency tables 124 3.2.1 Singular values of a noisy contingency table 127 3.2.2 Clustering the rows and columns via singular vector pairs 129 3.2.3 Perturbation results for correspondence matrices 132 3.2.4 Finding the blown-up skeleton 138 3.3 Regular cluster pairs 142 3.3.1 Normalized modularity and volume regularity of edge-weighted graphs 142 3.3.2 Correspondence matrices and volume regularity of contingency tables 150 3.3.3 Directed graphs 156 References 157 4 Testable graph and contingency table parameters 161 4.1 Convergent graph sequences 161 4.2 Testability of weighted graph parameters 164 4.3 Testability of minimum balanced multiway cuts 166 4.4 Balanced cuts and fuzzy clustering 172 4.5 Noisy graph sequences 175 4.6 Convergence of the spectra and spectral subspaces 177 4.7 Convergence of contingency tables 182 References 187 5 Statistical learning of networks 189 5.1 Parameter estimation in random graph models 189 5.1.1 EM algorithm for estimating the parameters of the block-model 189 5.1.2 Parameter estimation in the α and β models 192 5.2 Nonparametric methods for clustering networks 197 5.2.1 Spectral clustering of graphs and biclustering of contingency tables 199 5.2.2 Clustering of hypergraphs 201 5.3 Supervised learning 203 References 205 Appendix A Linear algebra and some functional analysis 207 A.1 Metric, normed vector, and Euclidean spaces 207 A.2 Hilbert spaces 209 A.3 Matrices 217 References 233 Appendix B Random vectors and matrices 235 B.1 Random vectors 235 B.2 Random matrices 239 References 245 Appendix C Multivariate statistical methods 246 C.1 Principal component analysis 246 C.2 Canonical correlation analysis 248 C.3 Correspondence analysis 250 C.4 Multivariate regression and analysis of variance 252 C.5 The k-means clustering 255 C.6 Multidimensional scaling 257 C.7 Discriminant analysis 258 References 261 Index 263

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Book SynopsisIn recent years, there has been a growing debate, particularly in the UK and Europe, over the merits of using discrete-event simulation (DES) and system dynamics (SD); there are now instances where both methodologies were employed on the same problem.Table of ContentsPreface xv List of contributors xvii 1 Introduction 1Sally Brailsford, Leonid Churilov and Brian Dangerfield 1.1 How this book came about 1 1.2 The editors 2 1.3 Navigating the book 3 References 9 2 Discrete-event simulation: A primer 10 Stewart Robinson 2.1 Introduction 10 2.2 An example of a discrete-event simulation: Modelling a hospital theatres process 11 2.3 The technical perspective: How DES works 12 2.3.1 Time handling in DES 14 2.3.2 Random sampling in DES 15 2.4 The philosophical perspective: The DES worldview 21 2.5 Software for DES 23 2.6 Conclusion 24 References 24 3 Systems thinking and system dynamics: A primer 26 Brian Dangerfield 3.1 Introduction 26 3.2 Systems thinking 28 3.2.1 ‘Behaviour over time’ graphs 28 3.2.2 Archetypes 29 3.2.3 Principles of influence (or causal loop) diagrams 30 3.2.4 From diagrams to behaviour 32 3.3 System dynamics 34 3.3.1 Principles of stock–flow diagramming 34 3.3.2 Model purpose and model conceptualisation 35 3.3.3 Adding auxiliaries, parameters and information links to the spinal stock–flow structure 36 3.3.4 Equation writing and dimensional checking 37 3.4 Some further important issues in SD modelling 40 3.4.1 Use of soft variables 40 3.4.2 Co-flows 42 3.4.3 Delays and smoothing functions 43 3.4.4 Model validation 46 3.4.5 Optimisation of SD models 48 3.4.6 The role of data in SD models 49 3.5 Further reading 49 References 50 4 Combining problem structuring methods with simulation: The philosophical and practical challenges 52 Kathy Kotiadis and John Mingers 4.1 Introduction 52 4.2 What are problem structuring methods? 53 4.3 Multiparadigm multimethodology in management science 54 4.3.1 Paradigm incommensurability 55 4.3.2 Cultural difficulties 57 4.3.3 Cognitive difficulties 58 4.3.4 Practical problems 59 4.4 Relevant projects and case studies 60 4.5 The case study: Evaluating intermediate care 62 4.5.1 The problem situation 62 4.5.2 Soft systems methodology 64 4.5.3 Discrete-event simulation modelling 66 4.5.4 Multimethodology 67 4.6 Discussion 68 4.6.1 The multiparadigm multimethodology position and strategy 68 4.6.2 The cultural difficulties 70 4.6.3 The cognitive difficulties 70 4.7 Conclusions 72 Acknowledgements 72 References 72 5 Philosophical positioning of discrete-event simulation and system dynamics as management science tools for process systems: A critical realist perspective 76 Kristian Rotaru, Leonid Churilov and Andrew Flitman 5.1 Introduction 76 5.2 Ontological and epistemological assumptions of CR 80 5.2.1 The stratified CR ontology 80 5.2.2 The abductive mode of reasoning 81 5.3 Process system modelling with SD and DES through the prism of CR scientific positioning 82 5.3.1 Lifecycle perspective on SD and DES methods 84 5.4 Process system modelling with SD and DES: Trends in and implications for MS 90 5.5 Summary and conclusions 97 References 99 6 Theoretical comparison of discrete-event simulation and system dynamics 105 Sally Brailsford 6.1 Introduction 105 6.2 System dynamics 106 6.3 Discrete-event simulation 108 6.4 Summary: The basic differences 110 6.5 Example: Modelling emergency care in Nottingham 112 6.5.1 Background 112 6.5.2 The ECOD project 113 6.5.3 Choice of modelling approach 114 6.5.4 Quantitative phase 114 6.5.5 Model validation 116 6.5.6 Scenario testing and model results 116 6.5.7 The ED model 118 6.5.8 Discussion 119 6.6 The $64 000 question: Which to choose? 120 6.7 Conclusion 123 References 123 7 Models as interfaces 125 Steffen Bayer, Tim Bolt, Sally Brailsford and Maria Kapsali 7.1 Introduction: Models at the interfaces or models as interfaces 125 7.2 The social roles of simulation 126 7.3 The modelling process 129 7.4 The modelling approach 131 7.5 Two case studies of modelling projects 134 7.6 Summary and conclusions 137 References 138 8 An empirical study comparing model development in discrete-event simulation and system dynamics 140 Antuela Tako and Stewart Robinson 8.1 Introduction 140 8.2 Existing work comparing DES and SD modelling 142 8.2.1 DES and SD model development process 143 8.2.2 Summary 146 8.3 The study 146 8.3.1 The case study 146 8.3.2 Verbal protocol analysis 147 8.3.3 The VPA sessions 149 8.3.4 The subjects 149 8.3.5 The coding process 150 8.4 Study results 151 8.4.1 Attention paid to modelling topics 152 8.4.2 The sequence of modelling stages 154 8.4.3 Pattern of iterations among topics 155 8.5 Observations from the DES and SD expert modellers’ behaviour 158 8.6 Conclusions 160 Acknowledgements 162 References 162 9 Explaining puzzling dynamics: A comparison of system dynamics and discrete-event simulation 165 John Morecroft and Stewart Robinson 9.1 Introduction 165 9.2 Existing comparisons of SD and DES 166 9.3 Research focus 169 9.4 Erratic fisheries – chance, destiny and limited foresight 170 9.5 Structure and behaviour in fisheries: A comparison of SD and DES models 173 9.5.1 Alternative models of a natural fishery 174 9.5.2 Alternative models of a simple harvested fishery 178 9.5.3 Alternative models of a harvested fishery with endogenous ship purchasing 184 9.6 Summary of findings 192 9.7 Limitations of the study 193 9.8 SD or DES? 194 Acknowledgements 196 References 196 10 DES view on simulation modelling: SIMUL8 199 Mark Elder 10.1 Introduction 199 10.2 How software fits into the project 200 10.3 Building a DES 202 10.4 Getting the right results from a DES 208 10.4.1 Verification and validation 210 10.4.2 Replications 211 10.5 What happens after the results? 212 10.6 What else does DES software do and why? 212 10.7 What next for DES software? 213 References 214 11 Vensim and the development of system dynamics 215 Lee Jones 11.1 Introduction 215 11.2 Coping with complexity: The need for system dynamics 216 11.3 Complexity arms race 219 11.4 The move to user-led innovation 221 11.5 Software support 222 11.5.1 Apples and oranges (basic model testing) 223 11.5.2 Confidence 224 11.5.3 Helping the practitioner do more 237 11.6 The future for SD software 245 11.6.1 Innovation 245 11.6.2 Communication 245 References 247 12 Multi-method modeling: AnyLogic 248 Andrei Borshchev 12.1 Architectures 249 12.1.1 The choice of model architecture and methods 251 12.2 Technical aspect of combining modeling methods 252 12.2.1 System dynamics ® discrete elements 252 12.2.2 Discrete elements ® system dynamics 253 12.2.3 Agent based « discrete event 255 12.3 Example: Consumer market and supply chain 257 12.3.1 The supply chain model 257 12.3.2 The market model 258 12.3.3 Linking the DE and the SD parts 259 12.3.4 The inventory policy 260 12.4 Example: Epidemic and clinic 262 12.4.1 The epidemic model 262 12.4.2 The clinic model and the integration of methods 264 12.5 Example: Product portfolio and investment policy 267 12.5.1 Assumptions 268 12.5.2 The model architecture 270 12.5.3 The agent product and agent population portfolio 271 12.5.4 The investment policy 274 12.5.5 Closing the loop and implementing launch of new products 275 12.5.6 Completing the investment policy 277 12.6 Discussion 278 References 279 13 Multiscale modelling for public health management: A practical guide 280 Rosemarie Sadsad and Geoff McDonnell 13.1 Introduction 280 13.2 Background 281 13.3 Multilevel system theories and methodologies 281 13.4 Multiscale simulation modelling and management 283 13.5 Discussion 289 13.6 Conclusion 290 References 290 14 Hybrid modelling case studies 295 Rosemarie Sadsad, Geoff McDonnell, Joe Viana, Shivam M. Desai, Paul Harper and Sally Brailsford 14.1 Introduction 295 14.2 A multilevel model of MRSA endemicity and its control in hospitals 296 14.2.1 Introduction 296 14.2.2 Method 296 14.2.3 Results 297 14.2.4 Conclusion 302 14.3 Chlamydia composite model 302 14.3.1 Introduction 302 14.3.2 Chlamydia 302 14.3.3 DES model of a GUM department 303 14.3.4 SD model of chlamydia 304 14.3.5 Why combine the models 304 14.3.6 How the models were combined 305 14.3.7 Experiments with the composite model 305 14.3.8 Conclusions 307 14.4 A hybrid model for social care services operations 308 14.4.1 Introduction 308 14.4.2 Population model 308 14.4.3 Model construction 309 14.4.4 Contact centre model 310 14.4.5 Hybrid model 311 14.4.6 Conclusions and lessons learnt 313 References 316 15 The ways forward: A personal view of system dynamics and discrete-event simulation 318 Michael Pidd 15.1 Genesis 318 15.2 Computer simulation in management science 319 15.3 The effect of developments in computing 320 15.4 The importance of process 324 15.5 My own comparison of the simulation approaches 324 15.5.1 Time handling 324 15.5.2 Stochastic and deterministic elements 326 15.5.3 Discrete entities versus continuous variables 327 15.6 Linking system dynamics and discrete-event simulation 328 15.7 The importance of intended model use 329 15.7.1 Decision automation 330 15.7.2 Routine decision support 331 15.7.3 System investigation and improvement 331 15.7.4 Providing insights for debate 332 15.8 The future? 333 15.8.1 Use of both methods will continue to grow 333 15.8.2 Developments in computing will continue to have an effect 334 15.8.3 Process really matters 335 References 335 Index 337

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Book SynopsisA comprehensive and accessible introduction to modern quantitative risk management. The business world is rife with risk and uncertainty, and risk management is a vitally important topic for managers. The best way to achieve a clear understanding of risk is to use quantitative tools and probability models.Table of ContentsPreface xiii 1 What is risk management? 1 1.1 Introduction 2 1.2 Identifying and documenting risk 5 1.3 Fallacies and traps in risk management 7 1.4 Why safety is different 9 1.5 The Basel framework 11 1.6 Hold or hedge? 12 1.7 Learning from a disaster 13 Notes 17 References 18 Exercises 19 2 The structure of risk 22 2.1 Introduction to probability and risk 23 2.2 The structure of risk 25 2.3 Portfolios and diversification 30 2.4 The impact of correlation 40 2.5 Using copulas to model multivariate distributions 49 Notes 58 References 59 Exercises 60 3 Measuring risk 63 3.1 How can we measure risk? 64 3.2 Value at risk 67 3.3 Combining and comparing risks 73 3.4 VaR in practice 76 3.5 Criticisms of VaR 79 3.6 Beyond value at risk 82 Notes 88 References 88 Exercises 89 4 Understanding the tails 92 4.1 Heavy-tailed distributions 93 4.2 Limiting distributions for the maximum 100 4.3 Excess distributions 109 4.4 Estimation using extreme value theory 115 Notes 121 References 122 Exercises 123 5 Making decisions under uncertainty 125 5.1 Decisions, states and outcomes 126 5.2 Expected Utility Theory 130 5.3 Stochastic dominance and risk profiles 148 5.4 Risk decisions for managers 156 Notes 160 References 161 Exercises 162 6 Understanding risk behavior 164 6.1 Why decision theory fails 165 6.2 Prospect Theory 172 6.3 Cumulative Prospect Theory 180 6.4 Decisions with ambiguity 189 6.5 How managers treat risk 191 Notes 194 References 194 Exercises 195 7 Stochastic optimization 198 7.1 Introduction to stochastic optimization 199 7.2 Choosing scenarios 212 7.3 Multistage stochastic optimization 218 7.4 Value at risk constraints 224 Notes 228 References 228 Exercises 229 8 Robust optimization 232 8.1 True uncertainty: Beyond probabilities 233 8.2 Avoiding disaster when there is uncertainty 234 8.3 Robust optimization and the minimax approach 250 Notes 261 References 262 Exercises 263 9 Real options 265 9.1 Introduction to real options 266 9.2 Calculating values with real options 267 9.3 Combining real options and net present value 273 9.4 The connection with financial options 278 9.5 Using Monte Carlo simulation to value real options 282 9.6 Some potential problems with the use of real options 285 Notes 287 References 287 Exercises 288 10 Credit risk 291 10.1 Introduction to credit risk 292 10.2 Using credit scores for credit risk 294 10.3 Consumer credit 301 10.4 Logistic regression 308 Notes 317 References 318 Exercises 319 Appendix A Tutorial on probability theory 323 A.1 Random events 323 A.2 Bayes’ rule and independence 326 A.3 Random variables 327 A.4 Means and variances 329 A.5 Combinations of random variables 332 A.6 The normal distribution and the Central Limit Theorem 336 Appendix B Answers to even-numbered exercises 340 Index 361

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Book SynopsisPresents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries.Table of ContentsPreface xi PART I MATHEMATICS IN HISTORY 1 The Ancient Roots of Mathematics 3 1.1 Introduction 3 1.2 Ancient Mesopotamia and Egypt 7 1.3 Early Greek Mathematics: The First Theorists 20 1.4 The Apex: Third Century Hellenistic Mathematics 42 1.5 The Slow Decline 58 2 The Growth of Mathematics to 1600 73 2.1 China 74 2.2 India 89 2.3 Islam 102 2.4 European Mathematics Awakens 120 3 Modern Mathematics 139 3.1 The 17th Century: Scientific Revolution 140 3.2 The 18th Century: Consolidation 156 3.3 The 19th Century: Expansion 170 3.4 The 20th and 21st Centuries: Explosion 193 3.5 The Future 217 II TWO PILLARS OF MATHEMATICS 4 Calculus 221 4.1 What Is Calculus? 221 4.2 Average and Instantaneous Velocity 222 4.3 Tangent Line to a Curve 226 4.4 The Derivative 232 4.5 Formulas for Derivatives 235 4.6 The Product Rule and Quotient Rule 241 4.7 The Chain Rule 248 4.8 Slopes and Optimization 253 4.9 Applying Optimization Methods 259 4.10 Differential Notation and Estimates 266 4.11 Marginal Revenue, Cost, and Profit 270 4.12 Exponential Growth 276 4.13 Periodic Functions of Trigonometry 287 4.14 The Fundamental Theorem of Calculus 293 4.15 The Riemann Integral 297 4.16 Signed Areas and Other Integrals 301 4.17 Application: Rocket Science 306 4.18 Infinite Sums 311 4.19 Exponential Growth and Doubling Times 317 4.20 Beyond Calculus 321 5 Number Theory 323 5.1 What Is Number Theory? 323 5.2 Divisibility 324 5.3 Irrational Numbers 329 5.4 Greatest Common Divisors 331 5.5 Primes 336 5.6 Relatively Prime Integers 339 5.7 Mersenne and Fermat Primes 343 5.8 The Fundamental Theorem of Arithmetic 345 5.9 Diophantine Equations 350 5.10 Linear Diophantine Equations 354 5.11 Pythagorean Triples 358 5.12 An Introduction to Modular Arithmetic 361 5.13 Congruence 366 5.14 Arithmetic with Congruences 370 5.15 Division with Congruences; Finite Fields 374 5.16 Fermat’s Last Theorem 381 5.17 Unfinished Business 383 A Answers to Selected Exercises 385 B Suggested Reading 401 Index 405

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Book SynopsisPraise for the First Edition . . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises.Zentralblatt MATH . . . carefully structured with many detailed worked examples.The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fielTrade Review“This is an excellent textbook for a numerical analysis course although it will be difficult to cover all the material in just one course. Because the text is so complete, it could as well be used for self-study.” (American Mathematical Society, 1 August 2014)Table of ContentsPreface xiii 1 Introductory Concepts and Calculus Review 1 2 A Survey of Simple Methods and Tools 43 3 Root-Finding 89 4 Interpolation and Approximation 171 5 Numerical Integration 269 6 Numerical Methods for Ordinary Differential Equations 329 7 Numerical Methods for the Solution of Systems of Equations 417 8 Approximate Solution of the Algebraic Eigenvalue Problem 479 9 A Survey of Numerical Methods for Partial Differential Equations 521 10 An Introduction to Spectral Methods 555 Appendix A: Proofs of Selected Theorems, and Other Additional Material 581 Index 587

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Book SynopsisThe first book to address how social media is revolutionizing the field of survey research, Social Media, Sociality, and Survey Research equips readers with a new ideology for conducting data collection and analysis in the face of emerging technologies.Trade Review“This book is a must read for any researcher who wants to make use of social media data; it is incisive, instructive, easy to read and, above all, fascinating.” (Social Research Association, 1 June 2014)Table of ContentsList of Figures xiii List of Tables xvii Contributors xix Preface xxi Acknowledgments xxv 1. Social Media, Sociality, and Survey Research 1 Joe Murphy, Craig A. Hill, and Elizabeth Dean What Is Social Media? 2 Social Media Origins 6 Social Networking Sites and Platforms 6 Blogs 8 Twitter 8 Facebook 9 LinkedIn 9 Second Life 9 Other Social Networking Platforms and Functionalities 10 Why Should Survey Researchers Be Interested in Social Media? 11 The Current State of Survey Research 11 Falling Response Rates 11 Frame Coverage Errors 13 The Coming Age of Ubiquity 14 Public vs. Private Data 17 Social Media Interaction: Next Wave (or Subwave)? 18 Adding Social Media to the Survey Research Toolbox 21 Toward Using the Concept of Sociality in Survey Research of the Future 22 How Can Survey Researchers Use Social Media Data? 26 References 28 2. Sentiment Analysis: Providing Categorical Insight into Unstructured Textual Data 35 Carol Haney Describing Emotional or Subjective Feeling in Textual Data 36 Definition of Machine-Augmented Sentiment Analysis 37 How Sentiment Analysis Is Used with Text Data 38 Different Ways of Representing Sentiment 42 Ordinal Scales 42 Nominal Emotion Classification 43 Neutral Sentiment 44 Techniques for Determining Sentiment 44 Precursors to Analysis 44 Harvesting 46 Structure and Understand 50 Approaches to Determining Sentiment 51 Machine-Coded Sentiment Analysis 51 Human-Coded Sentiment Analysis 53 Sentiment Analysis as a Subset of Text Analytics 54 Current Limitations of Sentiment Analysis 57 References 59 3. Can Tweets Replace Polls? A U.S. Health-Care Reform Case Study 61 Annice Kim, Joe Murphy, Ashley Richards, Heather Hansen, Rebecca Powell, and Carol Haney Methods 64 Twitter Data 64 Public Opinion About Health-Care Reform: Kaiser Health Tracking Poll 70 Analysis 70 Results 71 RQ1: To What Extent Was Health-Care Reform Discussed on Twitter? 71 RQ2: What Is the Distribution of Sentiment of Health-Care Reform Tweets? 74 RQ3. Do Trends in the Sentiment of Tweets About Health-Care Reform Correlate with Observed Trends in Public Opinion About Health-Care Reform from Nationally Representative Probability-Based Surveys? 75 KFF Trends 75 Comparison 77 RQ4. What Are the Key Topics Discussed in Health-Care Reform Tweets? 78 Discussion 80 Conclusions 84 References 85 4. The Facebook Platform and the Future of Social Research 87 Adam Sage The Changing Web: From Searchable to Social 88 Digital and Digitized Data 93 The Case for Facebook Integration 94 Data and the Graph API 97 Facebook Applications 99 Social Plugins 103 The Future, Mobile Apps, and the Ever Increasing Complexity of the Social Graph 104 References 104 5. Virtual Cognitive Interviewing Using Skype and Second Life 107 Elizabeth Dean, Brian Head, and Jodi Swicegood Brief Background on Cognitive Interviews 108 Cognitive Interviewing Current Practice 109 Practitioners’ Techniques 109 Cognitive Interviews in Practice: Present and Future 112 Second Life for Survey Research 114 Methods 115 Recruitment 115 Screening 117 Incentive 118 Think-Aloud and Probes 118 Results 118 Overall Participant Characteristics 118 Feasibility of Pilot Study 120 Quality of Cognitive Interviews by Mode 121 Participant Disengagement 122 Nonverbal Cues 125 Total Problems 126 Type and Severity of Problems 126 Conclusions 127 Discussion and Future Research 128 References 129 6. Second Life as a Survey Lab: Exploring the Randomized Response Technique in a Virtual Setting 133 Ashley Richards and Elizabeth Dean Overview of Second Life 134 Research in Second Life 134 The Randomized Response Technique 136 Study Design 137 Results 142 Discussion 144 References 146 7. Decisions, Observations, and Considerations for Developing a Mobile Survey App and Panel 149 David Roe, Yuying Zhang, and Michael Keating Impact of the Evolution of Technology on Data Collection 150 Telephone Interviewing 151 Web Interviewing 151 Cell Phones 152 Smartphones 153 Building an App 156 Goals 157 Preliminary Findings 168 Recruitment 170 Respondent Communication 170 Survey Topics 172 Respondent Impressions on Incentives, Survey Length, and Frequency 175 Next Steps 175 References 176 8. Crowdsourcing: A Flexible Method for Innovation, Data Collection, and Analysis in Social Science Research 179 Michael Keating, Bryan Rhodes, and Ashley Richards What Is Crowdsourcing? 180 Open Innovation 181 Cisco Systems I-Prize Challenge 182 RTI International’s 2012 Research Challenge 183 Options for Hosting Your Own Challenges 185 Legal Considerations 186 Data Collection 187 Crowdsourcing Survey Response on Mechanical Turk 187 Targeted Data Collection 190 Cost Considerations 194 MyHeartMap Challenge 195 Analysis by Crowdsourcing 197 Sentiment Analysis 197 Challenge-Based Data Analysis 198 Conclusion 199 References 200 9. Collecting Diary Data on Twitter 203 Ashley Richards, Elizabeth Dean, and Sarah Cook Background 204 Twitter 204 Diaries 204 Methods 206 Recruitment 208 Data Collection 210 Results 211 Nonresponse 212 Data Quality 216 Incentive Preference 221 Participant Feedback 222 Discussion 227 References 229 10. Recruiting Participants with Chronic Conditions in Second Life 231 Saira N. Haque and Jodi Swicegood Background 233 Methods 234 Instrument Development 235 Recruitment Methods 235 Survey Administration 244 Results 244 Discussion 247 Communities 247 Using Existing Second Life Resources 248 Other Effective Methods 249 The Importance of the Recruitment Avatar 249 Conclusion 250 References 251 11. Gamification of Market Research 253 Jon Puleston Significance of Gamification in Market Research 254 Apply Gamification to Market Research 256 Gamification in Survey Design 259 Apply Rules to Question Design 265 Add the Competitive Element 269 Add Reward Mechanics 271 Give Feedback 272 Make Tasks More Involving 273 Ensure the Challenge Can Be Accomplished 275 How to Design Questions To Be More Game-Like 275 Common Questions About Gamification 284 Who Responds to Gamification? 284 What Impact Does Gamification Have on the Data? 285 How Do These Techniques Work in Different Cultures? 289 Conclusions 291 References 292 12. The Future of Social Media, Sociality, and Survey Research 295 Craig A. Hill and Jill Dever Statistical Challenges with Social Media Data 296 Quality and Representativeness 297 Sampling from Social Media Sources 298 Population Estimation from Social Media Data 303 Future Opportunities 306 What Does the Future Hold? 307 Sociality Hierarchy Level 1: Broadcast 308 Sociality Hierarchy Level 2: Conversation 311 Sociality Hierarchy Level 3: Community 312 Final Thoughts 314 References 315 Index 319

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Book SynopsisAn exciting approach to the history and mathematics of number theory . . . the author's style is totally lucid and very easy to read . . .the result is indeed a wonderful story. Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 details the history behind how Pierre de Fermat's work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2<Table of ContentsPreface to the First Edition ixPreface to the Second Edition xiNotation xiiiIntroduction 1Chapter One: From Fermat to GaussChapter Two: Class Field TheoryChapter Three: Complex MultiplicationChapter Four: Additional TopicsRefrencesAdditional ReferencesIndex

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Book SynopsisA solutions manual to accompany An Introduction toNumerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, SecondEdition reflects the latest trends in the field, includesnew material and revised exercises, and offers a unique emphasis onapplications.Table of Contents1 Introductory Concepts and Calculus Review 1 1.1 Basic Tools of Calculus 1 1.2 Error, Approximate Equality, and Asymptotic Order Notation 12 1.3 A Primer on Computer Arithmetic 15 1.4 A Word on Computer Languages and Software 19 1.5 Simple Approximations 19 1.6 Application: Approximating the Natural Logarithm 22 1.7 A Brief History of Computing 25 2 A Survey of Simple Methods and Tools 27 2.1 Horner’s Rule and Nested Multiplication 27 2.2 Difference Approximations to the Derivative 30 2.3 Application: Euler’s Method for Initial Value Problems 40 2.4 Linear Interpolation 44 2.5 Application— The Trapezoid Rule 48 2.6 Solution of Tridiagonal Linear Systems 56 2.7 Application: Simple Two-Point Boundary Value Problems 61 3 Root-Finding 65 3.1 The Bisection Method 65 3.2 Newton’s Method: Derivation and Examples 69 3.3 How to Stop Newton’s Method 73 3.4 Application: Division Using Newton’s Method 77 3.5 The Newton Error Formula 81 3.6 Newton’s Method: Theory and Convergence 84 3.7 Application: Computation of the Square Root 88 3.8 The Secant Method: Derivation and Examples 92 3.9 Fixed Point Iteration 96 3.10 Roots of Polynomials (Part 1) 99 3.11 Special Topics in Root-finding Methods 102 3.12 Very High-order Methods and the Efficiency Index 114 4 Interpolation and Approximation 117 4.1 Lagrange Interpolation 117 4.2 Newton Interpolation and Divided Differences 120 4.3 Interpolation Error 132 4.4 Application: Muller’s Method and Inverse Quadratic Interpolation 139 4.5 Application: More Approximations to the Derivative 141 4.6 Hermite Interpolation 142 4.7 Piecewise Polynomial Interpolation 145 4.8 An Introduction to Splines 149 4.9 Application: Solution of Boundary Value Problems 156 4.10 Tension Splines 159 4.11 Least Squares Concepts in Approximation 160 4.12 Advanced Topics in Interpolation Error 166 5 Numerical Integration 171 5.1 A Review of the Definite Integral 171 5.2 Improving the Trapezoid Rule 173 5.3 Simpson’s Rule and Degree of Precision 177 5.4 The Midpoint Rule 187 5.5 Application: Stirling’s Formula 190 5.6 Gaussian Quadrature 192 5.7 Extrapolation Methods 199 5.8 Special Topics in Numerical Integration 203 6 Numerical Methods for Ordinary Differential Equations 211 6.1 The Initial Value Problem — Background 211 6.2 Euler’s Method 213 6.3 Analysis of Euler’s Method 216 6.4 Variants of Euler’s Method 217 6.5 Single Step Methods— Runge-Kutta 225 6.6 Multistep Methods 228 6.7 Stability Issues 234 6.8 Application to Systems of Equations 235 6.9 Adaptive Solvers 240 6.10 Boundary Value Problems 243 7 Numerical Methods for the Solution of Systems of Equations 247 7.1 Linear Algebra Review 247 7.2 Linear Systems and Gaussian Elimination 248 7.3 Operation Counts 254 7.4 The LU Factorization 256 7.5 Perturbation, Conditioning and Stability 262 7.6 SPD Matrices and the Cholesky Decomposition 269 7.7 Iterative Methods for Linear Systems – A Brief Survey 271 7.8 Nonlinear Systems: Newton’s Method and Related Ideas 273 7.9 Application: Numerical Solution of Nonlinear BVP’s 275 8 Approximate Solution of the Algebraic Eigenvalue Problem 277 8.1 Eigenvalue Review 277 8.2 Reduction to Hessenberg Form 280 8.3 Power Methods 281 8.4 An Overview of the QR Iteration 284 8.5 Application: Roots of Polynomials, II 288 9 A Survey of Numerical Methods for Partial Differential Equations 289 9.1 Difference Methods for the Diffusion Equation 289 9.2 Finite Element Methods for the Diffusion Equation 293 9.3 Difference Methods for Poisson Equations 294 10 An Introduction to Spectral Methods 299 10.1 Spectral Methods for Two-Point Boundary Value Problems 299 10.2 Spectral Methods for Time-Dependent Problems 301 10.3 Clenshaw-Curtis Quadrature 303

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Book SynopsisComplete guidance for mastering the tools and techniques of the digital revolution With the digital revolution opening up tremendous opportunities in many fields, there is a growing need for skilled professionals who can develop data-intensive systems and extract information and knowledge from them. This book frames for the first time a new systematic approach for tackling the challenges of data-intensive computing, providing decision makers and technical experts alike with practical tools for dealing with our exploding data collections. Emphasizing data-intensive thinking and interdisciplinary collaboration, The Data Bonanza: Improving Knowledge Discovery in Science, Engineering, and Business examines the essential components of knowledge discovery, surveys many of the current research efforts worldwide, and points to new areas for innovation. Complete with a wealth of examples and DISPEL-based methods demonstrating how to gain more from data in real-worTable of ContentsCONTRIBUTORS xv FOREWORD xvii PREFACE xix THE EDITORS xxix PART I STRATEGIES FOR SUCCESS IN THE DIGITAL-DATA REVOLUTION 1 1. The Digital-Data Challenge 5 Malcolm Atkinson and Mark Parsons 1.1 The Digital Revolution 5 1.2 Changing How We Think and Behave 6 1.3 Moving Adroitly in this Fast-Changing Field 8 1.4 Digital-Data Challenges Exist Everywhere 8 1.5 Changing How We Work 9 1.6 Divide and Conquer Offers the Solution 10 1.7 Engineering Data-to-Knowledge Highways 12 2. The Digital-Data Revolution 15 Malcolm Atkinson 2.1 Data, Information, and Knowledge 16 2.2 Increasing Volumes and Diversity of Data 18 2.3 Changing the Ways We Work with Data 28 3. The Data-Intensive Survival Guide 37 Malcolm Atkinson 3.1 Introduction: Challenges and Strategy 38 3.2 Three Categories of Expert 39 3.3 The Data-Intensive Architecture 41 3.4 An Operational Data-Intensive System 42 3.5 Introducing DISPEL 44 3.6 A Simple DISPEL Example 45 3.7 Supporting Data-Intensive Experts 47 3.8 DISPEL in the Context of Contemporary Systems 48 3.9 Datascopes 51 3.10 Ramps for Incremental Engagement 54 3.11 Readers’ Guide to the Rest of This Book 56 4. Data-Intensive Thinking with DISPEL 61 Malcolm Atkinson 4.1 Processing Elements 62 4.2 Connections 64 4.3 Data Streams and Structure 65 4.4 Functions 66 4.5 The Three-Level Type System 72 4.6 Registry, Libraries, and Descriptions 81 4.7 Achieving Data-Intensive Performance 86 4.8 Reliability and Control 108 4.9 The Data-to-Knowledge Highway 116 PART II DATA-INTENSIVE KNOWLEDGE DISCOVERY 123 5. Data-Intensive Analysis 127 Oscar Corcho and Jano van Hemert 5.1 Knowledge Discovery in Telco Inc. 128 5.2 Understanding Customers to Prevent Churn 130 5.3 Preventing Churn Across Multiple Companies 134 5.4 Understanding Customers by Combining Heterogeneous Public and Private Data 137 5.5 Conclusions 144 6. Problem Solving in Data-Intensive Knowledge Discovery 147 Oscar Corcho and Jano van Hemert 6.1 The Conventional Life Cycle of Knowledge Discovery 148 6.2 Knowledge Discovery Over Heterogeneous Data Sources 155 6.3 Knowledge Discovery from Private and Public, Structured and Nonstructured Data 158 6.4 Conclusions 162 7. Data-Intensive Components and Usage Patterns 165 Oscar Corcho 7.1 Data Source Access and Transformation Components 166 7.2 Data Integration Components 172 7.3 Data Preparation and Processing Components 173 7.4 Data-Mining Components 174 7.5 Visualization and Knowledge Delivery Components 176 8. Sharing and Reuse in Knowledge Discovery 181 Oscar Corcho 8.1 Strategies for Sharing and Reuse 182 8.2 Data Analysis Ontologies for Data Analysis Experts 185 8.3 Generic Ontologies for Metadata Generation 188 8.4 Domain Ontologies for Domain Experts 189 8.5 Conclusions 190 PART III DATA-INTENSIVE ENGINEERING 193 9. Platforms for Data-Intensive Analysis 197 David Snelling 9.1 The Hourglass Reprise 198 9.2 The Motivation for a Platform 200 9.3 Realization 201 10. Definition of the DISPEL Language 203 Paul Martin and Gagarine Yaikhom 10.1 A Simple Example 204 10.2 Processing Elements 205 10.3 Data Streams 213 10.4 Type System 217 10.5 Registration 222 10.6 Packaging 224 10.7 Workflow Submission 225 10.8 Examples of DISPEL 227 10.9 Summary 235 11. DISPEL Development 237 Adrian Mouat and David Snelling 11.1 The Development Landscape 237 11.2 Data-Intensive Workbenches 239 11.3 Data-Intensive Component Libraries 247 11.4 Summary 248 12. DISPEL Enactment 251 Chee Sun Liew, Amrey Krause, and David Snelling 12.1 Overview of DISPEL Enactment 251 12.2 DISPEL Language Processing 253 12.3 DISPEL Optimization 255 12.4 DISPEL Deployment 266 12.5 DISPEL Execution and Control 268 PART IV DATA-INTENSIVE APPLICATION EXPERIENCE 275 13. The Application Foundations of DISPEL 277 Rob Baxter 13.1 Characteristics of Data-Intensive Applications 277 13.2 Evaluating Application Performance 280 13.3 Reviewing the Data-Intensive Strategy 283 14. Analytical Platform for Customer Relationship Management 287 Maciej Jarka and Mark Parsons 14.1 Data Analysis in the Telecoms Business 288 14.2 Analytical Customer Relationship Management 289 14.3 Scenario 1: Churn Prediction 291 14.4 Scenario 2: Cross Selling 293 14.5 Exploiting the Models and Rules 296 14.6 Summary: Lessons Learned 299 15. Environmental Risk Management 301 Ladislav Hluchy, Ondrej Habala, Viet Tran, and Branislav Simo 15.1 Environmental Modeling 302 15.2 Cascading Simulation Models 303 15.3 Environmental Data Sources and Their Management 305 15.4 Scenario 1: ORAVA 309 15.5 Scenario 2: RADAR 313 15.6 Scenario 3: SVP 318 15.7 New Technologies for Environmental Data Mining 321 15.8 Summary: Lessons Learned 323 16. Analyzing Gene Expression Imaging Data in Developmental Biology 327 Liangxiu Han, Jano van Hemert, Ian Overton, Paolo Besana, and Richard Baldock 16.1 Understanding Biological Function 328 16.2 Gene Image Annotation 330 16.3 Automated Annotation of Gene Expression Images 331 16.4 Exploitation and Future Work 341 16.5 Summary 345 17. Data-Intensive Seismology: Research Horizons 353 Michelle Galea, Andreas Rietbrock, Alessandro Spinuso, and Luca Trani 17.1 Introduction 354 17.2 Seismic Ambient Noise Processing 356 17.3 Solution Implementation 358 17.4 Evaluation 369 17.5 Further Work 372 17.6 Conclusions 373 PART V DATA-INTENSIVE BEACONS OF SUCCESS 377 18. Data-Intensive Methods in Astronomy 381 Thomas D. Kitching, Robert G. Mann, Laura E. Valkonen, Mark S. Holliman, Alastair Hume, and Keith T. Noddle 18.1 Introduction 381 18.2 The Virtual Observatory 382 18.3 Data-Intensive Photometric Classification of Quasars 383 18.4 Probing the Dark Universe with Weak Gravitational Lensing 387 18.5 Future Research Issues 392 18.6 Conclusions 392 19. The World at One's Fingertips: Interactive Interpretation of Environmental Data 395 Jon Blower, Keith Haines, and Alastair Gemmell 19.1 Introduction 395 19.2 The Current State of the Art 397 19.3 The Technical Landscape 401 19.4 Interactive Visualization 403 19.5 From Visualization to Intercomparison 406 19.6 Future Development: The Environmental Cloud 409 19.7 Conclusions 411 20. Data-Driven Research in the Humanities—the DARIAH Research Infrastructure 417 Andreas Aschenbrenner, Tobias Blanke, Christiane Fritze, andWolfgang Pempe 20.1 Introduction 417 20.2 The Tradition of Digital Humanities 420 20.3 Humanities Research Data 422 20.4 Use Case 426 20.5 Conclusion and Future Development 429 21. Analysis of Large and Complex Engineering and Transport Data 431 Jim Austin 21.1 Introduction 431 21.2 Applications and Challenges 432 21.3 The Methods Used 434 21.4 Future Developments 438 21.5 Conclusions 439 References 440 22. Estimating Species Distributions—Across Space, Through Time, and with Features of the Environment 441 Steve Kelling, Daniel Fink, Wesley Hochachka, Ken Rosenberg, Robert Cook, Theodoros Damoulas, Claudio Silva, and William Michener 22.1 Introduction 442 22.2 Data Discovery, Access, and Synthesis 443 22.3 Model Development 448 22.4 Managing Computational Requirements 449 22.5 Exploring and Visualizing Model Results 450 22.6 Analysis Results 452 22.7 Conclusion 454 PART VI THE DATA-INTENSIVE FUTURE 459 23. Data-Intensive Trends 461 Malcolm Atkinson and Paolo Besana 23.1 Reprise 461 23.2 Data-Intensive Applications 469 24. Data-Rich Futures 477 Malcolm Atkinson 24.1 Future Data Infrastructure 478 24.2 Future Data Economy 485 24.3 Future Data Society and Professionalism 489 References 494 Appendix A: Glossary 499 Michelle Galea and Malcolm Atkinson Appendix B: DISPEL Reference Manual 507 Paul Martin Appendix C: Component Definitions 531 Malcolm Atkinson and Chee Sun Liew INDEX 537

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Book SynopsisBridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinking Combinatorics: An Introduction introduces readers to counting combinatorics, offers examples that feature unique approaches and ideas, and presents case-by-case methods for solving problems. Detailing how combinatorial problems arise in many areas of pure mathematics, most notably in algebra, probability theory, topology, and geometry, this book provides discussion on logic and paradoxes; sets and set notations; power sets and their cardinality; Venn diagrams; the multiplication principal; and permutations, combinations, and problems combining the multiplication principal. Additional features of this enlightening introduction include: Worked examples, proofs, and exercises in every chapter Detailed explanations of formulas to promote fundamental understanding Promotion of mathematical thinking by examininTable of ContentsPreface xiii 1 Logic 1 1.1 Formal Logic 1 1.2 Basic Logical Strategies 6 1.3 The Direct Argument 10 1.4 More Argument Forms 12 1.5 Proof By Contradiction 15 1.6 Exercises 23 2 Sets 25 2.1 Set Notation 25 2.2 Predicates 26 2.3 Subsets 28 2.4 Union and Intersection 30 2.5 Exercises 32 3 Venn Diagrams 35 3.1 Inclusion/Exclusion Principle 35 3.2 Two Circle Venn Diagrams 37 3.3 Three Square Venn Diagrams 42 3.4 Exercises 50 4 Multiplication Principle 55 4.1 What is the Principle? 55 4.2 Exercises 60 5 Permutations 63 5.1 Some Special Numbers 64 5.2 Permutations Problems 65 5.3 Exercises 68 6 Combinations 69 6.1 Some Special Numbers 69 6.2 Combination Problems 70 6.3 Exercises 74 7 Problems Combining Techniques 77 7.1 Significant Order 77 7.2 Order Not Significant 78 7.3 Exercises 83 8 Arrangement Problems 85 8.1 Examples of Arrangements 86 8.2 Exercises 91 9 At Least, At Most, and Or 93 9.1 Counting With Or 93 9.2 At Least, At Most 98 9.3 Exercises 102 10 Complement Counting 103 10.1 The Complement Formula 103 10.2 A New View of ?At Least? 105 10.3 Exercises 109 11 Advanced Permutations 111 11.1 Venn Diagrams and Permutations 111 11.2 Exercises 120 12 Advanced Combinations 125 12.1 Venn Diagrams and Combinations 125 12.2 Exercises 131 13 Poker and Counting 133 13.1 Warm Up Problems 133 13.2 Poker Hands 135 13.3 Jacks or Better 141 13.4 Exercises 143 14 Advanced Counting 145 14.1 Indistinguishable Objects 145 14.2 Circular Permutations 148 14.3 Bracelets 151 14.4 Exercises 155 15 Algebra and Counting 157 15.1 The Binomial Theorem 157 15.2 Identities 160 15.3 Exercises 165 16 Derangements 167 16.1 Fixed Point Theorems 168 16.2 His Own Coat 173 16.3 Exercises 174 17 Probability Vocabulary 175 17.1 Vocabulary 175 18 Equally Likely Outcomes 181 18.1 Exercises 188 19 Probability Trees 189 19.1 Tree Diagrams 189 19.2 Exercises 198 20 Independent Events 199 20.1 Independence 199 20.2 Logical Consequences of Influence 202 20.3 Exercises 206 21 Sequences and Probability 209 21.1 Sequences of Events 209 21.2 Exercises 215 22 Conditional Probability 217 22.1 What Does Conditional Mean? 217 22.2 Exercises 223 23 Bayes? Theorem 225 23.1 The Theorem 225 23.2 Exercises 230 24 Statistics 231 24.1 Introduction 231 24.2 Probability is not Statistics 231 24.3 Conversational Probability 232 24.4 Conditional Statistics 239 24.5 The Mean 241 24.6 Median 242 24.7 Randomness 244 25 Linear Programming 249 25.1 Continuous Variables 249 25.2 Discrete Variables 254 25.3 Incorrectly Applied Rules 258 26 Subjective Truth 261 Bibliography 267 Index 269

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Book SynopsisA systematic and integrated approach to Cantor Sets and their applications to various branches of mathematics The Elements of Cantor Sets: With Applications features a thorough introduction to Cantor Sets and applies these sets as a bridge between real analysis, probability, topology, and algebra. The author fills a gap in the current literature by providing an introductory and integrated perspective, thereby preparing readers for further study and building a deeper understanding of analysis, topology, set theory, number theory, and algebra. The Elements of Cantor Sets provides coverage of: Basic definitions and background theorems as well as comprehensive mathematical details A biography of Georg Ferdinand Ludwig Philipp Cantor, one of the most significant mathematicians of the last century Chapter coverage of fractals and self-similar sets, sums of Cantor Sets, the role of Cantor Sets in creating pathologicalTrade Review“This book could be used as a text for an undergraduate survey course of higher mathematics. It is an excellent reference for a graduate student, researcher or university instructor.” (American Mathematical Society, 1 March 2015) “Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (Choice, 1 March 2014) Table of ContentsForeword xiii Preface xv Acknowledgments xvii Introduction xix 1 A Quick Biography of Cantor 1 2 Basics 5 2.1 Review 5 Exercises 14 3 Introducing the Cantor Set 17 3.1 Some Definitions and Basics 17 3.2 Size of a Cantor Set 21 3.3 Large and Small 46 Exercises 48 4 Cantor Sets and Continued Fractions 51 4.1 Introducing Continued Fractions 52 4.2 Constructing a Cantor Set 59 4.3 Diophantine Equations 60 4.4 Miscellaneous 63 Exercises 65 5 p-adic Numbers and Valuations 67 5.1 Some Abstract Algebra 67 5.2 p-adic Numbers 72 5.3 p-adic Integers and Cantor Sets 80 5.4 p-adic Rational Numbers 82 Exercises 88 6 Self-Similar Objects 91 6.1 The Meaning of Self-Similar 91 6.2 Metric Spaces 92 6.3 Sequences in (S; d) 97 6.4 Affine Transformations 106 6.5 An Application for an IFS 112 Exercises 115 7 Various Notions of Dimension 117 7.1 Limit Supremum and Limit Infimum 117 7.2 Topological Dimension 121 7.3 Similarity Dimension 125 7.4 Box-Counting Dimension 126 7.5 Hausdorff Measure and Dimension 129 7.6 Miscellaneous Notions of Dimension 134 Exercises 138 8 Porosity and Thickness Looking at the Gaps 141 8.1 The Porosity of a Set 141 8.2 Symmetric Sets and Symmetric Porosity 144 8.3 A New and Different Definition of Cantor Set 147 8.4 Thickness of a Cantor Set 148 8.5 Applying Thickness 149 8.6 A Bit More on Thickness 151 8.7 Porosity in a Metric Space 152 Exercises 154 9 Creating Pathological Functions via C 155 9.1 Sequences of Functions 155 9.2 The Cantor Function 159 9.3 Space-Filling Curves 165 9.4 Baire Class One Functions 169 9.5 Darboux Functions 171 9.6 Linearly Continuous Functions 175 Exercises 178 10 Generalizations and Applications 179 10.1 Generalizing Cantor Sets 179 10.2 Fat Cantor Sets 183 10.3 Sums of Cantor Sets 184 10.4 Differences of Cantor Sets 191 10.5 Products of Cantor Sets 193 10.6 Cantor Target 195 10.7 Ana Sets 196 10.8 Average Distance 199 10.9 Non-Averaging Sets 201 10.10 Cantor Series and Cantor Sets 203 10.11 Liouville Numbers and Irrationality Exponents 205 10.12 Sets of Sums of Convergent Alternating Series 207 10.13 The Monty Hall Problem 209 11 Epilogue 215 References 217

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Book SynopsisA friendly and accessible approach to applying statistics in the real world With an emphasis on critical thinking, The Art of Data Analysis: How to Answer Almost Any Question Using Basic Statistics presents fun and unique examples, guides readers through the entire data collection and analysis process, and introduces basic statistical concepts along the way. Leaving proofs and complicated mathematics behind, the author portrays the more engaging side of statistics and emphasizes its role as a problem-solving tool. In addition, light-hearted case studies illustrate the application of statistics to real data analyses, highlighting the strengths and weaknesses of commonly used techniques. Written for the growing academic and industrial population that uses statistics in everyday life, The Art of Data Analysis: How to Answer Almost Any Question Using Basic Statistics highlights important issues that often arise when collecting and sifting tTrade Review“In summary, I can recommend Kristin Jarman’s textbook to interested students and researchers who want to smoothly slip into the world of statistics and prefer a rather prose-oriented introduction over mathematical terminology.” (Biometrical Journal, 1 January 2016) “It is simply one of the best books I have read in the last few years. It is pedagogical, intuitive, and light, all wrapped up in a beautiful sense of humor. This book provides a first step toward the vast world of data analysis." (Computing Reviews, 8 August 2014) “Summing Up: Recommended. Lower-division undergraduates, two-year technical program students, and general readers.” (Choice, 1 December 2013)"With a focus on presenting basic statistical concepts in a friendly and accessible style, this book focuses on the more subjective side of statistics- the art of data analysis. It provides fun, common sense examples that explore statistical concepts and methods and is aimed at helping anyone who has to make decisions based on raw data or compiled results." (Zentralblatt MATH 2016)Table of ContentsPreface ix Part 1 The Basics 1. Statistics: The Life of the Party 3 2. Lions, and Tigers, and . . . Bigfoot? Oh, My: How Questionable Data Can Screw Up an Otherwise Perfectly Good Statistical Analysis 7 3. Asteroid Belts and Spandex Cars: Using Descriptive Statistics to Answer Your Most Weighty Questions 23 4. Baseball, Game Shows, and Sidekicks: Who Cares about Probability Anyway? 43 5. What It’s Like to Be Normal: Probability Distributions and One Rule That Could Make You Wildly Popular 63 Part 2 What a Few Estimates and a Little Probability Can Do for You 6. Men are Insensitive and Women are Illogical. Really: Asserting Your Stereotypes with Confidence 89 7. Godzilla versus King Kong: How Hypothesis Tests Can Be Used to Settle the Battle of the Movie Monsters 109 8. Lab Rats and Roommates: Analysis of Variance and How to Channel Your Inner Mad Scientist 129 9. When the Zombie Flu Went Viral: Regressing the Myth Out of Urban Myths 143 Appendix A: Critical Values for the Standard Normal Distribution 161 Appendix B: Critical Values for the T-Distribution 163 Appendix C: Critical Values for the Chi-Squared Distribution 165 Glossary 167 References 173 Index 175

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Book SynopsisA highly accessible alternative approach to basic statistics Praise for the First Edition: Certainly one of the most impressive little paperback 200-page introductory statistics books that I will ever see . . . it would make a good nightstand book for every statistician.Technometrics Written in a highly accessible style, Introduction to Statistics through Resampling Methods and R, Second Edition guides students in the understanding of descriptive statistics, estimation, hypothesis testing, and model building. The book emphasizes the discovery method, enabling readers to ascertain solutions on their own rather than simply copy answers or apply a formula by rote. The Second Edition utilizes the R programming language to simplify tedious computations, illustrate new concepts, and assist readers in completing exercises. The text facilitates quick learning through the use of: More than 250 exerciseswith selected hintsscattered throughout to stimulate readers'' thTable of ContentsPreface xi 1. Variation 1 1.1 Variation 1 1.2 Collecting Data 2 1.2.1 A Worked-Through Example 3 1.3 Summarizing Your Data 4 1.3.1 Learning to Use R 5 1.4 Reporting Your Results 7 1.4.1 Picturing Data 8 1.4.2 Better Graphics 10 1.5 Types of Data 11 1.5.1 Depicting Categorical Data 12 1.6 Displaying Multiple Variables 12 1.6.1 Entering Multiple Variables 13 1.6.2 From Observations to Questions 14 1.7 Measures of Location 15 1.7.1 Which Measure of Location? 17 1.7.2 The Geometric Mean 18 1.7.3 Estimating Precision 18 1.7.4 Estimating with the Bootstrap 19 1.8 Samples and Populations 20 1.8.1 Drawing a Random Sample 22 1.8.2 Using Data That Are Already in Spreadsheet Form 23 1.8.3 Ensuring the Sample Is Representative 23 1.9 Summary and Review 23 2. Probability 25 2.1 Probability 25 2.1.1 Events and Outcomes 27 2.1.2 Venn Diagrams 27 2.2 Binomial Trials 29 2.2.1 Permutations and Rearrangements 30 2.2.2 Programming Your Own Functions in R 32 2.2.3 Back to the Binomial 33 2.2.4 The Problem Jury 33 2.3 Conditional Probability 34 2.3.1 Market Basket Analysis 36 2.3.2 Negative Results 36 2.4 Independence 38 2.5 Applications to Genetics 39 2.6 Summary and Review 40 3. Two Naturally Occurring Probability Distributions 43 3.1 Distribution of Values 43 3.1.1 Cumulative Distribution Function 44 3.1.2 Empirical Distribution Function 45 3.2 Discrete Distributions 46 3.3 The Binomial Distribution 47 3.3.1 Expected Number of Successes in n Binomial Trials 47 3.3.2 Properties of the Binomial 48 3.4 Measuring Population Dispersion and Sample Precision 51 3.5 Poisson: Events Rare in Time and Space 53 3.5.1 Applying the Poisson 53 3.5.2 Comparing Empirical and Theoretical Poisson Distributions 54 3.5.3 Comparing Two Poisson Processes 55 3.6 Continuous Distributions 55 3.6.1 The Exponential Distribution 56 3.7 Summary and Review 57 4. Estimation and the Normal Distribution 59 4.1 Point Estimates 59 4.2 Properties of the Normal Distribution 61 4.2.1 Student’s t-Distribution 63 4.2.2 Mixtures of Normal Distributions 64 4.3 Using Confidence Intervals to Test Hypotheses 65 4.3.1 Should We Have Used the Bootstrap? 65 4.3.2 The Bias-Corrected and Accelerated Nonparametric Bootstrap 66 4.3.3 The Parametric Bootstrap 68 4.4 Properties of Independent Observations 69 4.5 Summary and Review 70 5. Testing Hypotheses 71 5.1 Testing a Hypothesis 71 5.1.1 Analyzing the Experiment 72 5.1.2 Two Types of Errors 74 5.2 Estimating Effect Size 76 5.2.1 Effect Size and Correlation 76 5.2.2 Using Confidence Intervals to Test Hypotheses 78 5.3 Applying the t-Test to Measurements 79 5.3.1 Two-Sample Comparison 80 5.3.2 Paired t-Test 80 5.4 Comparing Two Samples 81 5.4.1 What Should We Measure? 81 5.4.2 Permutation Monte Carlo 82 5.4.3 One- vs. Two-Sided Tests 83 5.4.4 Bias-Corrected Nonparametric Bootstrap 83 5.5 Which Test Should We Use? 84 5.5.1 p-Values and Significance Levels 85 5.5.2 Test Assumptions 85 5.5.3 Robustness 86 5.5.4 Power of a Test Procedure 87 5.6 Summary and Review 89 6. Designing an Experiment or Survey 91 6.1 The Hawthorne Effect 91 6.1.1 Crafting an Experiment 92 6.2 Designing an Experiment or Survey 94 6.2.1 Objectives 94 6.2.2 Sample from the Right Population 95 6.2.3 Coping with Variation 97 6.2.4 Matched Pairs 98 6.2.5 The Experimental Unit 99 6.2.6 Formulate Your Hypotheses 99 6.2.7 What Are You Going to Measure? 100 6.2.8 Random Representative Samples 101 6.2.9 Treatment Allocation 102 6.2.10 Choosing a Random Sample 103 6.2.11 Ensuring Your Observations Are Independent 103 6.3 How Large a Sample? 104 6.3.1 Samples of Fixed Size 106 6.3.1.1 Known Distribution 106 6.3.1.2 Almost Normal Data 108 6.3.1.3 Bootstrap 110 6.3.2 Sequential Sampling 112 6.3.2.1 Stein’s Two-Stage Sampling Procedure 112 6.3.2.2 Wald Sequential Sampling 112 6.3.2.3 Adaptive Sampling 115 6.4 Meta-Analysis 116 6.5 Summary and Review 116 7. Guide to Entering, Editing, Saving, and Retrieving Large Quantities of Data Using R 119 7.1 Creating and Editing a Data File 120 7.2 Storing and Retrieving Files from within R 120 7.3 Retrieving Data Created by Other Programs 121 7.3.1 The Tabular Format 121 7.3.2 Comma-Separated Values 121 7.3.3 Data from Microsoft Excel 122 7.3.4 Data from Minitab, SAS, SPSS, or Stata Data Files 122 7.4 Using R to Draw a Random Sample 122 8. Analyzing Complex Experiments 125 8.1 Changes Measured in Percentages 125 8.2 Comparing More Than Two Samples 126 8.2.1 Programming the Multi-Sample Comparison in R 127 8.2.2 Reusing Your R Functions 128 8.2.3 What Is the Alternative? 129 8.2.4 Testing for a Dose Response or Other Ordered Alternative 129 8.3 Equalizing Variability 131 8.4 Categorical Data 132 8.4.1 Making Decisions with R 134 8.4.2 One-Sided Fisher’s Exact Test 135 8.4.3 The Two-Sided Test 136 8.4.4 Testing for Goodness of Fit 137 8.4.5 Multinomial Tables 137 8.5 Multivariate Analysis 139 8.5.1 Manipulating Multivariate Data in R 140 8.5.2 Hotelling’s T2 141 8.5.3 Pesarin–Fisher Omnibus Statistic 142 8.6 R Programming Guidelines 144 8.7 Summary and Review 148 9. Developing Models 149 9.1 Models 149 9.1.1 Why Build Models? 150 9.1.2 Caveats 152 9.2 Classification and Regression Trees 152 9.2.1 Example: Consumer Survey 153 9.2.2 How Trees Are Grown 156 9.2.3 Incorporating Existing Knowledge 158 9.2.4 Prior Probabilities 158 9.2.5 Misclassification Costs 159 9.3 Regression 160 9.3.1 Linear Regression 161 9.4 Fitting a Regression Equation 162 9.4.1 Ordinary Least Squares 162 9.4.2 Types of Data 165 9.4.3 Least Absolute Deviation Regression 166 9.4.4 Errors-in-Variables Regression 167 9.4.5 Assumptions 168 9.5 Problems with Regression 169 9.5.1 Goodness of Fit versus Prediction 169 9.5.2 Which Model? 170 9.5.3 Measures of Predictive Success 171 9.5.4 Multivariable Regression 171 9.6 Quantile Regression 174 9.7 Validation 176 9.7.1 Independent Verification 176 9.7.2 Splitting the Sample 177 9.7.3 Cross-Validation with the Bootstrap 178 9.8 Summary and Review 178 10. Reporting Your Findings 181 10.1 What to Report 181 10.1.1 Study Objectives 182 10.1.2 Hypotheses 182 10.1.3 Power and Sample Size Calculations 182 10.1.4 Data Collection Methods 183 10.1.5 Clusters 183 10.1.6 Validation Methods 184 10.2 Text, Table, or Graph? 185 10.3 Summarizing Your Results 186 10.3.1 Center of the Distribution 189 10.3.2 Dispersion 189 10.3.3 Categorical Data 190 10.4 Reporting Analysis Results 191 10.4.1 p-Values? Or Confidence Intervals? 192 10.5 Exceptions Are the Real Story 193 10.5.1 Nonresponders 193 10.5.2 The Missing Holes 194 10.5.3 Missing Data 194 10.5.4 Recognize and Report Biases 194 10.6 Summary and Review 195 11. Problem Solving 197 11.1 The Problems 197 11.2 Solving Practical Problems 201 11.2.1 Provenance of the Data 201 11.2.2 Inspect the Data 202 11.2.3 Validate the Data Collection Methods 202 11.2.4 Formulate Hypotheses 203 11.2.5 Choosing a Statistical Methodology 203 11.2.6 Be Aware of What You Don’t Know 204 11.2.7 Qualify Your Conclusions 204 Answers to Selected Exercises 205 Index 207

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Book SynopsisFeaturing a comprehensive approach to sample size determination for general statistical use, this book uniquely blends applications from a variety of fields including statistics, biostatistics, the health sciences, and engineering.Trade Review“This very comprehensive book is well structured.” (International Statistical Review, 1 October 2015) “In summary, this book succeeds in the author’s aim of providing a general purpose text for readers interested in methodology without much technical fuss. In general, the book focuses on providing wealth of discussions and reviews for sample size and power and is an excellent source for up-to-date software and references for a wide range of topics related to sample size determination.” (International Statistical Review, 1 March 2015)Table of ContentsPreface xv 1 Brief Review of Hypothesis Testing Concepts/Issues and Confidence Intervals 1 1.1 Basic Concepts of Hypothesis Testing, 1 1.2 Review of Confidence Intervals and Their Relationship to Hypothesis Tests, 5 1.3 Sports Applications, 9 1.4 Observed Power, Retrospective Power, Conditional Power, and Predictive Power, 9 1.5 Testing for Equality, Equivalence, Noninferiority, or Superiority, 10 1.5.1 Software, 11 References, 12 Exercises, 14 2 Methods of Determining Sample Sizes 17 2.1 Internal Pilot Study Versus External Pilot Study, 20 2.2 Examples: Frequentist and Bayesian, 24 2.2.1 Bayesian Approaches, 30 2.2.2 Probability Assessment Approach, 31 2.2.3 Reproducibility Probability Approach, 32 2.2.4 Competing Probability Approach, 32 2.2.5 Evidential Approach, 32 2.3 Finite Populations, 32 2.4 Sample Sizes for Confidence Intervals, 33 2.4.1 Using the Finite Population Correction Factor, 36 2.4.1.1 Estimating Population Totals, 38 2.5 Confidence Intervals on Sample Size and Power, 39 2.6 Specification of Power, 39 2.7 Cost of Sampling, 40 2.8 Ethical Considerations, 40 2.9 Standardization and Specification of Effect Sizes, 42 2.10 Equivalence Tests, 43 2.11 Software and Applets, 45 2.12 Summary, 47 References, 47 Exercises, 53 3 Means and Variances 57 3.1 One Mean, Normality, and Known Standard Deviation, 58 3.1.1 Using the Coefficient of Variation, 65 3.2 One Mean, Standard Deviation Unknown, Normality Assumed, 66 3.3 Confidence Intervals on Power and/or Sample Size, 67 3.4 One Mean, Standard Deviation Unknown, Nonnormality Assumed, 70 3.5 One Mean, Exponential Distribution, 71 3.6 Two Means, Known Standard Deviations—Independent Samples, 71 3.6.1 Unequal Sample Sizes, 74 3.7 Two Means, Unknown but Equal Standard Deviations—Independent Samples, 74 3.7.1 Unequal Sample Sizes, 76 3.8 Two Means, Unequal Variances and Sample Sizes—Independent Samples, 77 3.9 Two Means, Unknown and Unequal Standard Deviations—Independent Samples, 77 3.10 Two Means, Known and Unknown Standard Deviations—Dependent Samples, 78 3.11 Bayesian Methods for Comparing Means, 81 3.12 One Variance or Standard Deviation, 81 3.13 Two Variances, 83 3.14 More Than Two Variances, 84 3.15 Confidence Intervals, 84 3.15.1 Adaptive Confidence Intervals, 85 3.15.2 One Mean, Standard Deviation Unknown—With Tolerance Probability, 85 3.15.3 Difference Between Two Independent Means, Standard Deviations Known and Unknown—With and Without Tolerance Probability, 88 3.15.4 Difference Between Two Paired Means, 90 3.15.5 One Variance, 91 3.15.6 One-Sided Confidence Bounds, 92 3.16 Relative Precision, 93 3.17 Computing Aids, 94 3.18 Software, 94 3.19 Summary, 95 Appendix, 95 References, 96 Exercises, 99 4 Proportions and Rates 103 4.1 One Proportion, 103 4.1.1 One Proportion—With Continuity Correction, 107 4.1.2 Software Disagreement and Rectification, 108 4.1.3 Equivalence Tests and Noninferiority Tests for One Proportion, 109 4.1.4 Confidence Interval and Error of Estimation, 110 4.1.5 One Proportion—Exact Approach, 113 4.1.6 Bayesian Approaches, 115 4.2 Two Proportions, 115 4.2.1 Two Proportions—With Continuity Correction, 119 4.2.2 Two Proportions—Fisher’s Exact Test, 121 4.2.3 What Approach Is Recommended?, 122 4.2.4 Correlated Proportions, 123 4.2.5 Equivalence Tests for Two Proportions, 124 4.2.6 Noninferiority Tests for Two Proportions, 125 4.2.7 Need for Pilot Study?, 125 4.2.8 Linear Trend in Proportions, 125 4.2.9 Bayesian Method for Estimating the Difference of Two Binomial Proportions, 126 4.3 Multiple Proportions, 126 4.4 Multinomial Probabilities and Distributions, 129 4.5 One Rate, 130 4.5.1 Pilot Study Needed?, 132 4.6 Two Rates, 132 4.7 Bayesian Sample Size Determination Methods for Rates, 135 4.8 Software, 135 4.9 Summary, 136 Appendix, 136 References, 140 Exercises, 144 5 Regression Methods and Correlation 145 5.1 Linear Regression, 145 5.1.1 Simple Linear Regression, 146 5.1.2 Multiple Linear Regression, 150 5.1.2.1 Application: Predicting College Freshman Grade Point Average, 155 5.2 Logistic Regression, 155 5.2.1 Simple Logistic Regression, 156 5.2.1.1 Normally Distributed Covariate, 158 5.2.1.2 Binary Covariate, 162 5.2.2 Multiple Logistic Regression, 163 5.2.2.1 Measurement Error, 165 5.2.3 Polytomous Logistic Regression, 165 5.2.4 Ordinal Logistic Regression, 166 5.2.5 Exact Logistic Regression, 167 5.3 Cox Regression, 167 5.4 Poisson Regression, 169 5.5 Nonlinear Regression, 172 5.6 Other Types of Regression Models, 172 5.7 Correlation, 172 5.7.1 Confidence Intervals, 174 5.7.2 Intraclass Correlation, 175 5.7.3 Two Correlations, 175 5.8 Software, 176 5.9 Summary, 177 References, 177 Exercises, 180 6 Experimental Designs 183 6.1 One Factor—Two Fixed Levels, 184 6.1.1 Unequal Sample Sizes, 186 6.2 One Factor—More Than Two Fixed Levels, 187 6.2.1 Multiple Comparisons and Dunnett’s Test, 192 6.2.2 Analysis of Means (ANOM), 193 6.2.3 Unequal Sample Sizes, 195 6.2.4 Analysis of Covariance, 196 6.2.5 Randomized Complete Block Designs, 197 6.2.6 Incomplete Block Designs, 198 6.2.7 Latin Square Designs, 199 6.2.7.1 Graeco-Latin Square Designs, 202 6.3 Two Factors, 203 6.4 2k Designs, 205 6.4.1 22 Design with Equal and Unequal Variances, 206 6.4.2 Unreplicated 2k Designs, 206 6.4.3 Software for 2k Designs, 208 6.5 2k − p Designs, 209 6.6 Detecting Conditional Effects, 210 6.7 General Factorial Designs, 211 6.8 Repeated Measures Designs, 212 6.8.1 Crossover Designs, 215 6.8.1.1 Software, 217 6.9 Response Surface Designs, 218 6.10 Microarray Experiments, 219 6.10.1 Software, 220 6.11 Other Designs, 220 6.11.1 Plackett–Burman Designs, 220 6.11.2 Split-Plot and Strip-Plot Designs, 222 6.11.3 Nested Designs, 224 6.11.4 Ray designs, 225 6.12 Designs for Nonnormal Responses, 225 6.13 Designs with Random Factors, 227 6.14 Zero Patient Design, 228 6.15 Computer Experiments, 228 6.16 Noninferiority and Equivalence Designs, 229 6.17 Pharmacokinetic Experiments, 229 6.18 Bayesian Experimental Design, 229 6.19 Software, 230 6.20 Summary, 232 Appendix, 233 References, 234 Exercises, 239 7 Clinical Trials 243 7.1 Clinical Trials, 245 7.1.1 Cluster Randomized Trials, 247 7.1.2 Phase II Trials, 247 7.1.2.1 Phase II Cancer Trials, 247 7.1.3 Phase III Trials, 247 7.1.4 Longitudinal Clinical Trials, 248 7.1.5 Fixed Versus Adaptive Clinical Trials, 248 7.1.6 Noninferiority Trials, 249 7.1.7 Repeated Measurements, 249 7.1.8 Multiple Tests, 250 7.1.9 Use of Internal Pilot Studies for Clinical Trials, 250 7.1.10 Using Historical Controls, 250 7.1.11 Trials with Combination Treatments, 251 7.1.12 Group Sequential Trials, 251 7.1.13 Vaccine Efficacy Studies, 251 7.2 Bioequivalence Studies, 251 7.3 Ethical Considerations, 252 7.4 The Use of Power in Clinical Studies, 252 7.5 Preclinical Experimentation, 253 7.6 Pharmacodynamic, Pharmacokinetic, and Pharmacogenetic Experiments, 253 7.7 Method of Competing Probability, 254 7.8 Bayesian Methods, 255 7.9 Cost and Other Sample Size Determination Methods for Clinical Trials, 256 7.10 Meta-Analyses of Clinical Trials, 256 7.11 Miscellaneous, 257 7.12 Survey Results of Published Articles, 259 7.13 Software, 260 7.14 Summary, 263 References, 263 Exercises, 275 8 Quality Improvement 277 8.1 Control Charts, 277 8.1.1 Shewhart Measurement Control Charts, 278 8.1.2 Using Software to Determine Subgroup Size, 281 8.1.2.1 ¯X -Chart, 282 8.1.2.2 S-Chart and S2-Chart, 284 8.1.3 Attribute Control Charts, 286 8.1.4 CUSUM and EWMA Charts, 289 8.1.4.1 Subgroup Size Considerations for CUSUM Charts, 290 8.1.4.2 CUSUM and EWMA Variations, 291 8.1.4.3 Subgroup Size Determination for CUSUM and EWMA Charts and Their Variations, 291 8.1.4.4 EWMA Applied to Autocorrelated Data, 293 8.1.5 Adaptive Control Charts, 293 8.1.6 Regression and Cause-Selecting Control Charts, 293 8.1.7 Multivariate Control Charts, 295 8.2 Medical Applications, 296 8.3 Process Capability Indices, 297 8.4 Tolerance Intervals, 298 8.5 Measurement System Appraisal, 300 8.6 Acceptance Sampling, 300 8.7 Reliability and Life Testing, 301 8.8 Software, 301 8.9 Summary, 302 References, 302 Exercises, 305 9 Survival Analysis and Reliability 307 9.1 Survival Analysis, 307 9.1.1 Logrank Test, 308 9.1.1.1 Freedman Method, 311 9.1.1.2 Other Methods, 312 9.1.2 Wilcoxon–Breslow–Gehan Test, 313 9.1.3 Tarone–Ware Test, 313 9.1.4 Other Tests, 314 9.1.5 Cox Proportional Hazards Model, 314 9.1.6 Joint Modeling of Longitudinal and Survival Data, 315 9.1.7 Multistage Designs, 316 9.1.8 Comparison of Software and Freeware, 316 9.2 Reliability Analysis, 317 9.3 Summary, 318 References, 319 Exercise, 321 10 Nonparametric Methods 323 10.1 Wilcoxon One-Sample Test, 324 10.1.1 Wilcoxon Test for Paired Data, 327 10.2 Wilcoxon Two–Sample Test (Mann–Whitney Test), 327 10.2.1 van Elteren Test—A Stratified Mann–Whitney Test, 331 10.3 Kruskal–Wallis One-Way ANOVA, 331 10.4 Sign Test, 331 10.5 McNemar’s Test, 334 10.6 Contingency Tables, 334 10.7 Quasi-Likelihood Method, 334 10.8 Rank Correlation Coefficients, 335 10.9 Software, 335 10.10 Summary, 336 References, 336 Exercises, 339 11 Miscellaneous Topics 341 11.1 Case–Control Studies, 341 11.2 Epidemiology, 342 11.3 Longitudinal Studies, 342 11.4 Microarray Studies, 343 11.5 Receiver Operating Characteristic ROC Curves, 343 11.6 Meta-Analyses, 343 11.7 Sequential Sample Sizes, 343 11.8 Sample Surveys, 344 11.8.1 Vegetation Surveys, 344 11.9 Cluster Sampling, 345 11.10 Factor Analysis, 346 11.11 Multivariate Analysis of Variance and Other Multivariate Methods, 346 11.12 Structural Equation Modeling, 348 11.13 Multilevel Modeling, 349 11.14 Prediction Intervals, 349 11.15 Measures of Agreement, 350 11.16 Spatial Statistics, 350 11.17 Agricultural Applications, 350 11.18 Estimating the Number of Unseen Species, 351 11.19 Test Reliability, 351 11.20 Agreement Studies, 351 11.21 Genome-wide Association Studies, 351 11.22 National Security, 352 11.23 Miscellaneous, 352 11.24 Summary, 353 References, 354 Answers to Selected Exercises 363 Index 369

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Book SynopsisModeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method.Table of ContentsPreface xi About the Authors xv Acknowledgments xix 1 Introduction 1 2 Compositional Data and Their Sample Space 8 2.1 Basic concepts 8 2.2 Principles of compositional analysis 12 2.2.1 Scale invariance 12 2.2.2 Permutation invariance 15 2.2.3 Subcompositional coherence 16 2.3 Zeros, missing values, and other irregular components 16 2.3.1 Kinds of irregular components 16 2.3.2 Strategies to analyze irregular data 19 2.4 Exercises 21 3 The Aitchison Geometry 23 3.1 General comments 23 3.2 Vector space structure 24 3.3 Inner product, norm and distance 26 3.4 Geometric figures 28 3.5 Exercises 30 4 Coordinate Representation 32 4.1 Introduction 32 4.2 Compositional observations in real space 33 4.3 Generating systems 33 4.4 Orthonormal coordinates 36 4.5 Balances 38 4.6 Working on coordinates 43 4.7 Additive logratio coordinates (alr) 46 4.8 Orthogonal projections 48 4.9 Matrix operations in the simplex 54 4.9.1 Perturbation-linear combination of compositions 54 4.9.2 Linear transformations of óKòù: endomorphisms 55 4.9.3 Other matrix transformations on óKòù: nonlinear transformations 57 4.10 Coordinates leading to alternative Euclidean structures 59 4.11 Exercises 61 5 Exploratory Data Analysis 65 5.1 General remarks 65 5.2 Sample center, total variance, and variation matrix 66 5.3 Centering and scaling 68 5.4 The biplot: a graphical display 70 5.4.1 Construction of a biplot 70 5.4.2 Interpretation of a 2D compositional biplot 72 5.5 Exploratory analysis of coordinates 76 5.6 A geological example 79 5.7 Linear trends along principal components 85 5.8 A nutrition example 89 5.9 A political example 96 5.10 Exercises 100 6 Random Compositions 103 6.1 Sample space 103 6.1.1 Conventional approach to the sample space of compositions 105 6.1.2 A compositional approach to the sample space of compositions 106 6.1.3 Definitions related to random compositions 107 6.2 Variability and center 108 6.3 Probability distributions on the simplex 112 6.3.1 The normal distribution on the simplex 114 6.3.2 The Dirichlet distribution 121 6.3.3 Other distributions 127 6.4 Exercises 128 7 Statistical Inference 130 7.1 Point estimation of center and variability 130 7.2 Testing hypotheses on compositional normality 135 7.3 Testing hypotheses about two populations 136 7.4 Probability and confidence regions for normal data 142 7.5 Bayesian estimation with count data 144 7.6 Exercises 147 8 Linear Models 149 8.1 Linear regression with compositional response 150 8.2 Regression with compositional covariates 156 8.3 Analysis of variance with compositional response 160 8.4 Linear discrimination with compositional predictor 163 8.5 Exercises 165 9 Compositional Processes 172 9.1 Linear processes 173 9.2 Mixture processes 176 9.3 Settling processes 178 9.4 Simplicial derivative 183 9.5 Elementary differential equations 186 9.5.1 Constant derivative 187 9.5.2 Forced derivative 189 9.5.3 Complete first-order linear equation 194 9.5.4 Harmonic oscillator 200 9.6 Exercises 204 10 Epilogue 206 References 211 Appendix A Practical Recipes 222 A.1 Plotting a ternary diagram 222 A.2 Parameterization of an elliptic region 224 A.3 Matrix expressions of change of representation 226 Appendix B Random Variables 228 B.1 Probability spaces and random variables 228 B.2 Description of probability 232 List of Abbreviations and Symbols 234 Author Index 237 General Index 241

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Book SynopsisReflecting the fast pace and ever-evolving nature of the financial industry, the Handbook of High-Frequency Trading and Modeling in Finance details how high-frequency analysis presents new systematic approaches to implementing quantitative activities with high-frequency financial data. Introducing new and established mathematical foundations necessary to analyze realistic market models and scenarios, the handbook begins with a presentation of the dynamics and complexity of futures and derivatives markets as well as a portfolio optimization problem using quantum computers. Subsequently, the handbook addresses estimating complex model parameters using high-frequency data. Finally, the handbook focuses on the links between models used in financial markets and models used in other research areas such as geophysics, fossil records, and earthquake studies. The Handbook of High-Frequency Trading and Modeling in Finance also features: Contributions by well-knownTable of ContentsNotes on Contributors xiii Preface xv 1 Trends and Trades 1Michael Carlisle, Olympia Hadjiliadis, and Ioannis Stamos 1.1 Introduction 1 1.2 A trend-based trading strategy 3 1.2.1 Signaling and trends 3 1.2.2 Gain over a subperiod 5 1.3 CUSUM timing 7 1.3.1 Cusum process and stopping time 7 1.3.2 A CUSUM timing scheme 10 1.3.3 US treasury notes, CUSUM timing 11 1.4 Example: Random walk on ticks 12 1.4.1 Random walk expected gain over a subperiod 15 1.4.2 Simple random walk, CUSUM timing 18 1.4.3 Lazy simple random walk, cusum timing 21 1.5 CUSUM strategy Monte Carlo 24 1.6 The effect of the threshold parameter 27 1.7 Conclusions and future work 39 Appendix: Tables 40 References 47 2 Gaussian Inequalities and Tranche Sensitivities 51Claas Becker and Ambar N. Sengupta 2.1 Introduction 51 2.2 The tranche loss function 52 2.3 A sensitivity identity 54 2.4 Correlation sensitivities 55 Acknowledgment 58 References 58 3 A Nonlinear Lead Lag Dependence Analysis of Energy Futures: Oil, Coal, and Natural Gas 61Germán G. Creamer and Bernardo Creamer 3.1 Introduction 61 3.1.1 Causality analysis 62 3.2 Data 64 3.3 Estimation techniques 64 3.4 Results 65 3.5 Discussion 67 3.6 Conclusions 69 Acknowledgments 69 References 70 4 Portfolio Optimization: Applications in Quantum Computing 73Michael Marzec 4.1 Introduction 73 4.2 Background 75 4.2.1 Portfolios and optimization 76 4.2.2 Algorithmic complexity 77 4.2.3 Performance 78 4.2.4 Ising model 79 4.2.5 Adiabatic quantum computing 79 4.3 The models 80 4.3.1 Financial model 81 4.3.2 Graph-theoretic combinatorial optimization models 82 4.3.3 Ising and Qubo models 83 4.3.4 Mixed models 84 4.4 Methods 84 4.4.1 Model implementation 85 4.4.2 Input data 85 4.4.3 Mean-variance calculations 85 4.4.4 Implementing the risk measure 86 4.4.5 Implementation mapping 86 4.5 Results 88 4.5.1 The simple correlation model 88 4.5.2 The restricted minimum-risk model 91 4.5.3 The WMIS minimum-risk, max return model 94 4.6 Discussion 95 4.6.1 Hardware limitations 97 4.6.2 Model limitations 97 4.6.3 Implementation limitations 98 4.6.4 Future research 98 4.7 Conclusion 100 Acknowledgments 100 Appendix 4.A: WMIS Matlab Code 100 References 103 5 Estimation Procedure for Regime Switching Stochastic Volatility Model and Its Applications 107Ionut Florescu and Forrest Levin 5.1 Introduction 107 5.1.1 The original motivation 108 5.1.2 The model and the problem 108 5.1.3 A brief historical note 109 5.2 The methodology 110 5.2.1 Obtaining filtered empirical distributions at t1,…, tT 110 5.2.2 Obtaining the parameters of the Markov chain 112 5.3 Results obtained applying the model to real data 113 5.3.1 Part i: financial applications 113 5.3.2 Part ii: physical data application. temperature data 119 5.3.3 Part iii: analysis of seismometer readings during an earthquake 121 5.3.4 Analysis of the earthquake signal: beginning 123 5.3.5 Analysis: during the earthquake 125 5.3.6 Analysis: end of the earthquake signal, aftershocks 127 5.4 Conclusion 127 5.A Theoretical results and empirical testing 128 5.A.1 How does the particle filter work? 128 5.A.2 Theoretical results about convergence and parameter estimates 129 5.A.3 Markov chain parameter estimates 131 5.A.4 Empirical testing 132 5.A.5 A list of supplementary documents 133 References 133 6 Detecting Jumps in High-Frequency Prices Under Stochastic Volatility: A Review and a Data-Driven Approach 137Ping-Chen Tsai and Mark B. Shackleton 6.1 Introduction 137 6.2 Review on the intraday jump tests 140 6.2.1 Realized volatility measure and the BNS tests 140 6.2.2 The ABD and LM tests 142 6.3 A data-driven testing procedure 146 6.3.1 Spy data and microstructure noise 146 6.3.2 A generalized testing procedure 149 6.4 Simulation study 153 6.4.1 Model specification 153 6.4.2 Simulation results 158 6.5 Empirical results 161 6.5.1 Results on the backward-looking test 162 6.5.2 Results on the interpolated test 165 6.6 Conclusion 165 Acknowledgments 166 Appendix 6.A: Least-square estimation of HAR-MA (2) model for log(BP) of SPY 167 Appendix 6.B: Estimation of ARMA (2, 1) model for log(BP) of SPY 168 Appendix 6.C: Minimized loss function loss(𝜌1, 𝜌2) for SV2FJ_2𝜌 model, SPY 169 Appendix 6.D.1: Calibration of 𝜉 under SV2FJ_2𝜌 model at 2-min frequency, E[Nt] = 0.08 170 Appendix 6.D.2: Calibration of 𝜉 under SV2FJ_2𝜌 model at 2-min frequency, E[Nt] = 0.40 171 Appendix 6.D.3: Calibration of 𝜉 under SV2FJ_2𝜌 model at 5-min frequency, E[Nt] = 0.08 172 Appendix 6.D.4: Calibration of 𝜉 under SV2FJ_2𝜌 Model at 5-min frequency, E[Nt] = 0.40 173 Appendix 6.D.5: Calibration of 𝜉 under SV2FJ_2𝜌 model at 10-min frequency, E[Nt] = 0.08 174 Appendix 6.D.6: Calibration of 𝜉 under SV2FJ_2𝜌 model at 10-min frequency, E[Nt] = 0.40 175 References 175 7 Hawkes Processes and Their Applications to High-Frequency Data Modeling 183Baron Law and Frederi G. Viens 7.1 Introduction 183 7.2 Point processes 184 7.3 Hawkes processes 186 7.3.1 Branching structure representation 188 7.3.2 Stationarity 188 7.3.3 Convergence 189 7.4 Statistical inference of Hawkes processes 191 7.4.1 Simulation 191 7.4.2 Estimation 194 7.4.3 Hypothesis testing 197 7.5 Applications of Hawkes processes 198 7.5.1 Modeling order arrivals 199 7.5.2 Modeling price jumps 200 7.5.3 Modeling jump-diffusion 205 7.5.4 Measuring endogeneity (Reflexivity) 205 Appendix 7.A: Point Processes 207 7.A.1 Definition 207 7.A.2 Moments 208 7.A.3 Marked point processes 209 7.A.4 Stochastic intensity 209 7.A.5 Random time change 211 Appendix 7.B: A Brief History of Hawkes processes 211 References 212 8 Multifractal Random Walk Driven by a Hermite Process 221Alexis Fauth and Ciprian A. Tudor 8.1 Introduction 221 8.2 Preliminaries 224 8.2.1 Fractional brownian motion and hermite processes 224 8.2.2 Wiener integrals with respect to the hermite process 226 8.2.3 Infinitely divisible cascading noise 229 8.3 Multifractal random walk driven by a Hermite process 231 8.3.1 Definition and existence 231 8.3.2 Properties of the hermite multifractal random walk 233 8.4 Financial applications 234 8.4.1 Simulation of the Hmrw 235 8.4.2 Financial statistics 241 8.5 Concluding remarks 243 References 247 9 Interpolating Techniques and Nonparametric Regression Methods Applied to Geophysical and Financial Data Analysis 251K. Basu and Maria C. Mariani 9.1 Introduction 251 9.2 Nonparametric regression models 253 9.2.1 Local polynomial regression 255 9.2.2 Lowess/loess method 257 9.2.3 Numerical applications 259 9.3 Interpolation methods 271 9.3.1 Nearest-neighbor interpolation 271 9.3.2 Bilinear interpolation 272 9.3.3 Bicubic interpolation 276 9.3.4 Biharmonic interpolation 277 9.3.5 Thin plate splines 282 9.3.6 Numerical applications 285 9.4 Conclusion 287 Acknowledgments 292 References 292 10 Study of Volatility Structures in Geophysics and Finance Using Garch Models 295Maria C. Mariani, F. Biney, and I. SenGupta 10.1 Introduction 295 10.2 Short memory models 297 10.2.1 ARMA(p,q) model 297 10.2.2 GARCH(p,q) model 297 10.2.3 IGARCH(1,1) model 298 10.3 Long memory models 298 10.3.1 ARFIMA(p,d,q) model 299 10.3.2 ARFIMA(p,d,q)-GARCH(r,s) 299 10.3.3 Intermediate memory process 300 10.3.4 Figarch model 300 10.4 Detection and estimation of long memory 302 10.4.1 Augmented dickey–fuller test(ADF test) 302 10.4.2 KPSS test 303 10.4.3 Whittle method 304 10.5 Data collection, analysis, and result 306 10.5.1 Analysis on dow Jones index (DJIA) returns 306 10.5.2 Model selection and specification: conditional mean 306 10.5.3 Conditional mean model (returns) 309 10.5.4 Model diagnostics: ARMA(2, 2) 309 10.5.5 Test for ARCH effect 311 10.5.6 Model selection and specification: Conditional variance 313 10.5.7 Standardized residuals test 314 10.5.8 Model diagnostics 314 10.5.9 Returns and variance equation 315 10.5.10 standardized residuals test 317 10.5.11 Model diagnostic of conditional returns with conditional variance 318 10.5.12 One-step ahead prediction of last 10 observations 330 10.5.13 Analysis on high-frequency, earthquake, and explosives series 330 10.6 Discussion and conclusion 335 References 337 11 Scale Invariance and Lévy Models Applied to Earthquakes and Financial High-Frequency Data 341M. P. Beccar-Varela, Ionut Florescu, and I. SenGupta 11.1 Introduction 341 11.2 Governing equations for the deterministic model 342 11.2.1 Application to geophysical (earthquake data) 343 11.2.2 Results 344 11.3 L´evy flights and application to geophysics 345 11.3.1 Truncated L´evy flight distribution 353 11.3.2 Results 356 11.4 Application to the high-frequency market data 360 11.4.1 Methodology 360 11.4.2 Results 361 11.5 Brief program code description 362 11.6 Conclusion 364 11.A Appendix 366 11.A.1 Stable distributions 366 11.A.2 Characterization of stable distributions 367 References 368 12 Analysis of Generic Diversity in the Fossil Record, Earthquake Series, and High-Frequency Financial Data 371M. P. Beccar Varela, F. Biney, Maria C. Mariani, I. SenGupta, M. Shpak, and P. Bezdek 12.1 Introduction 371 12.2 Statistical preliminaries and results 373 12.2.1 Sum of exponential random variables with different parameters 374 12.3 Statistical and numerical analysis 377 12.4 Analysis with Lévy distribution 380 12.4.1 Characterization of Stable Distributions 383 12.4.2 Truncated Lévy flight (TLF) distribution 384 12.4.3 Data analysis with TLF distribution 389 12.4.4 Sum of Lévy random variables with different parameters 390 12.5 Analysis of the Stock Indices, high-frequency (tick) data, and explosive series 394 12.6 Results and discussion 409 Acknowledgments 421 12.A Appendix A—Big ‘O’ notation 421 References 422 Index 425

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Book SynopsisCollecting, analyzing, and extracting valuable information from a large amount of data requires easily accessible, robust, computational and analytical tools. Data Mining and Business Analytics with R utilizes the open source software R for the analysis, exploration, and simplification of large high-dimensional data sets.Trade Review"I first taught a Ph.D. level course in business applications of data mining 10 years ago. I regularly search the web, looking for business-oriented data mining books, and this is the first one I have found that is suitable for an MS in business analytics. I plan to use it. Anyone who teaches such a class and is inclined toward R should consider this text." (Journal of the American Statistical Association, 1 January 2014)Table of ContentsPreface ix Acknowledgments xi 1. Introduction 1 Reference 6 2. Processing the Information and Getting to Know Your Data 7 2.1 Example 1: 2006 Birth Data 7 2.2 Example 2: Alumni Donations 17 2.3 Example 3: Orange Juice 31 References 39 3. Standard Linear Regression 40 3.1 Estimation in R 43 3.2 Example 1: Fuel Efficiency of Automobiles 43 3.3 Example 2: Toyota Used-Car Prices 47 Appendix 3.A The Effects of Model Overfitting on the Average Mean Square Error of the Regression Prediction 53 References 54 4. Local Polynomial Regression: a Nonparametric Regression Approach 55 4.1 Model Selection 56 4.2 Application to Density Estimation and the Smoothing of Histograms 58 4.3 Extension to the Multiple Regression Model 58 4.4 Examples and Software 58 References 65 5. Importance of Parsimony in Statistical Modeling 67 5.1 How Do We Guard Against False Discovery 67 References 70 6. Penalty-Based Variable Selection in Regression Models with Many Parameters (LASSO) 71 6.1 Example 1: Prostate Cancer 74 6.2 Example 2: Orange Juice 78 References 82 7. Logistic Regression 83 7.1 Building a Linear Model for Binary Response Data 83 7.2 Interpretation of the Regression Coefficients in a Logistic Regression Model 85 7.3 Statistical Inference 85 7.4 Classification of New Cases 86 7.5 Estimation in R 87 7.6 Example 1: Death Penalty Data 87 7.7 Example 2: Delayed Airplanes 92 7.8 Example 3: Loan Acceptance 100 7.9 Example 4: German Credit Data 103 References 107 8. Binary Classification, Probabilities, and Evaluating Classification Performance 108 8.1 Binary Classification 108 8.2 Using Probabilities to Make Decisions 108 8.3 Sensitivity and Specificity 109 8.4 Example: German Credit Data 109 9. Classification Using a Nearest Neighbor Analysis 115 9.1 The k-Nearest Neighbor Algorithm 116 9.2 Example 1: Forensic Glass 117 9.3 Example 2: German Credit Data 122 Reference 125 10. The Na¨ýve Bayesian Analysis: a Model for Predicting a Categorical Response from Mostly Categorical Predictor Variables 126 10.1 Example: Delayed Airplanes 127 Reference 131 11. Multinomial Logistic Regression 132 11.1 Computer Software 134 11.2 Example 1: Forensic Glass 134 11.3 Example 2: Forensic Glass Revisited 141 Appendix 11.A Specification of a Simple Triplet Matrix 147 References 149 12. More on Classification and a Discussion on Discriminant Analysis 150 12.1 Fisher’s Linear Discriminant Function 153 12.2 Example 1: German Credit Data 154 12.3 Example 2: Fisher Iris Data 156 12.4 Example 3: Forensic Glass Data 157 12.5 Example 4: MBA Admission Data 159 Reference 160 13. Decision Trees 161 13.1 Example 1: Prostate Cancer 167 13.2 Example 2: Motorcycle Acceleration 179 13.3 Example 3: Fisher Iris Data Revisited 182 14. Further Discussion on Regression and Classification Trees, Computer Software, and Other Useful Classification Methods 185 14.1 R Packages for Tree Construction 185 14.2 Chi-Square Automatic Interaction Detection (CHAID) 186 14.3 Ensemble Methods: Bagging, Boosting, and Random Forests 188 14.4 Support Vector Machines (SVM) 192 14.5 Neural Networks 192 14.6 The R Package Rattle: A Useful Graphical User Interface for Data Mining 193 References 195 15. Clustering 196 15.1 k-Means Clustering 196 15.2 Another Way to Look at Clustering: Applying the Expectation-Maximization (EM) Algorithm to Mixtures of Normal Distributions 204 15.3 Hierarchical Clustering Procedures 212 References 219 16. Market Basket Analysis: Association Rules and Lift 220 16.1 Example 1: Online Radio 222 16.2 Example 2: Predicting Income 227 References 234 17. Dimension Reduction: Factor Models and Principal Components 235 17.1 Example 1: European Protein Consumption 238 17.2 Example 2: Monthly US Unemployment Rates 243 18. Reducing the Dimension in Regressions with Multicollinear Inputs: Principal Components Regression and Partial Least Squares 247 18.1 Three Examples 249 References 257 19. Text as Data: Text Mining and Sentiment Analysis 258 19.1 Inverse Multinomial Logistic Regression 259 19.2 Example 1: Restaurant Reviews 261 19.3 Example 2: Political Sentiment 266 Appendix 19.A Relationship Between the Gentzkow Shapiro Estimate of “Slant” and Partial Least Squares 268 References 271 20. Network Data 272 20.1 Example 1: Marriage and Power in Fifteenth Century Florence 274 20.2 Example 2: Connections in a Friendship Network 278 References 292 Appendix A: Exercises 293 Exercise 1 294 Exercise 2 294 Exercise 3 296 Exercise 4 298 Exercise 5 299 Exercise 6 300 Exercise 7 301 Appendix B: References 338 Index 341

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Book SynopsisAgent-based modelling in economics Lynne Hamill and Nigel Gilbert, Centre for Research in Social Simulation (CRESS), University of Surrey, UK New methods of economic modelling have been sought as a result of the global economic downturn in 2008.Table of ContentsPreface viiiCopyright notices ix1 Why agent]based modelling is useful for economists 11.1 Introduction 11.2 A very brief history of economic modelling 11.3 What is ABM? 41.4 The three themes of this book 51.5 Details of chapters 6References 92 Starting agent-based modelling 112.1 Introduction 112.2 A simple market: the basic model 122.3 The basic framework 132.4 Enhancing the basic model: adding prices 182.5 Enhancing the model: selecting traders 212.6 Final enhancement: more economically rational agents 232.7 Running experiments 252.8 Discussion 26Appendix 2.A The example model: full version 27References 283 Heterogeneous demand 293.1 Introduction 293.2 Modelling basic consumer demand theory 303.3 Practical demand modelling 393.4 Discussion 43Appendix 3.A How to do it 46References 524 Social demand 534.1 Introduction 534.2 Social networks 534.3 Threshold models 564.4 Adoption of innovative products 624.5 Case study: household adoption of fixed-line phones in Britain 644.6 Discussion 70Appendix 4.A How to do it 70References 785 Benefits of barter 805.1 Introduction 805.2 One-to-one barter 815.3 Red Cross parcels 885.4 Discussion 96Appendix 5.A How to do it 97References 1046 The market 1056.1 Introduction 1056.2 Cournot–Nash model 1056.3 Market model 1086.4 Digital world model 1176.5 Discussion 124Appendix 6.A How to do it 125References 1317 Labour market 1327.1 Introduction 1327.2 A simple labour market model 1427.3 Discussion 151Appendix 7.A How to do it 155References 1618 International trade 1638.1 Introduction 1638.2 Models 1728.3 Discussion 183Appendix 8.A How to do it 185References 1879 Banking 1899.1 Introduction 1899.2 The banking model 1989.3 Discussion 206Appendix 9.A How to do it 209References 21210 Tragedy of the commons 21410.1 Introduction 21410.2 Model 21810.3 Discussion 225Appendix 10.A How to do it 228References 23211 Summary and conclusions 23411.1 Introduction 23411.2 The models 23411.3 What makes a good model? 23711.4 Pros and cons of ABM 238References 239Index 242

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Book SynopsisMathematics for Elementary Teachers, 10th Edition establishes a solid math foundation for future teachers.Table of ContentsPreface xi 1 Introduction to Problem Solving 2 1.1 The Problem-Solving Process and Strategies 5 1.2 Three Additional Strategies 21 2 Sets, Whole Numbers, and Numeration 42 2.1 Sets as a Basis for Whole Numbers 45 2.2 Whole Numbers and Numeration 57 2.3 The Hindu–Arabic System 67 3 Whole Numbers: Operations and Properties 84 3.1 Addition and Subtraction 87 3.2 Multiplication and Division 101 3.3 Ordering and Exponents 116 4 Whole Number Computation—Mental, Electronic, and Written 128 4.1 Mental Math, Estimation, and Calculators 131 4.2 Written Algorithms for Whole-Number Operations 145 4.3 Algorithms in Other Bases 162 5 Number Theory 174 5.1 Primes, Composites, and Tests for Divisibility 177 5.2 Counting Factors, Greatest Common Factor, and Least Common Multiple 190 6 Fractions 206 6.1 The Set of Fractions 209 6.2 Fractions: Addition and Subtraction 223 6.3 Fractions: Multiplication and Division 233 7 Decimals, Ratio, Proportion, and Percent 250 7.1 Decimals 253 7.2 Operations with Decimals 262 7.3 Ratio and Proportion 274 7.4 Percent 283 8 Integers 302 8.1 Addition and Subtraction 305 8.2 Multiplication, Division, and Order 318 9 Rational Numbers, Real Numbers, and Algebra 338 9.1 The Rational Numbers 341 9.2 The Real Numbers 358 9.3 Relations and Functions 375 9.4 Functions and Their Graphs 391 10 Statistics 412 10.1 Statistical Problem Solving 415 10.2 Analyze and Interpret Data 440 10.3 Misleading Graphs and Statistics 460 11 Probability 484 11.1 Probability and Simple Experiments 487 11.2 Probability and Complex Experiments 502 11.3 Additional Counting Techniques 518 11.4 Simulation, Expected Value, Odds, and Conditional Probability 528 12 Geometric Shapes 546 12.1 Recognizing Geometric Shapes—Level 0 549 12.2 Analyzing Geometric Shapes—Level 1 564 12.3 Relationships between Geometric Shapes—Level 2 579 12.4 An Introduction to a Formal Approach to Geometry 589 12.5 Regular Polygons, Tessellations, and Circles 605 12.6 Describing Three-Dimensional Shapes 620 13 Measurement 644 13.1 Measurement with Nonstandard and Standard Units 647 13.2 Length and Area 665 13.3 Surface Area 686 13.4 Volume 696 14 Geometry Using Triangle Congruence and Similarity 716 14.1 Congruence of Triangles 719 14.2 Similarity of Triangles 729 14.3 Basic Euclidean Constructions 742 14.4 Additional Euclidean Constructions 755 14.5 Geometric Problem Solving Using Triangle Congruence and Similarity 765 15 Geometry Using Coordinates 780 15.1 Distance and Slope in the Coordinate Plane 783 15.2 Equations and Coordinates 795 15.3 Geometric Problem Solving Using Coordinates 807 16 Geometry Using Transformations 820 16.1 Transformations 823 16.2 Congruence and Similarity Using Transformations 846 16.3 Geometric Problem Solving Using Transformations 863 Epilogue: An Eclectic Approach to Geometry 877 Topic 1. Elementary Logic 881 Topic 2. Clock Arithmetic: A Mathematical System 891 Answers to Exercise/Problem Sets A and B, Chapter Reviews, Chapter Tests, and Topics Section A1 Index i1 Contents of Book Companion Web Site Resources for Technology Problems eManipulatives Spreadsheet Activities Geometer’s Sketchpad Activities Technology Tutorials Spreadsheets Geometer’s Sketchpad Programming in Logo Graphing Calculators Webmodules Algebraic Reasoning Children’s Literature Introduction to Graph Theory Additional Resources Guide to Problem Solving Problems for Writing/Discussion Research Articles Web Links Videos Book Overview Author Walk-Through Videos Children’s Videos

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Book SynopsisThis book provides practical guidance for statisticians, clinicians, and researchers involved in clinical trials in the biopharmaceutical industry, medical and public health organisations. Academics and students needing an introduction to handling missing data will also find this book invaluable. The authors describe how missing data can affect the outcome and credibility of a clinical trial, show by examples how a clinical team can work to prevent missing data, and present the reader with approaches to address missing data effectively. The book is illustrated throughout with realistic case studies and worked examples, and presents clear and concise guidelines to enable good planning for missing data. The authors show how to handle missing data in a way that is transparent and easy to understand for clinicians, regulators and patients. New developments are presented to improve the choice and implementation of primary and sensitivity analyses for missing datTrade Review“In summary, the book is a must-have tool for any biostatistician dealing with missing data. It is an excellent reference book for postgraduate students or researchers working in the area of missing data.” (Biometrical Journal, 1 June 2015) “This is an excellent addition to the field, dealing with problems arising from missing data or unobserved data in clinical trials. It successfully bridges the gap between clinicians and statisticians using relatively common language to build common ground.” (Doody’s, 9 January 2015)Table of ContentsPreface xv References xvii Acknowledgments xix Notation xxi Table of SAS code fragments xxv Contributors xxix 1 What’s the problem with missing data? 1Michael O’Kelly and Bohdana Ratitch 1.1 What do we mean by missing data? 2 1.1.1 Monotone and non-monotone missing data 3 1.1.2 Modeling missingness, modeling the missing value and ignorability 4 1.1.3 Types of missingness (MCAR, MAR and MNAR) 4 1.1.4 Missing data and study objectives 5 1.2 An illustration 6 1.3 Why can’t I use only the available primary endpoint data? 7 1.4 What’s the problem with using last observation carried forward? 9 1.5 Can we just assume that data are missing at random? 11 1.6 What can be done if data may be missing not at random? 14 1.7 Stress-testing study results for robustness to missing data 15 1.8 How the pattern of dropouts can bias the outcome 15 1.9 How do we formulate a strategy for missing data? 16 1.10 Description of example datasets 18 1.10.1 Example dataset in Parkinson’s disease treatment 18 1.10.2 Example dataset in insomnia treatment 23 1.10.3 Example dataset in mania treatment 28 Appendix 1.A: Formal definitions of MCAR, MAR and MNAR 33 References 34 2 The prevention of missing data 36Sara Hughes 2.1 Introduction 36 2.2 The impact of “too much” missing data 37 2.2.1 Example from human immunodeficiency virus 38 2.2.2 Example from acute coronary syndrome 38 2.2.3 Example from studies in pain 39 2.3 The role of the statistician in the prevention of missing data 39 2.3.1 Illustrative example from HIV 41 2.4 Methods for increasing subject retention 48 2.5 Improving understanding of reasons for subject withdrawal 49 Acknowledgments 49 Appendix 2.A: Example protocol text for missing data prevention 49 References 50 3 Regulatory guidance – a quick tour 53Michael O’Kelly 3.1 International conference on harmonization guideline: Statistical principles for clinical trials: E9 54 3.2 The US and EU regulatory documents 55 3.3 Key points in the regulatory documents on missing data 55 3.4 Regulatory guidance on particular statistical approaches 57 3.4.1 Available cases 57 3.4.2 Single imputation methods 57 3.4.3 Methods that generally assume MAR 59 3.4.4 Methods that are used assuming MNAR 60 3.5 Guidance about how to plan for missing data in a study 62 3.6 Differences in emphasis between the NRC report and EU guidance documents 63 3.6.1 The term “conservative” 63 3.6.2 Last observation carried forward 63 3.6.3 Post hoc analyses 63 3.6.4 Non-monotone or intermittently missing data 63 3.6.5 Assumptions should be readily interpretable 65 3.6.6 Study report 65 3.6.7 Training 65 3.7 Other technical points from the NRC report 66 3.7.1 Time-to-event analyses 66 3.7.2 Tipping point sensitivity analyses 66 3.8 Other US/EU/international guidance documents that refer to missing data 66 3.8.1 Committee for medicinal products for human use guideline on anti-cancer products, recommendations on survival analysis 66 3.8.2 US guidance on considerations when research supported by office of human research protections is discontinued 67 3.8.3 FDA guidance on data retention 67 3.9 And in practice? 67 References 69 4 A guide to planning for missing data 71Michael O’Kelly and Bohdana Ratitch 4.1 Introduction 72 4.1.1 Missing data may bias trial results or make them more difficult to generalize to subjects outside the trial 72 4.1.2 Credibility of trial results when there is missing data 74 4.1.3 Demand for better practice with regard to missing data 74 4.2 Planning for missing data 76 4.2.1 The case report form and non-statistical sections of the protocol 76 4.2.2 The statistical sections of the protocol and the statistical analysis plan 81 4.2.3 Using historic data to narrow the choice of primary analysis and sensitivity analyses 88 4.2.4 Key points in choosing an approach for missing data 108 4.3 Exploring and presenting missingness 113 4.4 Model checking 114 4.5 Interpreting model results when there is missing data 116 4.6 Sample size and missing data 117 Appendix 4.A: Sample protocol/SAP text for study in Parkinson’s disease 119 Appendix 4.B: A formal definition of a sensitivity parameter 125 References 126 5 Mixed models for repeated measures using categorical time effects (MMRM) 130Sonia Davis 5.1 Introduction 131 5.2 Specifying the mixed model for repeated measures 132 5.2.1 The mixed model 132 5.2.2 Covariance structures 135 5.2.3 Mixed model for repeated measures versus generalized estimating equations 139 5.2.4 Mixed model for repeated measures versus last observation carried forward 140 5.3 Understanding the data 141 5.3.1 Parkinson’s disease example 141 5.3.2 A second example showing the usefulness of plots: The CATIE study 144 5.4 Applying the mixed model for repeated measures 145 5.4.1 Specifying the model 146 5.4.2 Interpreting and presenting results 150 5.5 Additional mixed model for repeated measures topics 162 5.5.1 Treatment by subgroup and treatment by site interactions 162 5.5.2 Calculating the effect size 164 5.5.3 Another strategy to model baseline 166 5.6 Logistic regression mixed model for repeated measures using the generalized linear mixed model 168 5.6.1 The generalized linear mixed model 168 5.6.2 Specifying the model 170 5.6.3 Interpreting and presenting results 173 5.6.4 Other modeling options 181 References 182 Table of SAS Code Fragments 183 6 Multiple imputation 185Bohdana Ratitch 6.1 Introduction 185 6.1.1 How is multiple imputation different from single imputation? 186 6.1.2 How is multiple imputation different from maximum likelihood methods? 187 6.1.3 Multiple imputation’s assumptions about missingness mechanism 188 6.1.4 A general three-step process for multiple imputation and inference 189 6.1.5 Imputation versus analysis model 190 6.1.6 Note on notation use 192 6.2 Imputation phase 192 6.2.1 Missing patterns: Monotone and non-monotone 192 6.2.2 How do we get multiple imputations? 195 6.2.3 Imputation strategies: Sequential univariate versus joint multivariate 197 6.2.4 Overview of the imputation methods 199 6.2.5 Reusing the multiply-imputed dataset for different analyses or summary scales 212 6.3 Analysis phase: Analyzing multiple imputed datasets 213 6.4 Pooling phase: Combining results from multiple datasets 216 6.4.1 Combination rules 216 6.4.2 Pooling analyses of continuous outcomes 219 6.4.3 Pooling analyses of categorical outcomes 222 6.5 Required number of imputations 227 6.6 Some practical considerations 231 6.6.1 Choosing an imputation model 231 6.6.2 Multivariate normality 235 6.6.3 Rounding and restricting the range for the imputed values 238 6.6.4 Convergence of Markov chain Monte Carlo 240 6.7 Pre-specifying details of analysis with multiple imputation 244 Appendix 6.A: Additional methods for multiple imputation 245 References 251 Table of SAS Code Fragments 255 7 Analyses under missing-not-at-random assumptions 257Michael O’Kelly and Bohdana Ratitch 7.1 Introduction 258 7.2 Background to sensitivity analyses and pattern-mixture models 259 7.2.1 The purpose of a sensitivity analysis 259 7.2.2 Pattern-mixture models as sensitivity analyses 261 7.3 Two methods of implementing sensitivity analyses via pattern-mixture models 264 7.3.1 A sequential method of implementing pattern-mixture models with multiple imputation 264 7.3.2 Providing stress-testing “what ifs” using pattern-mixture models 266 7.3.3 Two implementations of pattern-mixture models for sensitivity analyses 267 7.3.4 Characteristics and limitations of the sequential modeling method of implementing pattern-mixture models 268 7.3.5 Pattern-mixture models implemented using the joint modeling method 271 7.3.6 Characteristics of the joint modeling method of implementing pattern-mixture models 279 7.3.7 Summary of differences between the joint modelling and sequential modeling methods 281 7.4 A “toolkit”: Implementing sensitivity analyses via SAS 284 7.4.1 Reminder: General approach using multiple imputation with regression 284 7.4.2 Sensitivity analyses assuming withdrawals have trajectory of control arm 288 7.4.3 Sensitivity analyses assuming withdrawals have distribution of control arm 292 7.4.4 Baseline-observation-carried-forward-like and last-observation-carried-forward-like analyses 297 7.4.5 The general principle of using selected subsets of observed data as the basis to implement “what if” stress tests 306 7.4.6 Using a mixture of “what ifs,” depending on reason for discontinuation 306 7.4.7 Assuming trajectory of withdrawals is worse by some 𝛿: Delta adjustment and tipping point analysis 308 7.5 Examples of realistic strategies and results for illustrative datasets of three indications 320 7.5.1 Parkinson’s disease 320 7.5.2 Insomnia 323 7.5.3 Mania 330 Appendix 7.A How one could implement the neighboring case missing value assumption using visit-by-visit multiple imputation 335 Appendix 7.B SAS code to model withdrawals from the experimental arm, using observed data from the control arm 336 Appendix 7.C SAS code to model early withdrawals from the experimental arm, using the last-observation-carried-forward-like values 342 Appendix 7.D SAS macro to impose delta adjustment on a responder variable in the mania dataset 345 Appendix 7.E SAS code to implement tipping point via exhaustive scenarios for withdrawals in the mania dataset 346 Appendix 7.F SAS code to perform sensitivity analyses for the Parkinson’s disease dataset 348 Appendix 7.G SAS code to perform sensitivity analyses for the insomnia dataset 351 Appendix 7.H SAS code to perform sensitivity analyses for the mania dataset 356 Appendix 7.I Selection models 358 Appendix 7.J Shared parameter models 362 References 365 Table of SAS Code Fragments 368 8 Doubly robust estimation 369Belinda Hernandez, Ilya Lipkovich and Michael O’Kelly 8.1 Introduction 370 8.2 Inverse probability weighted estimation 370 8.2.1 Inverse probability weighting estimators for estimating equations 372 8.2.2 Summary of inverse probability weighting advantages 373 8.2.3 Inverse probability weighting disadvantages 373 8.3 Doubly robust estimation 374 8.3.1 Doubly robust methods explained 375 8.3.2 Advantages of doubly robust methods 376 8.3.3 Limitations of doubly robust methods 376 8.4 Vansteelandt et al. method for doubly robust estimation 377 8.4.1 Theoretical justification for the Vansteelandt et al. method 378 8.4.2 Implementation of the Vansteelandt et al. method for doubly robust estimation 379 8.5 Implementing the Vansteelandt et al. method via SAS 383 8.5.1 Mania dataset 383 8.5.2 Insomnia dataset 390 Appendix 8.A How to implement Vansteelandt et al. method for mania dataset (binary response) 392 Appendix 8.B SAS code to calculate estimates from the bootstrapped datasets 400 Appendix 8.C How to implement Vansteelandt et al. method for insomnia dataset 401 References 408 Table of SAS Code Fragments 408 Bibliography 409 Index 423

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Book SynopsisPraise for the Third Edition Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference. MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and natural sciences. The Fourth Edition covers both standard and modern topics, including scaling and dimensional analysis; regular and singular perturbation; calculus of variations; Green's functions and integral equations; nonlinear wave propagation; and stability and bifurcation. The book provides extended coverage of mathematical biology, including biochemical kinetics, epidemiology, Table of ContentsPreface xiii 1. Dimensional Analysis and One-Dimensional Dynamics 1 1.1 Dimensional Analysis 2 1.2 Scaling 30 1.3 Differential Equations 46 2. Two-Dimensional Dynamical Systems 77 2.1 Phase Plane Phenomena 77 2.2 Linear Systems 87 2.3 Nonlinear Systems 94 2.4 Bifurcations 103 2.5 Reaction Kinetics112 2.6 Pathogens 126 3. Perturbation Methods and Asymptotic Expansions 149 3.1 Regular Perturbation 150 3.2 Singular Perturbation 170 3.3 Boundary Layer Analysis 179 3.4 Initial Layers 191 3.5 The WKB Approximation 202 3.6 Asymptotic Expansion of Integrals 210 4. Calculus of Variations 221 4.1 Variational Problems 221 4.2 Necessary Conditions for Extrema 227 4.3 The Simplest Problem 236 4.4 Generalizations 245 4.5 Hamilton's Principle 253 4.6 Isoperimetric Problems 266 5. Eigenvalue Problems, Integral Equations, and Green's Functions 275 5.1 Boundary-Value Problems 277 5.2 Sturm--Liouville Problems 284 5.3 Classical Fourier Series 310 5.4 Integral Equations 317 5.5 Green's Functions 339 5.6 Distributions 352 6. Partial Differential Equations 365 6.1 Basic Concepts 365 6.2 Conservation Laws 375 6.3 Equilibrium Equations 397 6.4 Eigenfunction Expansions 404 6.5 Integral Transforms 415 6.6 Stability of Solutions 435 6.7 Distributions 443 7. Wave Phenomena 457 7.1 Waves 457 7.2 Nonlinear Waves 470 7.3 Quasi-linear Equations 488 7.4 The Wave Equation 497 8. Mathematical Models of Continua 523 8.1 Kinematics and Mass Conservation 524 8.2 Momentum and Energy 534 8.3 Gas Dynamics 551 8.4 Fluid Motions in R3 560 9. Discrete Models 585 9.1 One-Dimensional Models. 586 9.2 Systems of Difference Equations 599 9.3 Stochastic Models 619 9.4 Probability-Based Models 636 Index 653

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Book SynopsisFourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processorsably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers. Class-tested at Dartmouth Provides the same solid background as classic texts in the field, but with an emphasis on digital and other contemporary applications to signal and image processing Modular coverage of material allows for topics to be covered by preference MATLAB files and Solutions Manual available to instructors Over 300 figures, 200 worked examples, aTrade Review“It is convenient that every chapter ends up with a summary of the results considered and a bunch of exercises. I hope the author's experience and expertise are what had inspired him to write this book of the present form, size and choice of matter. I also hope that it will find additional readers beyond the author's students.” (Zentralblatt MATH, 1 May 2015) Table of ContentsPREFACE xi CHAPTER 1 REVIEW OF PREREQUISITE MATHEMATICS 1 1.1 Common Notation 1 1.2 Vectors in Space 3 1.3 Complex Numbers 8 1.4 Matrix Algebra 11 1.5 Mappings and Functions 15 1.6 Sinusoidal Functions 20 1.7 Complex Exponentials 22 1.8 Geometric Series 24 1.9 Results from Calculus 25 1.10 Top 10 Ways to Avoid Errors in Calculations 33 Problems 33 CHAPTER 2 VECTOR SPACES 36 2.1 Signals and Vector Spaces 37 2.2 Finite-dimensional Vector Spaces 39 2.3 Infinite-dimensional Vector Spaces 64 2.4 ⋆ Operators 86 2.5 ⋆ Creating Orthonormal Bases–the Gram–Schmidt Process 94 2.6 Summary 99 Problems 101 CHAPTER 3 THE DISCRETE FOURIER TRANSFORM 109 3.1 Sinusoidal Sequences 109 3.2 The Discrete Fourier Transform 114 3.3 Interpreting the DFT 117 3.4 DFT Properties and Theorems 126 3.5 Fast Fourier Transform 152 3.6 ⋆ Discrete Cosine Transform 156 3.7 Summary 164 Problems 165 CHAPTER 4 THE FOURIER SERIES 177 4.1 Sinusoids and Physical Systems 178 4.2 Definitions and Interpretation 178 4.3 Convergence of the Fourier Series 187 4.4 Fourier Series Properties and Theorems 199 4.5 The Heat Equation 215 4.6 The Vibrating String 223 4.7 Antenna Arrays 227 4.8 Computing the Fourier Series 233 4.9 Discrete Time Fourier Transform 238 4.10 Summary 256 Problems 259 CHAPTER 5 THE FOURIER TRANSFORM 273 5.1 From Fourier Series to Fourier Transform 274 5.2 Basic Properties and Some Examples 276 5.3 Fourier Transform Theorems 281 5.4 Interpreting the Fourier Transform 299 5.5 Convolution 300 5.6 More about the Fourier Transform 310 5.7 Time–bandwidth Relationships 318 5.8 Computing the Fourier Transform 322 5.9 ⋆ Time–frequency Transforms 336 5.10 Summary 349 Problems 351 CHAPTER 6 GENERALIZED FUNCTIONS 367 6.1 Impulsive Signals and Spectra 367 6.2 The Delta Function in a Nutshell 371 6.3 Generalized Functions 382 6.4 Generalized Fourier Transform 404 6.5 Sampling Theory and Fourier Series 414 6.6 Unifying the Fourier Family 429 6.7 Summary 433 Problems 436 CHAPTER 7 COMPLEX FUNCTION THEORY 454 7.1 Complex Functions and Their Visualization 455 7.2 Differentiation 460 7.3 Analytic Functions 466 7.4 exp z and Functions Derived from It 470 7.5 Log z and Functions Derived from It 472 7.6 Summary 489 Problems 490 CHAPTER 8 COMPLEX INTEGRATION 494 8.1 Line Integrals in the Plane 494 8.2 The Basic Complex Integral: ∫↺ Γ zndz 497 8.3 Cauchy’s Integral Theorem 502 8.4 Cauchy’s Integral Formula 512 8.5 Laurent Series and Residues 520 8.6 Using Contour Integration to Calculate Integrals of Real Functions 531 8.7 Complex Integration and the Fourier Transform 543 8.8 Summary 556 Problems 557 CHAPTER 9 LAPLACE, Z, AND HILBERT TRANSFORMS 563 9.1 The Laplace Transform 563 9.2 The Z Transform 607 9.3 The Hilbert Transform 629 9.4 Summary 652 Problems 654 CHAPTER 10 FOURIER TRANSFORMS IN TWO AND THREE DIMENSIONS 669 10.1 Two-Dimensional Fourier Transform 669 10.2 Fourier Transforms in Polar Coordinates 684 10.3 Wave Propagation 696 10.4 Image Formation and Processing 709 10.5 Fourier Transform of a Lattice 722 10.6 Discrete Multidimensional Fourier Transforms 731 10.7 Summary 736 Problems 737 BIBLIOGRAPHY 743 INDEX 747

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Book SynopsisA road map for implementing quantitative financial models Financial Derivative and Energy Market Valuation brings the application of financial models to a higher level by helping readers capture the true behavior of energy markets and related financial derivatives. The book provides readers with a range of statistical and quantitative techniques and demonstrates how to implement the presented concepts and methods in Matlab. Featuring an unparalleled level of detail, this unique work provides the underlying theory and various advanced topics without requiring a prior high-level understanding of mathematics or finance. In addition to a self-contained treatment of applied topics such as modern Fourier-based analysis and affine transforms, Financial Derivative and Energy Market Valuation also: Provides the derivation, numerical implementation, and documentation of the corresponding Matlab for each topic Extends seminaTrade Review“The book is also ideal for graduate-level courses in quantitative finance, mathematical finance, and financial engineering.” (Zentralblatt MATH, 1 August 2013)Table of ContentsPreface vii 1 Financial Models 1 2 Jump Models 35 3 Options 65 4 Binomial Trees 105 5 Trinomial Trees 131 6 Finite Difference Methods 167 7 Kalman Filter 231 8 Futures and Forwards 245 9 Nonlinear and Non-Gaussian Kalman Filter 295 10 Short-Term Deviation/Long-Term Equilibrium Model 349 11 Futures and Forwards Options 359 12 Fourier Transform 397 13 Fundamentals of Characteristic Functions 459 14 Application of Characteristic Functions 467 15 Levy Processes 505 16 Fourier-Based Option Analysis 547 17 Fundamentals of Stochastic Finance 585 18 Affine Jump-Diffusion Processes 605 Index 645

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Book SynopsisA clear easy-to-read guide to presenting your message using statistical data Poor presentation of data is everywhere; basic principles are forgotten or ignored. As a result, audiences are presented with confusing tables and charts that do not make immediate sense. This book is intended to be read by all who present data in any form. The author, a chartered statistician who has run many courses on the subject of data presentation, presents numerous examples alongside an explanation of how improvements can be made and basic principles to adopt. He advocates following four key C' words in all messages: Clear, Concise, Correct and Consistent. Following the principles in the book will lead to clearer, simpler and easier to understand messages which can then be assimilated faster. Anyone from student to researcher, journalist to policy adviser, charity worker to government statistician, will benefit from reading this book. More importantly, it will also benefit the reTrade Review�Highly recommended to a very wide audience.� (Mathematical Association of America, 1 January 2015) �Presenting data is, of course, more than a good table or an informative graphic. The words that describe the data must also be correct, clear, concise and consistent, and the author devotes a chapter to ensuring that the expert�s hard work is not undone by commentary that is too technical or too laboured to be understood by non-expert audiences.� (The Royal Statistical Society, 1 February 2015) �This book must be mandatory to any data analyst and statistician, and indeed anyone who presents numeric data. The word "numeric" is important, as non-numeric data are not discussed in the book.� (ENBIS News, 10 December 2014) �The words that describe the data, and the messages it may have, must also be correct, clear, concise and consistent, and the author devotes a chapter to ensuring that the expert�s hard work is not undone by commentary that is too technical or too laboured to be understood by non-expert audiences.� (Significance, 1 February 2014) "The book is easy to read and can be consumed in a single train journey. It is also easy to look at and the illustrations and graphics occupy as much space as the text. The author has indeed put his money where his mouth is and the graphics both illustrate his points and makes them alone. The highlight for me was in the chapter on tables where the author reduces a table containing seven columns and five rows to a two by two table which beautifully makes the point when previously it had been lost in a forest of figures... This is an excellent book and I would recommend it as essential reading to anyone who is writing a thesis or dissertation, making a presentation or writing a paper. That�s all of us." (Occupational Medicine, 15th February 2016)Table of ContentsList of Tables vii List of Figures ix Introduction xiii Preface xvii Acknowledgements xix 1 Understanding number 1 1.1 Thousands separator 2 1.2 Decimal separator 3 1.3 Level of detail in comparisons 4 1.4 Justification of data 5 1.5 Basic rounding 7 1.6 Effective rounding 9 Notes 16 2 Tables 17 2.1 Position of totals in tables 17 2.2 What is a table? 19 2.3 Reference tables 19 2.4 Summary tables 22 2.5 How tables are read 24 2.6 Layout of data in tables 25 2.7 Capital letters for table titles and headings in tables 29 2.8 Use of bold typeface 30 2.9 Use of gridlines and other lines in tables 30 Notes 31 3 Charts (bar charts, histograms, pie charts, graphs) 33 3.1 How the user interprets charts 33 3.2 Written aims for charts 35 3.3 Scale definition and display 37 3.4 Difference between bar charts and histograms 49 3.5 Pie chart principles 51 3.6 Issues with pie charts 55 3.7 Graph principles 63 3.8 Issues with graphs 64 3.9 Pictogram principles 79 3.10 Comparative charts: Multiple pies, multiple bar charts, double scale graphs 82 3.11 Graphics 88 3.12 Three-dimensional charts 90 Notes 92 4 Numbers in text 93 4.1 Numbers written as text 94 4.1.1 Correct numbers 94 4.1.2 Clear numbers 94 4.1.3 Concise numbers 95 4.1.4 Consistent numbers 96 4.2 Ordering of data 97 4.3 Technical terms 98 4.4 Plain language 100 4.5 Emotive language 102 4.6 Key messages 103 Notes 105 5 Data presentation on the Internet 107 5.1 The early years 110 5.2 Statistics on CD-ROMs 113 5.3 Data on the Internet 116 5.4 Charts on the Internet 120 5.5 Text on the Internet 128 Notes 130

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Book SynopsisThis bookpresents material on both the analysis of the classical concepts of correlation and on the development of their robust versions, as well as discussing the related concepts of correlation matrices, partial correlation, canonical correlation, rank correlations, with the corresponding robust and non-robust estimation procedures.Trade Review“This book can be used as a reference book for professional statisticians and users of statistical methods. It can also serve as a graduate level textbook for a special topic course on robust correlation” Yuehua Wu, MathSciNet, Aug 2017Table of ContentsPreface xv Acknowledgements xvii About the Companion Website xix 1 Introduction 1 1.1 Historical Remarks 1 1.2 Ontological Remarks 4 1.2.1 Forms of data representation 5 1.2.2 Types of data statistics 5 1.2.3 Principal aims of statistical data analysis 6 1.2.4 Prior information about data distributions and related approaches to statistical data analysis 6 References 8 2 Classical Measures of Correlation 10 2.1 Preliminaries 10 2.2 Pearson’s Correlation Coefficient: Definitions and Interpretations 12 2.2.1 Introductory remarks 13 2.2.2 Correlation via regression 13 2.2.3 Correlation via the coefficient of determination 16 2.2.4 Correlation via the variances of the principal components 18 2.2.5 Correlation via the cosine of the angle between the variable vectors 21 2.2.6 Correlation via the ratio of two means 22 2.2.7 Pearson’s correlation coefficient between random events 23 2.3 Nonparametric Measures of Correlation 24 2.3.1 Introductory remarks 24 2.3.2 The quadrant correlation coefficient 26 2.3.3 The Spearman rank correlation coefficient 27 2.3.4 The Kendall 𝜏-rank correlation coefficient 28 2.3.5 Concluding remark 29 2.4 Informational Measures of Correlation 29 2.5 Summary 31 References 31 3 Robust Estimation of Location 33 3.1 Preliminaries 33 3.2 Huber’s Minimax Approach 35 3.2.1 Introductory remarks 35 3.2.2 Minimax variance M-estimates of location 36 3.2.3 Minimax bias M-estimates of location 43 3.2.4 L-estimates of location 44 3.2.5 R-estimates of location 45 3.2.6 The relations between M-, L- and R-estimates of location 46 3.2.7 Concluding remarks 47 3.3 Hampel’s Approach Based on Influence Functions 47 3.3.1 Introductory remarks 47 3.3.2 Sensitivity curve 47 3.3.3 Influence function and its properties 49 3.3.4 Local measures of robustness 51 3.3.5 B- and V-robustness 52 3.3.6 Global measure of robustness: the breakdown point 52 3.3.7 Redescending M-estimates 53 3.3.8 Concluding remark 56 3.4 Robust Estimation of Location: A Sequel 56 3.4.1 Introductory remarks 56 3.4.2 Huber’s minimax variance approach in distribution density models of a non-neighborhood nature 57 3.4.3 Robust estimation of location in distribution models with a bounded variance 62 3.4.4 On the robustness of robust solutions: stability of least informative distributions 69 3.4.5 Concluding remark 73 3.5 Stable Estimation 73 3.5.1 Introductory remarks 73 3.5.2 Variance sensitivity 74 3.5.3 Estimation stability 76 3.5.4 Robustness of stable estimates 78 3.5.5 Maximin stable redescending M-estimates 83 3.5.6 Concluding remarks 84 3.6 Robustness Versus Gaussianity 85 3.6.1 Introductory remarks 85 3.6.2 Derivations of the Gaussian distribution 87 3.6.3 Properties of the Gaussian distribution 92 3.6.4 Huber’s minimax approach and Gaussianity 100 3.6.5 Concluding remarks 101 3.7 Summary 102 References 102 4 Robust Estimation of Scale 107 4.1 Preliminaries 107 4.1.1 Introductory remarks 107 4.1.2 Estimation of scale in data analysis 108 4.1.3 Measures of scale defined by functionals 110 4.2 M- and L-Estimates of Scale 111 4.2.1 M-estimates of scale 111 4.2.2 L-estimates of scale 115 4.3 Huber Minimax Variance Estimates of Scale 116 4.3.1 Introductory remarks 116 4.3.2 The least informative distribution 117 4.3.3 Minimax variance M- and L-estimates of scale 118 4.4 Highly Efficient Robust Estimates of Scale 119 4.4.1 Introductory remarks 119 4.4.2 The median of absolute deviations and its properties 120 4.4.3 The quartile of pair-wise absolute differences Qn estimate and its properties 121 4.4.4 M-estimate approximations to the Qn estimate: MQ𝛼n, FQ𝛼n , and FQn estimates of scale 122 4.5 Monte Carlo Experiment 130 4.5.1 A remark on the Monte Carlo experiment accuracy 131 4.5.2 Monte Carlo experiment: distribution models 131 4.5.3 Monte Carlo experiment: estimates of scale 132 4.5.4 Monte Carlo experiment: characteristics of performance 133 4.5.5 Monte Carlo experiment: results 134 4.5.6 Monte Carlo experiment: discussion 136 4.5.7 Concluding remarks 138 4.6 Summary 138 References 139 5 Robust Estimation of Correlation Coefficients 140 5.1 Preliminaries 140 5.2 Main Groups of Robust Estimates of the Correlation Coefficient 141 5.2.1 Introductory remarks 141 5.2.2 Direct robust counterparts of Pearson’s correlation coefficient 142 5.2.3 Robust correlation via nonparametric measures of correlation 143 5.2.4 Robust correlation via robust regression 143 5.2.5 Robust correlation via robust principal component variances 145 5.2.6 Robust correlation via two-stage procedures 147 5.2.7 Concluding remarks 147 5.3 Asymptotic Properties of the Classical Estimates of the Correlation Coefficient 148 5.3.1 Pearson’s sample correlation coefficient 148 5.3.2 The maximum likelihood estimate of the correlation coefficient at the normal 149 5.4 Asymptotic Properties of Nonparametric Estimates of Correlation 151 5.4.1 Introductory remarks 151 5.4.2 The quadrant correlation coefficient 152 5.4.3 The Kendall rank correlation coefficient 152 5.4.4 The Spearman rank correlation coefficient 153 5.5 Bivariate Independent Component Distributions 155 5.5.1 Definition and properties 155 5.5.2 Independent component and Tukey gross-error distribution models 156 5.6 Robust Estimates of the Correlation Coefficient Based on Principal Component Variances 158 5.7 Robust Minimax Bias and Variance Estimates of the Correlation Coefficient 161 5.7.1 Introductory remarks 161 5.7.2 Minimax property 162 5.7.3 Concluding remarks 163 5.8 Robust Correlation via Highly Efficient Robust Estimates of Scale 163 5.8.1 Introductory remarks 163 5.8.2 Asymptotic bias and variance of generalized robust estimates of the correlation coefficient 164 5.8.3 Concluding remarks 165 5.9 Robust M-Estimates of the Correlation Coefficient in Independent Component Distribution Models 165 5.9.1 Introductory remarks 165 5.9.2 The maximum likelihood estimate of the correlation coefficient in independent component distribution models 165 5.9.3 M-estimates of the correlation coefficient 166 5.9.4 Asymptotic variance of M-estimators 166 5.9.5 Minimax variance M-estimates of the correlation coefficient 167 5.9.6 Concluding remarks 168 5.10 Monte Carlo Performance Evaluation 168 5.10.1 Introductory remarks 168 5.10.2 Monte Carlo experiment set-up 168 5.10.3 Discussion 171 5.10.4 Concluding remarks 173 5.11 Robust Stable Radical M-Estimate of the Correlation Coefficient of the Bivariate Normal Distribution 173 5.11.1 Introductory remarks 173 5.11.2 Asymptotic characteristics of the stable radical estimate of the correlation coefficient 174 5.11.3 Concluding remarks 175 5.12 Summary 176 References 176 6 Classical Measures of Multivariate Correlation 178 6.1 Preliminaries 178 6.2 Covariance Matrix and Correlation Matrix 179 6.3 Sample Mean Vector and Sample Covariance Matrix 181 6.4 Families of Multivariate Distributions 182 6.4.1 Construction of multivariate location-scatter models 182 6.4.2 Multivariate symmetrical distributions 183 6.4.3 Multivariate normal distribution 184 6.4.4 Multivariate elliptical distributions 184 6.4.5 Independent component model 186 6.4.6 Copula models 186 6.5 Asymptotic Behavior of Sample Covariance Matrix and Sample Correlation Matrix 187 6.6 First Uses of Covariance and Correlation Matrices 189 6.7 Working with the Covariance Matrix–Principal Component Analysis 191 6.7.1 Principal variables 191 6.7.2 Interpretation of principal components 193 6.7.3 Asymptotic behavior of the eigenvectors and eigenvalues 194 6.8 Working with Correlations–Canonical Correlation Analysis 195 6.8.1 Canonical variates and canonical correlations 195 6.8.2 Testing for independence between subvectors 197 6.9 Conditionally Uncorrelated Components 199 6.10 Summary 200 References 200 7 Robust Estimation of Scatter and Correlation Matrices 202 7.1 Preliminaries 202 7.2 Multivariate Location and Scatter Functionals 202 7.3 Influence Functions and Asymptotics 205 7.4 M-functionals for Location and Scatter 208 7.5 Breakdown Point 210 7.6 Use of Robust Scatter Matrices 211 7.6.1 Ellipticity assumption 211 7.6.2 Robust correlation matrices 212 7.6.3 Principal component analysis 212 7.6.4 Canonical correlation analysis 213 7.7 Further Uses of Location and Scatter Functionals 213 7.8 Summary 215 References 215 8 Nonparametric Measures of Multivariate Correlation 217 8.1 Preliminaries 217 8.2 Univariate Signs and Ranks 218 8.3 Marginal Signs and Ranks 220 8.4 Spatial Signs and Ranks 222 8.5 Affine Equivariant Signs and Ranks 226 8.6 Summary 229 References 230 9 Applications to Exploratory Data Analysis: Detection of Outliers 231 9.1 Preliminaries 231 9.2 State of the Art 232 9.2.1 Univariate boxplots 232 9.2.2 Bivariate boxplots 234 9.3 Problem Setting 237 9.4 A New Measure of Outlier Detection Performance 239 9.4.1 Introductory remarks 240 9.4.2 H-mean: motivation, definition and properties 241 9.5 Robust Versions of the Tukey Boxplot with Their Application to Detection of Outliers 243 9.5.1 Data generation and performance measure 243 9.5.2 Scale and shift contamination 243 9.5.3 Real-life data results 244 9.5.4 Concluding remarks 245 9.6 Robust Bivariate Boxplots and Their Performance Evaluation 245 9.6.1 Bivariate FQ-boxplot 245 9.6.2 Bivariate FQ-boxplot performance 247 9.6.3 Measuring the elliptical deviation from the convex hull 249 9.7 Summary 253 References 253 10 Applications to Time Series Analysis: Robust Spectrum Estimation 255 10.1 Preliminaries 255 10.2 Classical Estimation of a Power Spectrum 256 10.2.1 Introductory remarks 256 10.2.2 Classical nonparametric estimation of a power spectrum 258 10.2.3 Parametric estimation of a power spectrum 259 10.3 Robust Estimation of a Power Spectrum 259 10.3.1 Introductory remarks 259 10.3.2 Robust analogs of the discrete Fourier transform 261 10.3.3 Robust nonparametric estimation 262 10.3.4 Robust estimation of power spectrum through the Yule–Walker equations 263 10.3.5 Robust estimation through robust filtering 263 10.4 Performance Evaluation 264 10.4.1 Robustness of the median Fourier transform power spectra 264 10.4.2 Additive outlier contamination model 264 10.4.3 Disorder contamination model 264 10.4.4 Concluding remarks 270 10.5 Summary 270 References 270 11 Applications to Signal Processing: Robust Detection 272 11.1 Preliminaries 272 11.1.1 Classical approach to detection 272 11.1.2 Robust minimax approach to hypothesis testing 273 11.1.3 Asymptotically optimal robust detection of a weak signal 274 11.2 Robust Minimax Detection Based on a Distance Rule 275 11.2.1 Introductory remarks 275 11.2.2 Asymptotic robust minimax detection of a known constant signal with the 𝜌-distance rule 276 11.2.3 Detection performance in asymptotics and on finite samples 278 11.2.4 Concluding remarks 283 11.3 Robust Detection of a Weak Signal with Redescending M-Estimates 285 11.3.1 Introductory remarks 285 11.3.2 Detection error sensitivity and stability 287 11.3.3 Performance evaluation: a comparative study 289 11.3.4 Concluding remarks 291 11.4 A Unified Neyman–Pearson Detection of Weak Signals in a Fusion Model with Fading Channels and Non-Gaussian Noises 296 11.4.1 Introductory remarks 296 11.4.2 Problem setting—an asymptotic fusion rule 298 11.4.3 Asymptotic performance analysis 299 11.4.4 Numerical results 303 11.4.5 Concluding remarks 305 11.5 Summary 306 References 306 12 Final Remarks 308 12.1 Points of Growth: Open Problems in Multivariate Statistics 308 12.2 Points of Growth: Open Problems in Applications 309 Index 311

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Book SynopsisThis book introduces Software Quality Assurance (SQA) and provides an overview of standards used to implement SQA. It defines ways to assess the effectiveness of how one approaches software quality across key industry sectors such as telecommunications, transport, defense, and aerospace.Table of ContentsPreface xv Acknowledgments xxiii 1. Software Quality Fundamentals 1 1.1 Introduction 1 1.2 Defining Software Quality 2 1.3 Software Errors, Defects, and Failures 4 1.3.1 Problems with Defining Requirements 10 1.3.2 Maintaining Effective Communications Between Client and Developer 13 1.3.3 Deviations from Specifications 14 1.3.4 Architecture and Design Errors 15 1.3.5 Coding Errors 15 1.3.6 Non-Compliance with Current Processes/Procedures 16 1.3.7 Inadequate Reviews and Tests 17 1.3.8 Documentation Errors 17 1.4 Software Quality 19 1.5 Software Quality Assurance 20 1.6 Business Models and the Choice of Software Engineering Practices 22 1.6.1 Description of the Context 23 1.6.2 Anxiety and Fear 24 1.6.3 Choice of Software Practices 25 1.6.4 Business Model Descriptions 25 1.6.5 Description of Generic Situational Factors 26 1.6.6 Detailed Description of Each Business Model 27 1.7 Success Factors 32 1.8 Further Reading 33 1.9 Exercises 34 2. Quality Culture 35 2.1 Introduction 35 2.2 Cost of Quality 39 2.3 Quality Culture 49 2.4 The Five Dimensions of a Software Project 53 2.5 The Software Engineering Code of Ethics 56 2.5.1 Abridged Version: Preamble 58 2.5.2 The Example of the Code of Ethics of the Ordre des ingénieurs du Québec 60 2.5.3 Whistle Blowers 61 2.6 Success Factors 62 2.7 Further Reading 63 2.8 Exercises 63 3. Software Quality Requirements 66 3.1 Introduction 66 3.2 Software Quality Models 69 3.2.1 Initial Model Proposed by McCall 71 3.2.2 The First Standardized Model: IEEE 1061 73 3.2.3 Current Standardized Model: ISO 25000 Set of Standards 77 3.3 Definition of Software Quality Requirements 86 3.3.1 Specifying Quality Requirements: The Process 91 3.4 Requirement Traceability During the Software Life Cycle 95 3.5 Software Quality Requirements and the Software Quality Plan 95 3.6 Success Factors 96 3.7 Further Reading 97 3.8 Exercises 97 4. Software Engineering Standards and Models 101 4.1 Introduction 101 4.2 Standards, Cost of Quality, and Business Models 108 4.3 Main Standards for Quality Management 109 4.3.1 ISO 9000 Family 109 4.3.2 ISO/IEC 90003 Standard 115 4.4 ISO/IEC/IEEE 12207 Standard 117 4.4.1 Limitations of the ISO 12207 Standard 121 4.5 ISO/IEC/IEEE 15289 Standard for the Description of Information Elements 121 4.6 IEEE 730 Standard for SQA Processes 123 4.6.1 Activities and Tasks of SQA 125 4.7 Other Quality Models, Standards, References, and Processes 129 4.7.1 Process Maturity Models of the SEI 130 4.7.2 Software Maintenance Maturity Model (S 3m) 135 4.7.3 ITIL Framework and ISO/IEC 20000 138 4.7.4 CobiT Process 142 4.7.5 ISO/IEC 27000 Family of Standards for Information Security 143 4.7.6 ISO/IEC 29110 Standards and Guides for Very Small Entities 144 4.7.7 ISO/IEC 29110 Standards for VSEs Developing Systems 155 4.8 Specific Standards for an Application Domain 156 4.8.1 DO-178 and ED-12 Guidance for Airborne Systems 156 4.8.2 EN 50128 Standard for Railway Applications 159 4.8.3 ISO 13485 Standard for Medical Devices 161 4.9 Standards and the SQAP 163 4.10 Success Factors 165 4.11 Further Reading 165 4.12 Exercises 166 5. Reviews 167 5.1 Introduction 167 5.2 Personal Review and Desk-Check Review 172 5.2.1 Personal Review 172 5.2.2 Desk-Check Reviews 175 5.3 Standards and Models 179 5.3.1 ISO/IEC 20246 Software and Systems Engineering: Work Product Reviews 179 5.3.2 Capability Maturity Model Integration 180 5.3.3 The IEEE 1028 Standard 181 5.4 Walk-Through 184 5.4.1 Usefulness of a Walk-Through 184 5.4.2 Identification of Roles and Responsibilities 186 5.5 Inspection Review 187 5.6 Project Launch Reviews and Project Assessments 189 5.6.1 Project Launch Review 190 5.6.2 Project Retrospectives 192 5.7 Agile Meetings 197 5.8 Measures 199 5.9 Selecting the Type of Review 202 5.10 Reviews and Business Models 205 5.11 Software Quality Assurance Plan 205 5.12 Success Factors 206 5.13 Tools 208 5.14 Further Reading 208 5.15 Exercises 208 6. Software Audits 210 6.1 Introduction 210 6.2 Types of Audits 215 6.2.1 Internal Audit 215 6.2.2 Second-Party Audit 215 6.2.3 Third-Party Audit 217 6.3 Audit and Software Problem Resolution According to Iso/iec/ieee 12207 217 6.3.1 Project Assessment and Control Process 218 6.3.2 Decision Management Process 218 6.4 Audit According to the IEEE 1028 Standard 218 6.4.1 Roles and Responsibilities 220 6.4.2 IEEE 1028 Audit Clause 221 6.4.3 Audit Conducted According to IEEE 1028 222 6.5 Audit Process and the ISO 9001 Standard 225 6.5.1 Steps of a Software Audit 226 6.6 Audit According to the CMMI 230 6.6.1 SCAMPI Assessment Method 231 6.7 Corrective Actions 233 6.7.1 Corrective Actions Process 234 6.8 Audits for Very Small Entities 238 6.9 Audit and the SQA Plan 239 6.10 Presentation of an Audit Case Study 241 6.11 Success Factors 246 6.12 Further Reading 247 6.13 Exercises 247 7. Verification and Validation 249 7.1 Introduction 249 7.2 Benefits and Costs of V&V 255 7.2.1 V&V and the Business Models 257 7.3 V&V Standards and Process Models 257 7.3.1 IEEE 1012 V&V Standard 258 7.3.2 Integrity Levels 260 7.3.3 Recommended V&V Activities for Software Requirements 262 7.4 V&V According to ISO/IEC/IEEE 12207 263 7.4.1 Verification Process 265 7.4.2 Validation Process 265 7.5 V&V According to the CMMI Model 266 7.6 ISO/IEC 29110 and V&V 267 7.7 Independent V&V 268 7.7.1 IV&V Advantages with Regards to SQA 271 7.8 Traceability 271 7.8.1 Traceability Matrix 273 7.8.2 Implementing Traceability 276 7.9 Validation Phase of Software Development 277 7.9.1 Validation Plan 279 7.10 Tests 281 7.11 Checklists 282 7.11.1 How to Develop a Checklist 283 7.11.2 How to Use a Checklist 285 7.11.3 How to Improve and Manage a Checklist 286 7.12 V&V Techniques 287 7.12.1 Introduction to V&V Techniques 287 7.12.2 Some V&V Techniques 288 7.13 V&V Plan 289 7.14 Limitations of V&V 290 7.15 V&V in the SQA Plan 291 7.16 Success Factors 292 7.17 Further Reading 293 7.18 Exercises 293 8. Software Configuration Management 295 8.1 Introduction 295 8.2 Software Configuration Management 296 8.3 Benefits of Good Configuration Management 297 8.3.1 cm According to ISO 12207 298 8.3.2 cm According to IEEE 828 299 8.3.3 cm According to the cmMI 299 8.4 SCM Activities 301 8.4.1 Organizational Context of SCM 301 8.4.2 Developing a SCM Plan 302 8.4.3 Identification of CI to be Controlled 303 8.5 Baselines 309 8.6 Software Repository and Its Branches 311 8.6.1 A Simple Branching Strategy 315 8.6.2 A Typical Branching Strategy 316 8.7 Configuration Control 318 8.7.1 Requests, Evaluation, and Approval of Changes 319 8.7.2 Configuration Control Board 321 8.7.3 Request for Waivers 322 8.7.4 Change Management Policy 322 8.8 Configuration Status Accounting 323 8.8.1 Information Concerning the Status of ci 323 8.8.2 Configuration Item Status Reporting 325 8.9 Software Configuration Audit 325 8.9.1 Functional Configuration Audit 327 8.9.2 Physical Configuration Audit 327 8.9.3 Audits Performed During a Project 328 8.10 Implementing SCM in Very Small Entities with Iso/iec 29110 329 8.11 SCM and the SQAP 330 8.12 Success Factors 331 8.13 Further Reading 333 8.14 Exercises 333 9. Policies, Processes, and Procedures 335 9.1 Introduction 335 9.1.1 Standards, the Cost of Quality, and Business Models 341 9.2 Policies 341 9.3 Processes 345 9.4 Procedures 351 9.5 Organizational Standards 352 9.6 Graphical Representation of Processes and Procedures 353 9.6.1 Some Pitfalls to Avoid 356 9.6.2 Process Mapping 357 9.6.3 ETVX Process Notation 357 9.6.4 IDEF Notation 366 9.6.5 BPMN Notation 370 9.7 Process Notation of ISO/IEC 29110 376 9.8 Case Study 383 9.9 Personal Improvement Process 388 9.10 Policies, Processes, and Procedures in the SQA Plan 393 9.11 Success Factors 394 9.12 Further Reading 395 9.13 Exercises 396 10. Measurement 397 10.1 Introduction—the Importance of Measurement 397 10.1.1 Standards, the Cost of Quality, and Software Business Models 401 10.2 Software Measurement According to Iso/iec/ieee 12207 402 10.3 Measurement According to ISO 9001 403 10.4 The Practical Software and Systems Measurement Method 404 10.5 ISO/IEC/IEEE 15939 Standard 411 10.5.1 Measurement Process According to ISO 15939 412 10.5.2 Activities and Tasks of the Measurement Process 412 10.5.3 An Information Measurement Model of ISO 15939 412 10.6 Measurement According to the CMMI Model 418 10.7 Measurement in Very Small Entities 421 10.8 The Survey as a Measurement Tool 421 10.9 Implementing a Measurement Program 425 10.9.1 Step 1: Management Commitment Build-Up 426 10.9.2 Step 2: Staff Commitment Build-Up 427 10.9.3 Step 3: Selection of Key Processes to be Improved 427 10.9.4 Step 4: Identification of the Goals and Objectives Related to the Key Process 427 10.9.5 Step 5: Design of the Measurement Program 427 10.9.6 Step 6: Description of the Information System to Support Measurement 428 10.9.7 Step 7: Deployment of the Measurement Program 428 10.10 Practical Considerations 430 10.10.1 Some Pitfalls with Regards to Measurement 432 10.11 The Human Side of Measurement 435 10.11.1 Cost of Measurement 438 10.12 Measurement and the IEEE 730 SQAP 439 10.12.1 Software Process Measurement 440 10.12.2 Software Product Measurement 441 10.13 Success Factors 443 10.14 Further Reading 443 10.15 Exercises 444 11. Risk Management 445 11.1 Introduction 445 11.1.1 Risk, the Cost of Quality and Business Models 451 11.1.2 Costs and Benefits of Risk Management 453 11.2 Risk Management According to Standards and Models 454 11.2.1 Risk Management According to ISO 9001 454 11.2.2 Risk Management According to ISO/IEC/IEEE 12207 455 11.2.3 Risk Management According to ISO/IEC/IEEE 16085 456 11.2.4 Risk Management According to the CMMI Model 459 11.2.5 Risk Management According to PMBOK ® Guide 461 11.2.6 Risk Management According to ISO 29110 462 11.2.7 Risk Management and the SQA According to IEEE 730 465 11.3 Practical Considerations for Risk Management 466 11.3.1 Risk Evaluation Step 468 11.3.2 Risk Control Step 474 11.3.3 Lessons Learned Activity 477 11.4 Risk Management Roles 478 11.5 Measurement and Risk Management 479 11.6 Human Factors and Risk Management 483 11.7 Success Factors 485 11.8 Conclusion 486 11.9 Further Reading 487 11.10 Exercises 487 12. Supplier Management and Agreements 489 12.1 Introduction 489 12.2 Supplier Requirements of ISO 9001 490 12.3 Agreement Processes of ISO 12207 491 12.4 Supplier Agreement Management According to the CMMI 494 12.5 Managing Suppliers 496 12.6 Software Acquisition Life Cycle 497 12.7 Software Contract Types 499 12.7.1 Fixed Price Contract 501 12.7.2 Cost plus Percentage of Cost 502 12.7.3 Cost plus Fixed Fee 502 12.7.4 Risk Sharing 502 12.8 Software Contract Reviews 505 12.8.1 Two Reviews: Initial and Final 505 12.8.2 Initial Contract Review 506 12.8.3 Final Contract Review 509 12.9 Supplier and Acquirer Relationship and the SQAP 510 12.10 Success Factors 511 12.11 Further Reading 512 12.12 Exercises 512 13. Software Quality Assurance Plan 514 13.1 Introduction 514 13.2 SQA Planning 518 13.2.1 Purpose and Scope 518 13.2.2 Definitions and Acronyms 518 13.2.3 Reference Documents 519 13.2.4 SQAP Overview—Organization and Independence 520 13.2.5 SQAP Overview—Software Product Risk 524 13.2.6 SQAP Overview—Tools 525 13.2.7 SQAP Overview—Standards, Practices, and Conventions 525 13.2.8 SQAP Overview—Effort, Resources, and Schedule 526 13.2.9 Activities, Outcomes, and Tasks—Product Assurance 528 13.2.10 Activities, Outcomes, and Tasks—Process Assurance 529 13.2.11 Additional Considerations 531 13.2.12 SQA Records 536 13.3 Executing the SQAP 537 13.4 Conclusion 539 13.5 Further Reading 539 13.6 Exercises 540 Appendix 1. Software Engineering Code of Ethics and Professional Practice (Version 5.2) 541 Appendix 2. Incidents and Horror Stories Involving Software 549 Glossary – Abbreviations – Acronyms 555 References 576 Index 591

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Book SynopsisTable of ContentsForeword by A.G. MALLIARIS, Loyola University, Chicago xi Main Notations xiii Introduction xv PART I THE DETERMINISTIC ENVIRONMENT 1 Prior to the Yield Curve: Spot and Forward Rates 3 2 The Term Structure or Yield Curve 13 3 Spot Instruments 23 4 Equities and Stock Indexes 47 5 Forward Instruments 75 6 Swaps 91 7 Futures 119 PART II THE PROBABILISTIC ENVIRONMENT 8 The Basis of Stochastic Calculus 147 9 Other Financial Models: From ARMA to the GARCH Family 165 10 Option Pricing in General 175 11 Options on Specific Underlyings and Exotic Options 209 12 Volatility and Volatility Derivatives 237 13 Credit Derivatives 257 14 Market Performance and Risk Measures 275 15 Beyond the Gaussian Hypothesis: Potential Troubles with Derivatives Valuation 303 Bibliography 319 Index 323

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Book SynopsisMarkov Chains: Analytic and Monte Carlo Computations introduces the main notions related to Markov chains and provides explanations on how to characterize, simulate, and recognize them. Starting with basic notions, this book leads progressively to advanced and recent topics in the field, allowing the reader to master the main aspects of the classical theory. This book also features: Numerous exercises with solutions as well as extended case studies. A detailed and rigorous presentation of Markov chains with discrete time and state space. An appendix presenting probabilistic notions that are necessary to the reader, as well as giving more advanced measure-theoretic notions. Table of ContentsPreface ix List of Figures xi Nomenclature xiii Introduction xv 1 First steps 1 1.1 Preliminaries 1 1.2 First properties of Markov chains 2 1.2.1 Markov chains, finite-dimensional marginals, and laws 2 1.2.2 Transition matrix action and matrix notation 5 1.2.3 Random recursion and simulation 9 1.2.4 Recursion for the instantaneous laws, invariant laws 10 1.3 Natural duality: algebraic approach 11 1.3.1 Complex eigenvalues and spectrum 11 1.3.2 Doeblin condition and strong irreducibility 15 1.3.3 Finite state space Markov chains 17 1.4 Detailed examples 21 1.4.1 Random walk on a network 21 1.4.2 Gambler’s ruin 22 1.4.3 Branching process: evolution of a population 25 1.4.4 Ehrenfest’s Urn 27 1.4.5 Renewal process 33 1.4.6 Word search in a character chain 36 1.4.7 Product chain 38 Exercises 40 2 Past, present, and future 47 2.1 Markov property and its extensions 47 2.1.1 Past -field, filtration, and translation operators 47 2.1.2 Markov property 48 2.1.3 Stopping times and strong Markov property 50 2.2 Hitting times and distribution 51 2.2.1 Hitting times, induced chain, and hitting distribution 51 2.2.2 “One step forward” method, Dirichlet problem 53 2.3 Detailed examples 60 2.3.1 Gambler’s ruin 60 2.3.2 Unilateral hitting time for a random walk 64 2.3.3 Exit time from a box 67 2.3.4 Branching process 67 2.3.5 Word search 71 Exercises 73 3 Transience and recurrence 79 3.1 Sample paths and state space 79 3.1.1 Communication and closed irreducible classes 79 3.1.2 Transience and recurrence, recurrent class decomposition 80 3.1.3 Detailed examples 83 3.2 Invariant measures and recurrence 87 3.2.1 Invariant laws and measures 87 3.2.2 Canonical invariant measure 89 3.2.3 Positive recurrence, invariant law criterion 91 3.2.4 Detailed examples 93 3.3 Complements 97 3.3.1 Hitting times and superharmonic functions 97 3.3.2 Lyapunov functions 99 3.3.3 Time reversal, reversibility, and adjoint chain 105 3.3.4 Birth-and-death chains 108 Exercises 111 4 Long-time behavior 119 4.1 Path regeneration and convergence 119 4.1.1 Pointwise ergodic theorem, extensions 120 4.1.2 Central limit theorem for Markov chains 124 4.1.3 Detailed examples 126 4.2 Long-time behavior of the instantaneous laws 128 4.2.1 Period and aperiodic classes 128 4.2.2 Coupling of Markov chains and convergence in law 132 4.2.3 Detailed examples 139 4.3 Elements on the rate of convergence for laws 140 4.3.1 The Hilbert space framework 140 4.3.2 Dirichlet form, spectral gap, and exponential bounds 143 4.3.3 Spectral theory for reversible matrices 146 4.3.4 Continuous-time Markov chains 149 Exercises 150 5 Monte Carlo methods 155 5.1 Approximate solution of the Dirichlet problem 155 5.1.1 General principles 155 5.1.2 Heat equation in equilibrium 156 5.1.3 Heat equation out of equilibrium 158 5.1.4 Parabolic partial differential equations 159 5.2 Invariant law simulation 162 5.2.1 Monte Carlo methods and ergodic theorems 162 5.2.2 Metropolis algorithm, Gibbs law, and simulated annealing 163 5.2.3 Exact simulation and backward recursion 166 Appendix A Complements 171 A.1 Basic probabilistic notions 171 A.1.1 Discrete random variable, expectation, and generating function 171 A.1.2 Conditional probabilities and independence 175 A.2 Discrete measure convergence 177 A.2.1 Total variation norm and maximal coupling 177 A.2.2 Duality between measures and functions 180 A.2.3 Weak convergence of laws and convergence in law 182 A.3 Measure-theoretic framework 183 A.3.1 Probability spaces 183 A.3.2 Measurable spaces and functions: signed and nonnegative 185 A.3.3 Random variables, their laws, and expectations 186 A.3.4 Random sequences and Kolmogorov extension theorem 192 References 195 Solutions for the exercises 197 Index 229

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Book SynopsisNonlinear Parameter Optimization Using R John C.Trade Review"The book chapters are enriched by little anecdotes, and the reader obviously benefits from John C. Nash's experience of more than 30 years in the field of nonlinear optimization. This experience translates into many practical recommendations and tweaks. The book provides plenty of code examples and useful code snippets." (Biometrical Journal, 2016)Table of ContentsPreface xv 1 Optimization problem tasks and how they arise 1 1.1 The general optimization problem 1 1.2 Why the general problem is generally uninteresting 2 1.3 (Non-)Linearity 4 1.4 Objective function properties 4 1.4.1 Sums of squares 4 1.4.2 Minimax approximation 5 1.4.3 Problems with multiple minima 5 1.4.4 Objectives that can only be imprecisely computed 5 1.5 Constraint types 5 1.6 Solving sets of equations 6 1.7 Conditions for optimality 7 1.8 Other classifications 7 References 8 2 Optimization algorithms – an overview 9 2.1 Methods that use the gradient 9 2.2 Newton-like methods 12 2.3 The promise of Newton’s method 13 2.4 Caution: convergence versus termination 14 2.5 Difficulties with Newton’s method 14 2.6 Least squares: Gauss–Newton methods 15 2.7 Quasi-Newton or variable metric method 17 2.8 Conjugate gradient and related methods 18 2.9 Other gradient methods 19 2.10 Derivative-free methods 19 2.10.1 Numerical approximation of gradients 19 2.10.2 Approximate and descend 19 2.10.3 Heuristic search 20 2.11 Stochastic methods 20 2.12 Constraint-based methods – mathematical programming 21 References 22 3 Software structure and interfaces 25 3.1 Perspective 25 3.2 Issues of choice 26 3.3 Software issues 27 3.4 Specifying the objective and constraints to the optimizer 28 3.5 Communicating exogenous data to problem definition functions 28 3.5.1 Use of “global” data and variables 31 3.6 Masked (temporarily fixed) optimization parameters 32 3.7 Dealing with inadmissible results 33 3.8 Providing derivatives for functions 34 3.9 Derivative approximations when there are constraints 36 3.10 Scaling of parameters and function 36 3.11 Normal ending of computations 36 3.12 Termination tests – abnormal ending 37 3.13 Output to monitor progress of calculations 37 3.14 Output of the optimization results 38 3.15 Controls for the optimizer 38 3.16 Default control settings 39 3.17 Measuring performance 39 3.18 The optimization interface 39 References 40 4 One-parameter root-finding problems 41 4.1 Roots 41 4.2 Equations in one variable 42 4.3 Some examples 42 4.3.1 Exponentially speaking 42 4.3.2 A normal concern 44 4.3.3 Little Polly Nomial 46 4.3.4 A hypothequial question 49 4.4 Approaches to solving 1D root-finding problems 51 4.5 What can go wrong? 52 4.6 Being a smart user of root-finding programs 54 4.7 Conclusions and extensions 54 References 55 5 One-parameter minimization problems 56 5.1 The optimize() function 56 5.2 Using a root-finder 57 5.3 But where is the minimum? 58 5.4 Ideas for 1D minimizers 59 5.5 The line-search subproblem 61 References 62 6 Nonlinear least squares 63 6.1 nls() from package stats 63 6.1.1 A simple example 63 6.1.2 Regression versus least squares 65 6.2 A more difficult case 65 6.3 The structure of the nls() solution 72 6.4 Concerns with nls() 73 6.4.1 Small residuals 74 6.4.2 Robustness – “singular gradient” woes 75 6.4.3 Bounds with nls() 77 6.5 Some ancillary tools for nonlinear least squares 79 6.5.1 Starting values and self-starting problems 79 6.5.2 Converting model expressions to sum-of-squares functions 80 6.5.3 Help for nonlinear regression 80 6.6 Minimizing Rfunctions that compute sums of squares 81 6.7 Choosing an approach 82 6.8 Separable sums of squares problems 86 6.9 Strategies for nonlinear least squares 93 References 93 7 Nonlinear equations 95 7.1 Packages and methods for nonlinear equations 95 7.1.1 BB 96 7.1.2 nleqslv 96 7.1.3 Using nonlinear least squares 96 7.1.4 Using function minimization methods 96 7.2 A simple example to compare approaches 97 7.3 A statistical example 103 References 106 8 Function minimization tools in the base R system 108 8.1 optim() 108 8.2 nlm() 110 8.3 nlminb() 111 8.4 Using the base optimization tools 112 References 114 9 Add-in function minimization packages for R 115 9.1 Package optimx 115 9.1.1 Optimizers in optimx 116 9.1.2 Example use of optimx() 117 9.2 Some other function minimization packages 118 9.2.1 nloptr and nloptwrap 118 9.2.2 trust and trustOptim 119 9.3 Should we replace optim() routines? 121 References 122 10 Calculating and using derivatives 123 10.1 Why and how 123 10.2 Analytic derivatives – by hand 124 10.3 Analytic derivatives – tools 125 10.4 Examples of use of R tools for differentiation 125 10.5 Simple numerical derivatives 127 10.6 Improved numerical derivative approximations 128 10.6.1 The Richardson extrapolation 128 10.6.2 Complex-step derivative approximations 128 10.7 Strategy and tactics for derivatives 129 References 131 11 Bounds constraints 132 11.1 Single bound: use of a logarithmic transformation 132 11.2 Interval bounds: Use of a hyperbolic transformation 133 11.2.1 Example of the tanh transformation 134 11.2.2 A fly in the ointment 134 11.3 Setting the objective large when bounds are violated 135 11.4 An active set approach 136 11.5 Checking bounds 138 11.6 The importance of using bounds intelligently 138 11.6.1 Difficulties in applying bounds constraints 139 11.7 Post-solution information for bounded problems 139 Appendix 11.A Function transfinite 141 References 142 12 Using masks 143 12.1 An example 143 12.2 Specifying the objective 143 12.3 Masks for nonlinear least squares 147 12.4 Other approaches to masks 148 References 148 13 Handling general constraints 149 13.1 Equality constraints 149 13.1.1 Parameter elimination 151 13.1.2 Which parameter to eliminate? 153 13.1.3 Scaling and centering? 154 13.1.4 Nonlinear programming packages 154 13.1.5 Sequential application of an increasing penalty 156 13.2 Sumscale problems 158 13.2.1 Using a projection 162 13.3 Inequality constraints 163 13.4 A perspective on penalty function ideas 167 13.5 Assessment 167 References 168 14 Applications of mathematical programming 169 14.1 Statistical applications of math programming 169 14.2 R packages for math programming 170 14.3 Example problem: L1 regression 171 14.4 Example problem: minimax regression 177 14.5 Nonlinear quantile regression 179 14.6 Polynomial approximation 180 References 183 15 Global optimization and stochastic methods 185 15.1 Panorama of methods 185 15.2 R packages for global and stochastic optimization 186 15.3 An example problem 187 15.3.1 Method SANN from optim() 187 15.3.2 Package GenSA 188 15.3.3 Packages DEoptim and RcppDE 189 15.3.4 Package smco 191 15.3.5 Package soma 192 15.3.6 Package Rmalschains 193 15.3.7 Package rgenoud 193 15.3.8 Package GA 194 15.3.9 Package gaoptim 195 15.4 Multiple starting values 196 References 202 16 Scaling and reparameterization 203 16.1 Why scale or reparameterize? 203 16.2 Formalities of scaling and reparameterization 204 16.3 Hobbs’ weed infestation example 205 16.4 The KKT conditions and scaling 210 16.5 Reparameterization of the weeds problem 214 16.6 Scale change across the parameter space 214 16.7 Robustness of methods to starting points 215 16.7.1 Robustness of optimization techniques 218 16.7.2 Robustness of nonlinear least squares methods 220 16.8 Strategies for scaling 222 References 223 17 Finding the right solution 224 17.1 Particular requirements 224 17.1.1 A few integer parameters 225 17.2 Starting values for iterative methods 225 17.3 KKT conditions 226 17.3.1 Unconstrained problems 226 17.3.2 Constrained problems 227 17.4 Search tests 228 References 229 18 Tuning and terminating methods 230 18.1 Timing and profiling 230 18.1.1 rbenchmark 231 18.1.2 microbenchmark 231 18.1.3 Calibrating our timings 232 18.2 Profiling 234 18.2.1 Trying possible improvements 235 18.3 More speedups of R computations 238 18.3.1 Byte-code compiled functions 238 18.3.2 Avoiding loops 238 18.3.3 Package upgrades - an example 239 18.3.4 Specializing codes 241 18.4 External language compiled functions 242 18.4.1 Building an R function using Fortran 244 18.4.2 Summary of Rayleigh quotient timings 246 18.5 Deciding when we are finished 247 18.5.1 Tests for things gone wrong 248 References 249 19 Linking R to external optimization tools 250 19.1 Mechanisms to link R to external software 251 19.1.1 R functions to call external (sub)programs 251 19.1.2 File and system call methods 251 19.1.3 Thin client methods 252 19.2 Prepackaged links to external optimization tools 252 19.2.1 NEOS 252 19.2.2 Automatic Differentiation Model Builder (ADMB) 252 19.2.3 NLopt 253 19.2.4 BUGS and related tools 253 19.3 Strategy for using external tools 253 References 254 20 Differential equation models 255 20.1 The model 255 20.2 Background 256 20.3 The likelihood function 258 20.4 A first try at minimization 258 20.5 Attempts with optimx 259 20.6 Using nonlinear least squares 260 20.7 Commentary 261 Reference 262 21 Miscellaneous nonlinear estimation tools for R 263 21.1 Maximum likelihood 263 21.2 Generalized nonlinear models 266 21.3 Systems of equations 268 21.4 Additional nonlinear least squares tools 268 21.5 Nonnegative least squares 270 21.6 Noisy objective functions 273 21.7 Moving forward 274 References 275 Appendix A R packages used in examples 276 Index 279

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Book SynopsisA comprehensive and practical overview of the identification, conduct and analysis of optimal Phase II trial design.Table of ContentsContributors xv Foreword I xvii Elizabeth A. Eisenhauer Foreword II xix Roger A’Hern Preface xxi 1 Introduction 1 Sarah Brown, Julia Brown, Walter Gregory and Chris Twelves 1.1 The role of phase II trials in cancer 3 1.2 The importance of appropriate phase II trial design 5 1.3 Current use of phase II designs 6 1.4 Identifying appropriate phase II trial designs 7 1.5 Potential trial designs 9 1.6 Using the guidance to design your trial 10 2 Key Points for Consideration 12 Sarah Brown, Julia Brown, Marc Buyse, Walter Gregory, Mahesh Parmar and Chris Twelves 2.1 Stage 1 – Trial questions 14 2.1.1 Therapeutic considerations 14 2.1.2 Primary intention of trial 16 2.1.3 Number of experimental treatment arms 17 2.1.4 Primary outcome of interest 18 2.2 Stage 2 – Design components 18 2.2.1 Outcome measure and distribution 18 2.2.2 Randomisation 21 2.2.3 Design category 26 2.3 Stage 3 – Practicalities 33 2.3.1 Practical considerations 33 2.4 Summary 35 3 Designs for Single Experimental Therapies with a Single Arm 36 Sarah Brown 3.1 One-stage designs 36 3.1.1 Binary outcome measure 36 3.1.2 Continuous outcome measure 38 3.1.3 Multinomial outcome measure 39 3.1.4 Time-to-event outcome measure 40 3.1.5 Ratio of times to progression 40 3.2 Two-stage designs 41 3.2.1 Binary outcome measure 41 3.2.2 Continuous outcome measure 50 3.2.3 Multinomial outcome measure 50 3.2.4 Time-to-event outcome measure 53 3.2.5 Ratio of times to progression 54 3.3 Multi-stage designs 55 3.3.1 Binary outcome measure 55 3.3.2 Continuous outcome measure 59 3.3.3 Multinomial outcome measure 59 3.3.4 Time-to-event outcome measure 60 3.3.5 Ratio of times to progression 60 3.4 Continuous monitoring designs 60 3.4.1 Binary outcome measure 60 3.4.2 Continuous outcome measure 63 3.4.3 Multinomial outcome measure 63 3.4.4 Time-to-event outcome measure 63 3.4.5 Ratio of times to progression 64 3.5 Decision-theoretic designs 64 3.5.1 Binary outcome measure 64 3.5.2 Continuous outcome measure 65 3.5.3 Multinomial outcome measure 65 3.5.4 Time-to-event outcome measure 65 3.5.5 Ratio of times to progression 65 3.6 Three-outcome designs 65 3.6.1 Binary outcome measure 65 3.6.2 Continuous outcome measure 66 3.6.3 Multinomial outcome measure 66 3.6.4 Time-to-event outcome measure 66 3.6.5 Ratio of times to progression 67 3.7 Phase II/III designs 67 4 Designs for Single Experimental Therapies Including Randomisation 68 Sarah Brown 4.1 One-stage designs 68 4.1.1 Binary outcome measure 68 4.1.2 Continuous outcome measure 70 4.1.3 Multinomial outcome measure 70 4.1.4 Time-to-event outcome measure 70 4.1.5 Ratio of times to progression 72 4.2 Two-stage designs 72 4.2.1 Binary outcome measure 72 4.2.2 Continuous outcome measure 73 4.2.3 Multinomial outcome measure 74 4.2.4 Time-to-event outcome measure 75 4.2.5 Ratio of times to progression 75 4.3 Multi-stage designs 75 4.3.1 Binary outcome measure 75 4.3.2 Continuous outcome measure 75 4.3.3 Multinomial outcome measure 75 4.3.4 Time-to-event outcome measure 76 4.3.5 Ratio of times to progression 76 4.4 Continuous monitoring designs 76 4.4.1 Binary outcome measure 76 4.4.2 Continuous outcome measure 76 4.4.3 Multinomial outcome measure 76 4.4.4 Time-to-event outcome measure 76 4.4.5 Ratio of times to progression 76 4.5 Three-outcome designs 77 4.5.1 Binary outcome measure 77 4.5.2 Continuous outcome measure 77 4.5.3 Multinomial outcome measure 77 4.5.4 Time-to-event outcome measure 77 4.5.5 Ratio of times to progression 77 4.6 Phase II/III designs 77 4.6.1 Binary outcome measure 77 4.6.2 Continuous outcome measure 79 4.6.3 Multinomial outcome measure 80 4.6.4 Time-to-event outcome measure 81 4.6.5 Ratio of times to progression 81 4.7 Randomised discontinuation designs 82 4.7.1 Binary outcome measure 82 4.7.2 Continuous outcome measure 82 4.7.3 Multinomial outcome measure 82 4.7.4 Time-to-event outcome measure 82 4.7.5 Ratio of times to progression 82 5 Treatment Selection Designs 83 Sarah Brown 5.1 Including a control arm 84 5.1.1 One-stage designs 84 5.1.2 Two-stage designs 84 5.1.3 Multi-stage designs 88 5.1.4 Continuous monitoring designs 89 5.1.5 Decision-theoretic designs 89 5.1.6 Three-outcome designs 89 5.1.7 Phase II/III designs – same primary outcome measure at phase II and phase III 89 5.1.8 Phase II/III designs – different primary outcome measures at phase II and phase III 99 5.1.9 Randomised discontinuation designs 102 5.2 Not including a control arm 103 5.2.1 One-stage designs 103 5.2.2 Two-stage designs 106 5.2.3 Multi-stage designs 108 5.2.4 Continuous monitoring designs 109 5.2.5 Decision-theoretic designs 110 5.2.6 Three-outcome designs 110 5.2.7 Phase II/III designs – same primary outcome measure at phase II and phase III 110 5.2.8 Randomised discontinuation designs 111 6 Designs Incorporating Toxicity as a Primary Outcome 112 Sarah Brown 6.1 Including a control arm 112 6.1.1 One-stage designs 112 6.1.2 Two-stage designs 114 6.1.3 Multi-stage designs 115 6.2 Not including a control arm 117 6.2.1 One-stage designs 117 6.2.2 Two-stage designs 118 6.2.3 Multi-stage designs 122 6.2.4 Continuous monitoring designs 125 6.3 Toxicity alone 126 6.3.1 One stage 126 6.3.2 Continuous monitoring 127 6.4 Treatment selection based on activity and toxicity 128 6.4.1 Two-stage designs 128 6.4.2 Multi-stage designs 129 6.4.3 Continuous monitoring designs 129 7 Designs Evaluating Targeted Subgroups 131 Sarah Brown 7.1 One-stage designs 131 7.1.1 Binary outcome measure 131 7.2 Two-stage designs 132 7.2.1 Binary outcome measure 132 7.3 Multi-stage designs 135 7.3.1 Binary outcome measure 135 7.3.2 Time-to-event outcome measure 137 7.4 Continuous monitoring designs 138 7.4.1 Binary outcome measure 138 7.4.2 Time-to-event outcome measure 139 8 ‘Chemo-radio-sensitisation’ in Head and Neck Cancer 141 John Chester and Sarah Brown Stage 1 – Trial questions 141 Therapeutic considerations 141 Primary intention of trial 142 Number of experimental treatment arms 142 Primary outcome of interest 142 Stage 2 – Design components 142 Outcome measure and distribution 142 Randomisation 143 Design category 143 Possible designs 144 Stage 3 – Practicalities 146 Practical considerations for selecting between designs 146 Proposed trial design 148 Summary 150 9 Combination Chemotherapy in Second-line Treatment of Non-small Cell Lung Cancer 151 Ornella Belvedere and Sarah Brown Stage 1 – Trial questions 152 Therapeutic considerations 152 Primary intention of trial 152 Number of experimental treatment arms 152 Primary outcome of interest 152 Stage 2 – Design components 153 Outcome measure and distribution 153 Randomisation 153 Design category 153 Possible designs 154 Stage 3 – Practicalities 155 Practical considerations for selecting between designs 155 Proposed trial design 158 Summary 162 10 Selection by Biomarker in Prostate Cancer 163 Rick Kaplan and Sarah Brown Stage 1 – Trial questions 164 Therapeutic considerations 164 Primary intention of trial 164 Number of experimental treatment arms 164 Primary outcome of interest 164 Stage 2 – Design components 165 Outcome measure and distribution 165 Randomisation 165 Design category 166 Possible designs 167 Stage 3 – Practicalities 168 Practical considerations for selecting between designs 168 Proposed trial design 170 Summary 171 11 Dose Selection in Advanced Multiple Myeloma 174 Sarah Brown and Steve Schey Stage 1 – Trial questions 174 Therapeutic considerations 174 Primary intention of trial 175 Number of experimental arms 175 Primary outcome of interest 175 Stage 2 – Design components 176 Outcome measure and distribution 176 Randomisation 176 Design category 177 Possible designs 177 Stage 3 – Practicalities 178 Practical considerations for selecting between designs 178 Proposed trial design 181 Summary 182 12 Targeted Therapy for Advanced Colorectal Cancer 185 Matthew Seymour and Sarah Brown Stage 1 – Trial questions 185 Therapeutic considerations 185 Primary intention of trial 186 Number of experimental treatment arms 186 Primary outcome of interest 186 Stage 2 – Design components 187 Outcome measure and distribution 187 Randomisation 187 Design category 188 Possible designs 189 Stage 3 – Practicalities 190 Practical considerations for selecting between designs 190 Proposed trial design 191 Summary 194 13 Phase II Oncology Trials: Perspective from Industry 195 Anthony Rossini, Steven Green and William Mietlowski 13.1 Introduction 195 13.2 Commercial challenges, drivers and considerations 196 13.3 Selecting designs by strategy 197 13.3.1 Basic strategies addressed by phase II studies 198 13.3.2 Potential registration 198 13.3.3 Exploratory activity 203 13.3.4 Regimen selection 204 13.3.5 Phase II to Support Predicting Success in Phase IIi 206 13.3.6 Phase II safety trials 208 13.3.7 Prospective identification of target populations 209 13.4 Discussion 210 References 213 Index 227

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Book SynopsisUseful in analyzing electromagnetic problems in a variety of engineering circumstances, the finite element method is a powerful simulation technique. This book explains the method's processes and techniques in careful, meticulous prose. It covers not only essential finite element method theory, but also its latest developments and applications.Table of ContentsPreface xix Preface to the First Edition xxiii Preface to the Second Edition xxvii 1 Basic Electromagnetic Theory 1 1.1 Brief Review of Vector Analysis 2 1.2 Maxwell's Equations 4 1.3 Scalar and Vector Potentials 6 1.4 Wave Equations 7 1.5 Boundary Conditions 8 1.6 Radiation Conditions 11 1.7 Fields in an Infinite Homogeneous Medium 11 1.8 Huygen's Principle 13 1.9 Radar Cross Sections 14 1.10 Summary 15 2 Introduction to the Finite Element Method 17 2.1 Classical Methods for Boundary-Value Problems 17 2.2 Simple Example 21 2.3 Basic Steps of the Finite Element Method 27 2.4 Alternative Presentation of the Finite Element Formulation 34 2.5 Summary 36 3 One-Dimensional Finite Element Analysis 39 3.1 Boundary-Value Problem 39 3.2 Variational Formulation 40 3.3 Finite Element Analysis 42 3.4 Plane-Wave Reflection by a Metal-Backed Dielectric Slab 53 3.5 Scattering by a Smooth, Convex Impedance Cylinder 59 3.6 Higher-Order Elements 62 3.7 Summary 74 4 Two-Dimensional Finite Element Analysis 77 4.1 Boundary-Value Problem 77 4.2 Variational Formulation 79 4.3 Finite Element Analysis 81 4.4 Application to Electrostatic Problems 98 4.5 Application to Magnetostatic Problems 103 4.6 Application to Quasistatic Problems: Analysis of Multiconductor Transmission Lines 105 4.7 Application to Time-Harmonic Problems 109 4.8 Higher-Order Elements 128 4.9 Isoparametric Elements 144 4.10 Summary 149 5 Three-Dimensional Finite Element Analysis 151 5.1 Boundary-Value Problem 151 5.2 Variational Formulation 152 5.3 Finite Element Analysis 153 5.4 Higher-Order Elements 160 5.5 Isoparametric Elements 162 5.6 Application to Electrostatic Problems 168 5.7 Application to Magnetostatic Problems 169 5.8 Application to Time-Harmonic Field Problems 176 5.9 Summary 188 6 Variational Principles for Electromagnetics 191 6.1 Standard Variational Principle 192 6.2 Modified Variational Principle 197 6.3 Generalized Variational Principle 201 6.4 Variational Principle for Anisotrpic Medium 203 6.5 Variational Principle for Resistive Sheets 207 6.6 Concluding Remarks 209 7 Eigenvalue Problems: Waveguides and Cavities 211 7.1 Scalar Formulations for Closed Waveguides 212 7.2 Vector Formulations for Closed Waveguides 225 7.3 Open Waveguides 235 7.4 Three-Dimensional Cavities 238 7.5 Summary 239 8 Vector Finite Elements 243 8.1 Two-Dimensional Edge Elements 244 8.2 Waveguide Problem Revisited 256 8.3 Three-Dimensional Edge Elements 259 8.4 Cavity Problem Revisited 270 8.5 Waveguide Discontinuities 274 8.6 Higher-Order Interpolatory Vector Elements 278 8.7 Higher-Order Hierarchical Vector Elements 293 8.8 Computational Issues 305 8.9 Summary 309 9 Absorbing Boundary Conditions 315 9.1 Two-Dimensional Absorbing Boundary Conditions 316 9.2 Three-Dimensional Absorbing Boundary Conditions 323 9.3 Scattering Analysis Using Absorbing Boundary Conditons 328 9.4 Adaptive Absorbing Boundary Conditons 339 9.5 Fictitious Absorbers 348 9.6 Perfectly Matched Layers 350 9.7 Application of PML to Body-of-Revolutions Problems 368 9.8 Summary 371 10 Finite Element-Boundary Integral Methods 379 10.1 Scattering by Two-Dimensional Cavity-Backed Apertures 381 10.2 Scattering by Two-Dimensional Cylindrical Structures 399 10.3 Scattering by Three-Dimensional Cavity-Backed Apertures 411 10.4 Radiation by Microstrip Patch Antennas in a Cavity 425 10.5 Scattering by General Three-Dimensional Bodies 430 10.6 Solution of the Finite Element-Boundary Integral System 436 10.7 Symmetric Finite Element-Boundary Integral Formulations 447 10.8 Summary 462 11 Finite Element-Eigenfunction Expansion Methods 469 11.1 Waveguide Port Boundary Conditions 470 11.2 Open-Region Scattering 487 11.3 Coupled Basis Functions: The Unimoment Method 494 11.4 Finite Element-Extended Boundary Condition Method 502 11.5 Summary 509 12 Finite Element Analysis in the Time Domain 513 12.1 Finite Element Formulation and Temporal Excitation 514 12.2 Time-Domain Discretization 518 12.3 Stability Analysis 523 12.4 Modeling of Dispersive Media 529 12.5 Truncation via Absorbing Boundary Conditions 538 12.6 Truncation via Perfectly Matched Layers 541 12.7 Truncation via Boundary Integral Equations 551 12.8 Time-Domain Wqaveguide Port Boundary Conditions 562 12.9 Hybrid Field-Circuit Analysis 569 12.10 Dual-Field Domain Decomposition and Element-Level Methods 587 12.11 Discontinuous Galerkin Time-Domain Methods 605 12.12 Summary 625 13 Finite Element Analysis of Periodic Structures 637 13.1 Finite Element Formulation for a Unit Cell 638 13.2 Scattering by One-Dimensional Periodic Structures: Frequency-Domain Analysis 651 13.3 Scattering by One-Dimensional Periodic Structures: Time-Domain Analysis 656 13.4 Scattering by Two-Dimensional Periodic Structures: Frequency-Domain Analysis 663 13.5 Scattering by Two-Dimensonal Periodic Structures: Time-Domain Analysis 670 13.6 Analysis of Angular Periodic Strctures 678 13.7 Summary 682 14 Domain Decompsition for Large-Scale Analysis 687 14.1 Schwarz Methods 688 14.2 Schur Complement Methods 693 14.3 FETI-DP Method for Low-Frequency Problems 705 14.4 FETI-DP Method for High-Frequency Problems 728 14.5 Noncomformal FETI-DP Method Based on Cement Elements 743 14.6 Application of Second-Order Transmission Conditions 753 14.7 Summary 760 15 Solution of Finite Element Equations 767 15.1 Decomposition Methods 769 15.2 Conjugate Gradient Methods 778 15.3 Solution of Eigenvalue Problems 791 15.4 Fast Frequency-Sweep Computation 797 15.5 Summary 803 Appendix A: Basic Vector Identities and Integral Theorems 809 Appendix B: The Ritz Procedure for Complex-Valued Problems 813 Appendix C: Green's Functions 817 Appendix D: Singular Integral Evaluation 825 Appendix E: Some Special Functions 829 Index 837

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Book SynopsisThis Sixth Edition of Calculus continues the effort to promote courses in which understanding and computation reinforce each other. Calculus: Multivariable 6th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. For instructors wishing to emphasize the connection between calculus and other fields, the text includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics. In addition, new problems on the mathematics of sustainability and new case studies on calculus in medicine by David E. Sloane, MD have been added.Table of ContentsChapter 12: Functions of Several Variables Chapter 13: A Fundamental Tool: Vectors Chapter 14: Differentiating Functions of Several Variables Chapter 15: Optimization: Local and Global Extrema Chapter 16: Integrating Functions of Several Variables Chapter 17: Parameterization and Vector Fields Chapter 18: Line Integrals Chapter 19: Flux Integrals and Divergence Chapter 20: The Curl and Stokes’ Theorem Chapter 21: Parameters, Coordinates, and Integrals

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Book SynopsisAn introduction to state-of-the-art modeling and simulation approaches for social and economic determinants of population health New Horizons in Modeling and Simulation for Social Epidemiology and Public Health offers a comprehensive introduction to modeling and simulation that addresses the many complex research questions in social epidemiology and public health. This book highlights a variety of practical applications and illustrative examples with a focus on modeling and simulation approaches for the social and economic determinants of population health. The book contains classic case examples in agent-based modeling (ABM) as well as essential information on ABM applications to public health including for infectious disease modeling, obesity, and tobacco control. This book also surveys applications of microsimulation (MSM) including of tax-benefit policies to project impacts of the social determinants of health. Specifically, this book: Table of ContentsSection I: Introduction Chapter 1: A Primer on the Social Determinants of Health (Daniel Kim) Chapter 2: Rationale for New Modeling and Simulation Tools: Agent-Based Modeling and Microsimulation (Daniel Kim, Ross A. Hammond) Section II: Agent-Based Modeling Chapter 3: Overview of Current Concepts and Process for Agent-Based Modeling (Ross A. Hammond) Chapter 4: Agent-Based Modeling in the Social Sciences (Joseph T. Ornstein and Ross A. Hammond) Chapter 5: Agent-Based Modeling in Public Health (Joseph T. Ornstein and Ross A. Hammond) Chapter 6: Section Summary (Ross A. Hammond) Section III: Microsimulation Modeling Chapter 7: Concepts and Methods for Microsimulation Modeling in the Social Sciences (Gerlinde Verbist and Hilde Philips) Chapter 8: Empirical Evidence Using Microsimulation Models in the Social Sciences (Francesco Figari and Emanuela Lezzi) Chapter 9: Applications of Microsimulation Models to the Social Determinants of Health and Public Health: A Systematic Review of the Literature (Daniel Kim) Chapter 10: Section Summary (Daniel Kim) Section IV: Conclusions Chapter 11: Future Directions (Daniel Kim, Ross A. Hammond)

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Book SynopsisA self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models.Trade Review“This book seems suitable for an advanced undergraduate and/or introductory master's level course . . . Four appealing features of this book are its inclusion of an overview, a summary, exercises (with answers provided), and numerical examples for all sections.” (American Mathematical Society, 1 November 2015) “The book is suitable for graduate and postgraduate students and researchers. This book is highly recommended.” (Zentralblatt, 1 April 2015) “This is an excellent and comprehensive presentation of the use of matrices for linear models. The writing is very clear, and the layout is excellent. It would serve well either as a class text or as the foundation for individual personal study.” (International Statistical Review, 18 March 2014)Table of ContentsPreface xiii Acknowledgments xv Part I Basic Ideas about Matrices and Systems of Linear Equations 1 Section 1 What Matrices are and Some Basic Operations with Them 3 1.1 Introduction 3 1.2 What are Matrices and why are they Interesting to a Statistician? 3 1.3 Matrix Notation Addition and Multiplication 6 1.4 Summary 10 Exercises 10 Section 2 Determinants and Solving a System of Equations 14 2.1 Introduction 14 2.2 Definition of and Formulae for Expanding Determinants 14 2.3 Some Computational Tricks for the Evaluation of Determinants 16 2.4 Solution to Linear Equations Using Determinants 18 2.5 Gauss Elimination 22 2.6 Summary 27 Exercises 27 Section 3 The Inverse of a Matrix 30 3.1 Introduction 30 3.2 The Adjoint Method of Finding the Inverse of a Matrix 30 3.3 Using Elementary Row Operations 31 3.4 Using the Matrix Inverse to Solve a System of Equations 33 3.5 Partitioned Matrices and Their Inverses 34 3.6 Finding the Least Square Estimator 38 3.7 Summary 44 Exercises 44 Section 4 Special Matrices and Facts about Matrices that will be used in the Sequel 47 4.1 Introduction 47 4.2 Matrices of the Form aIn + bJn 47 4.3 Orthogonal Matrices 49 4.4 Direct Product of Matrices 52 4.5 An Important Property of Determinants 53 4.6 The Trace of a Matrix 56 4.7 Matrix Differentiation 57 4.8 The Least Square Estimator Again 62 4.9 Summary 62 Exercises 63 Section 5 Vector Spaces 66 5.1 Introduction 66 5.2 What is a Vector Space? 66 5.3 The Dimension of a Vector Space 68 5.4 Inner Product Spaces 70 5.5 Linear Transformations 73 5.6 Summary 76 Exercises 76 Section 6 The Rank of a Matrix and Solutions to Systems of Equations 79 6.1 Introduction 79 6.2 The Rank of a Matrix 79 6.3 Solving Systems of Equations with Coefficient Matrix of Less than Full Rank 84 6.4 Summary 87 Exercises 87 Part II Eigenvalues the Singular Value Decomposition and Principal Components 91 Section 7 Finding the Eigenvalues of a Matrix 93 7.1 Introduction 93 7.2 Eigenvalues and Eigenvectors of a Matrix 93 7.3 Nonnegative Definite Matrices 101 7.4 Summary 104 Exercises 105 Section 8 The Eigenvalues and Eigenvectors of Special Matrices 108 8.1 Introduction 108 8.2 Orthogonal Nonsingular and Idempotent Matrices 109 8.3 The Cayley–Hamilton Theorem 112 8.4 The Relationship between the Trace the Determinant and the Eigenvalues of a Matrix 114 8.5 The Eigenvalues and Eigenvectors of the Kronecker Product of Two Matrices 116 8.6 The Eigenvalues and the Eigenvectors of a Matrix of the Form aI + bJ 117 8.7 The Loewner Ordering 119 8.8 Summary 121 Exercises 122 Section 9 The Singular Value Decomposition (SVD) 124 9.1 Introduction 124 9.2 The Existence of the SVD 125 9.3 Uses and Examples of the SVD 127 9.4 Summary 134 Exercises 134 Section 10 Applications of the Singular Value Decomposition 137 10.1 Introduction 137 10.2 Reparameterization of a Non-full-Rank Model to a Full-Rank Model 137 10.3 Principal Components 141 10.4 The Multicollinearity Problem 143 10.5 Summary 144 Exercises 145 Section 11 Relative Eigenvalues and Generalizations of the Singular Value Decomposition 146 11.1 Introduction 146 11.2 Relative Eigenvalues and Eigenvectors 146 11.3 Generalizations of the Singular Value Decomposition:Overview 151 11.4 The First Generalization 152 11.5 The Second Generalization 157 11.6 Summary 160 Exercises 160 Part III Generalized Inverses 163 Section 12 Basic Ideas about Generalized Inverses 165 12.1 Introduction 165 12.2 What is a Generalized Inverse and how is One Obtained? 165 12.3 The Moore–Penrose Inverse 170 12.4 Summary 173 Exercises 173 Section 13 Characterizations of Generalized Inverses Using the Singular Value Decomposition 175 13.1 Introduction 175 13.2 Characterization of the Moore–Penrose Inverse 175 13.3 Generalized Inverses in Terms of the Moore–Penrose Inverse 177 13.4 Summary 185 Exercises 186 Section 14 Least Square and Minimum Norm Generalized Inverses 188 14.1 Introduction 188 14.2 Minimum Norm Generalized Inverses 189 14.3 Least Square Generalized Inverses 193 14.4 An Extension of Theorem 7.3 to Positive-Semi-definite Matrices 196 14.5 Summary 197 Exercises 197 Section 15 More Representations of Generalized Inverses 200 15.1 Introduction 200 15.2 Another Characterization of the Moore–Penrose Inverse 200 15.3 Still another Representation of the Generalized Inverse 204 15.4 The Generalized Inverse of a Partitioned Matrix 207 15.5 Summary 211 Exercises 211 Section 16 Least Square Estimators for Less than Full-Rank Models 213 16.1 Introduction 213 16.2 Some Preliminaries 213 16.3 Obtaining the LS Estimator 214 16.4 Summary 221 Exercises 221 Part IV Quadratic Forms and the Analysis of Variance 223 Section 17 Quadratic Forms and their Probability Distributions 225 17.1 Introduction 225 17.2 Examples of Quadratic Forms 225 17.3 The Chi-Square Distribution 228 17.4 When does the Quadratic Form of a Random Variable have a Chi-Square Distribution? 230 17.5 When are Two Quadratic Forms with the Chi-Square Distribution Independent? 231 17.6 Summary 234 Exercises 235 Section 18 Analysis of Variance: Regression Models and the One- and Two-Way Classification 237 18.1 Introduction 237 18.2 The Full-Rank General Linear Regression Model 237 18.3 Analysis of Variance: One-Way Classification 241 18.4 Analysis of Variance: Two-Way Classification 244 18.5 Summary 249 Exercises 249 Section 19 More ANOVA 253 19.1 Introduction 253 19.2 The Two-Way Classification with Interaction 254 19.3 The Two-Way Classification with One Factor Nested 258 19.4 Summary 262 Exercises 262 Section 20 The General Linear Hypothesis 264 20.1 Introduction 264 20.2 The Full-Rank Case 264 20.3 The Non-full-Rank Case 267 20.4 Contrasts 270 20.5 Summary 273 Exercises 273 Part V Matrix Optimization Problems 275 Section 21 Unconstrained Optimization Problems 277 21.1 Introduction 277 21.2 Unconstrained Optimization Problems 277 21.3 The Least Square Estimator Again 281 21.4 Summary 283 Exercises 283 Section 22 Constrained Minimization Problems with Linear Constraints 287 22.1 Introduction 287 22.2 An Overview of Lagrange Multipliers 287 22.3 Minimizing a Second-Degree Form with Respect to a Linear Constraint 293 22.4 The Constrained Least Square Estimator 295 22.5 Canonical Correlation 299 22.6 Summary 302 Exercises 302 Section 23 The Gauss–Markov Theorem 304 23.1 Introduction 304 23.2 The Gauss–Markov Theorem and the Least Square Estimator 304 23.3 The Modified Gauss–Markov Theorem and the Linear Bayes Estimator 306 23.4 Summary 311 Exercises 311 Section 24 Ridge Regression-Type Estimators 314 24.1 Introduction 314 24.2 Minimizing a Second-Degree Form with Respect to a Quadratic Constraint 314 24.3 The Generalized Ridge Regression Estimators 315 24.4 The Mean Square Error of the Generalized Ridge Estimator without Averaging over the Prior Distribution 317 24.5 The Mean Square Error Averaging over the Prior Distribution 321 24.6 Summary 321 Exercises 321 Answers to Selected Exercises 324 References 366 Index 368

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Book SynopsisProviding an explanation of the fundamentals, methods, and applications of chemometrics, this title acts as a practical guide to multivariate data analysis techniques. It explains the methods used in Chemometrics and teaches the reader to perform all relevant calculations. It presents the basic chemometric methods as worksheet functions in Excel.Trade Review“The book is for sure very interesting and very well written, and it covers all the major topics of chemometrics.” (Journal of Chemometrics, 14 July 2015) Table of ContentsPreface xvii PART I INTRODUCTION 1 1 What is Chemometrics? 3 1.1 Subject of Chemometrics, 3 1.2 Historical Digression, 5 2 What the Book Is About? 8 2.1 Useful Hints, 8 2.2 Book Syllabus, 9 2.3 Notations, 10 3 Installation of Chemometrics Add-In 11 3.1 Installation, 11 3.2 General Information, 14 4 Further Reading on Chemometrics 15 4.1 Books, 15 4.1.1 The Basics, 15 4.1.2 Chemometrics, 16 4.1.3 Supplements, 16 4.2 The Internet, 17 4.2.1 Tutorials, 17 4.3 Journals, 17 4.3.1 Chemometrics, 17 4.3.2 Analytical, 18 4.3.3 Mathematical, 18 4.4 Software, 18 4.4.1 Specialized Packages, 18 4.4.2 General Statistic Packages, 19 4.4.3 Free Ware, 19 PART II THE BASICS 21 5 Matrices and Vectors 23 5.1 The Basics, 23 5.1.1 Matrix, 23 5.1.2 Simple Matrix Operations, 24 5.1.3 Matrices Multiplication, 25 5.1.4 Square Matrix, 26 5.1.5 Trace and Determinant, 27 5.1.6 Vectors, 28 5.1.7 Simple Vector Operations, 29 5.1.8 Vector Products, 29 5.1.9 Vector Norm, 30 5.1.10 Angle Between Vectors, 30 5.1.11 Vector Representation of a Matrix, 30 5.1.12 Linearly Dependent Vectors, 31 5.1.13 Matrix Rank, 31 5.1.14 Inverse Matrix, 31 5.1.15 Pseudoinverse, 32 5.1.16 Matrix–Vector Product, 33 5.2 Advanced Information, 33 5.2.1 Systems of Linear Equations, 33 5.2.2 Bilinear and Quadratic Forms, 34 5.2.3 Positive Definite Matrix, 34 5.2.4 Cholesky Decomposition, 34 5.2.5 Polar Decomposition, 34 5.2.6 Eigenvalues and Eigenvectors, 35 5.2.7 Eigenvalues, 35 5.2.8 Eigenvectors, 35 5.2.9 Equivalence and Similarity, 36 5.2.10 Diagonalization, 37 5.2.11 Singular Value Decomposition (SVD), 37 5.2.12 Vector Space, 38 5.2.13 Space Basis, 39 5.2.14 Geometric Interpretation, 39 5.2.15 Nonuniqueness of Basis, 39 5.2.16 Subspace, 40 5.2.17 Projection, 40 6 Statistics 42 6.1 The Basics, 42 6.1.1 Probability, 42 6.1.2 Random Value, 43 6.1.3 Distribution Function, 43 6.1.4 Mathematical Expectation, 44 6.1.5 Variance and Standard Deviation, 44 6.1.6 Moments, 44 6.1.7 Quantiles, 45 6.1.8 Multivariate Distributions, 45 6.1.9 Covariance and Correlation, 45 6.1.10 Function, 46 6.1.11 Standardization, 46 6.2 Main Distributions, 46 6.2.1 Binomial Distribution, 46 6.2.2 Uniform Distribution, 47 6.2.3 Normal Distribution, 48 6.2.4 Chi-Squared Distribution, 50 6.2.5 Student’s Distribution, 52 6.2.6 F-Distribution, 53 6.2.7 Multivariate Normal Distribution, 54 6.2.8 Pseudorandom Numbers, 55 6.3 Parameter Estimation, 56 6.3.1 Sample, 56 6.3.2 Outliers and Extremes, 56 6.3.3 Statistical Population, 56 6.3.4 Statistics, 57 6.3.5 Sample Mean and Variance, 57 6.3.6 Sample Covariance and Correlation, 58 6.3.7 Order Statistics, 59 6.3.8 Empirical Distribution and Histogram, 60 6.3.9 Method of Moments, 61 6.3.10 The Maximum Likelihood Method, 62 6.4 Properties of the Estimators, 62 6.4.1 Consistency, 62 6.4.2 Bias, 63 6.4.3 Effectiveness, 63 6.4.4 Robustness, 63 6.4.5 Normal Sample, 64 6.5 Confidence Estimation, 64 6.5.1 Confidence Region, 64 6.5.2 Confidence Interval, 65 6.5.3 Example of a Confidence Interval, 65 6.5.4 Confidence Intervals for the Normal Distribution, 65 6.6 Hypothesis Testing, 66 6.6.1 Hypothesis, 66 6.6.2 Hypothesis Testing, 66 6.6.3 Type I and Type II Errors, 67 6.6.4 Example, 67 6.6.5 Pearson’s Chi-Squared Test, 67 6.6.6 F-Test, 69 6.7 Regression, 70 6.7.1 Simple Regression, 70 6.7.2 The Least Squares Method, 71 6.7.3 Multiple Regression, 72 Conclusion, 73 7 Matrix Calculations in Excel 74 7.1 Basic Information, 74 7.1.1 Region and Language, 74 7.1.2 Workbook, Worksheet, and Cell, 76 7.1.3 Addressing, 77 7.1.4 Range, 78 7.1.5 Simple Calculations, 78 7.1.6 Functions, 78 7.1.7 Important Functions, 81 7.1.8 Errors in Formulas, 85 7.1.9 Formula Dragging, 86 7.1.10 Create a Chart, 87 7.2 Matrix Operations, 88 7.2.1 Array Formulas, 88 7.2.2 Creating and Editing an Array Formula, 90 7.2.3 Simplest Matrix Operations, 91 7.2.4 Access to the Part of a Matrix, 91 7.2.5 Unary Operations, 93 7.2.6 Binary Operations, 95 7.2.7 Regression, 95 7.2.8 Critical Bug in Excel 2003, 99 7.2.9 Virtual Array, 99 7.3 Extension of Excel Possibilities, 100 7.3.1 VBA Programming, 100 7.3.2 Example, 101 7.3.3 Macro Example, 103 7.3.4 User-Defined Function Example, 104 7.3.5 Add-Ins, 105 7.3.6 Add-In Installation, 106 Conclusion, 107 8 Projection Methods in Excel 108 8.1 Projection Methods, 108 8.1.1 Concept and Notation, 108 8.1.2 PCA, 109 8.1.3 PLS, 110 8.1.4 Data Preprocessing, 111 8.1.5 Didactic Example, 112 8.2 Application of Chemometrics Add-In, 113 8.2.1 Installation, 113 8.2.2 General, 113 8.3 PCA, 114 8.3.1 ScoresPCA, 114 8.3.2 LoadingsPCA, 114 8.4 PLS, 116 8.4.1 ScoresPLS, 116 8.4.2 UScoresPLS, 117 8.4.3 LoadingsPLS, 118 8.4.4 WLoadingsPLS, 119 8.4.5 QLoadingsPLS, 120 8.5 PLS2, 121 8.5.1 ScoresPLS2, 121 8.5.2 UScoresPLS2, 122 8.5.3 LoadingsPLS2, 124 8.5.4 WLoadingsPLS2, 125 8.5.5 QLoadingsPLS2, 126 8.6 Additional Functions, 127 8.6.1 MIdent, 127 8.6.2 MIdentD2, 127 8.6.3 MCutRows, 129 8.6.4 MTrace, 129 Conclusion, 130 PART IIICHEMOMETRICS 131 9 Principal Component Analysis (PCA) 133 9.1 The Basics, 133 9.1.1 Data, 133 9.1.2 Intuitive Approach, 134 9.1.3 Dimensionality Reduction, 136 9.2 Principal Component Analysis, 136 9.2.1 Formal Specifications, 136 9.2.2 Algorithm, 137 9.2.3 PCA and SVD, 137 9.2.4 Scores, 138 9.2.5 Loadings, 139 9.2.6 Data of Special Kind, 140 9.2.7 Errors, 140 9.2.8 Validation, 143 9.2.9 Decomposition “Quality”, 143 9.2.10 Number of Principal Components, 144 9.2.11 The Ambiguity of PCA, 145 9.2.12 Data Preprocessing, 146 9.2.13 Leverage and Deviation, 146 9.3 People and Countries, 146 9.3.1 Example, 146 9.3.2 Data, 147 9.3.3 Data Exploration, 147 9.3.4 Data Pretreatment, 148 9.3.5 Scores and Loadings Calculation, 149 9.3.6 Scores Plots, 151 9.3.7 Loadings Plot, 152 9.3.8 Analysis of Residuals, 153 Conclusion, 153 10 Calibration 156 10.1 The Basics, 156 10.1.1 Problem Statement, 156 10.1.2 Linear and Nonlinear Calibration, 157 10.1.3 Calibration and Validation, 158 10.1.4 Calibration “Quality”, 160 10.1.5 Uncertainty, Precision, and Accuracy, 162 10.1.6 Underfitting and Overfitting, 163 10.1.7 Multicollinearity, 164 10.1.8 Data Preprocessing, 166 10.2 Simulated Data, 166 10.2.1 The Principle of Linearity, 166 10.2.2 “Pure” Spectra, 166 10.2.3 “Standard” Samples, 166 10.2.4 X Data Creation, 167 10.2.5 Data Centering, 168 10.2.6 Data Overview, 168 10.3 Classic Calibration, 169 10.3.1 Univariate (Single Channel) Calibration, 169 10.3.2 The Vierordt Method, 172 10.3.3 Indirect Calibration, 174 10.4 Inverse Calibration, 176 10.4.1 Multiple Linear Calibration, 177 10.4.2 Stepwise Calibration, 178 10.5 Latent Variables Calibration, 180 10.5.1 Projection Methods, 180 10.5.2 Latent Variables Regression, 184 10.5.3 Implementation of Latent Variable Calibration, 185 10.5.4 Principal Component Regression (PCR), 186 10.5.5 Projection on the Latent Structures-1 (PLS1), 188 10.5.6 Projection on the Latent Structures-2 (PLS2), 191 10.6 Methods Comparison, 193 Conclusion, 197 11 Classification 198 11.1 The Basics, 198 11.1.1 Problem Statement, 198 11.1.2 Types of Classes, 199 11.1.3 Hypothesis Testing, 199 11.1.4 Errors in Classification, 200 11.1.5 One-Class Classification, 200 11.1.6 Training and Validation, 201 11.1.7 Supervised and Unsupervised Training, 201 11.1.8 The Curse of Dimensionality, 201 11.1.9 Data Preprocessing, 201 11.2 Data, 202 11.2.1 Example, 202 11.2.2 Data Subsets, 203 11.2.3 Workbook Iris.xls, 204 11.2.4 Principal Component Analysis, 205 11.3 Supervised Classification, 205 11.3.1 Linear Discriminant Analysis (LDA), 205 11.3.2 Quadratic Discriminant Analysis (QDA), 210 11.3.3 PLS Discriminant Analysis (PLSDA), 214 11.3.4 SIMCA, 217 11.3.5 k-Nearest Neighbors (kNN), 223 11.4 Unsupervised Classification, 225 11.4.1 PCA Again (Revisited), 225 11.4.2 Clustering by K-Means, 225 Conclusion, 229 12 Multivariate Curve Resolution 230 12.1 The Basics, 230 12.1.1 Problem Statement, 230 12.1.2 Solution Ambiguity, 232 12.1.3 Solvability Conditions, 234 12.1.4 Two Types of Data, 235 12.1.5 Known Spectrum or Profile, 236 12.1.6 Principal Component Analysis (PCA), 236 12.1.7 PCA and MCR, 237 12.2 Simulated Data, 237 12.2.1 Example, 237 12.2.2 Data, 238 12.2.3 PCA, 238 12.2.4 The HELP Plot, 240 12.3 Factor Analysis, 241 12.3.1 Procrustes Analysis, 241 12.3.2 Evolving Factor Analysis (EFA), 244 12.3.3 Windows Factor Analysis (WFA), 246 12.4 Iterative Methods, 249 12.4.1 Iterative Target Transform Factor Analysis (ITTFA), 249 12.4.2 Alternating Least Squares (ALS), 250 Conclusion, 252 PART IV SUPPLEMENTS 255 13 Extension Of Chemometrics Add-In 257 13.1 Using Virtual Arrays, 257 13.1.1 Simulated Data, 257 13.1.2 Virtual Array, 259 13.1.3 Data Preprocessing, 259 13.1.4 Decomposition, 260 13.1.5 Residuals Calculation, 260 13.1.6 Eigenvalues Calculation, 262 13.1.7 Orthogonal Distances Calculation, 263 13.1.8 Leverages Calculation, 264 13.2 Using VBA Programming, 265 13.2.1 VBA Advantages, 265 13.2.2 Virtualization of Real Arrays, 265 13.2.3 Data Preprocessing, 266 13.2.4 Residuals Calculation, 267 13.2.5 Eigenvalues Calculation, 268 13.2.6 Orthogonal Distances Calculation, 269 13.2.7 Leverages Calculation, 270 Conclusion, 271 14 Kinetic Modeling of Spectral Data 272 14.1 The “Grey” Modeling Method, 272 14.1.1 Problem Statement, 272 14.1.2 Example, 274 14.1.3 Data, 274 14.1.4 Soft Method of Alternating Least Squares (Soft-ALS), 275 14.1.5 Hard Method of Alternating Least Squares (Hard-ALS), 277 14.1.6 Using Solver Add-In, 279 Conclusions, 282 15 MATLAB®: Beginner’s Guide 283 15.1 The Basics, 283 15.1.1 Workspace, 283 15.1.2 Basic Calculations, 285 15.1.3 Echo, 285 15.1.4 Workspace Saving: MAT-Files, 286 15.1.5 Diary, 286 15.1.6 Help, 287 15.2 Matrices, 287 15.2.1 Scalars, Vectors, and Matrices, 287 15.2.2 Accessing Matrix Elements, 289 15.2.3 Basic Matrix Operations, 289 15.2.4 Special Matrices, 290 15.2.5 Matrix Calculations, 292 15.3 Integrating Excel and MATLAB®, 294 15.3.1 Configuring Excel, 294 15.3.2 Data Exchange, 294 15.4 Programming, 295 15.4.1 M-Files, 295 15.4.2 Script File, 296 15.4.3 Function File, 297 15.4.4 Plotting, 298 15.4.5 Plot Printing, 300 15.5 Sample Programs, 301 15.5.1 Centering and Scaling, 301 15.5.2 SVD/PCA, 301 15.5.3 PCA/NIPALS, 302 15.5.4 PLS1, 303 15.5.5 PLS2, 304 Conclusion, 306 Afterword. The Fourth Paradigm 307 Index 311

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Book SynopsisWith big data analytics comes big insights into profitability Big data is big business. But having the data and the computational power to process it isn't nearly enough to produce meaningful results.Trade Reviewexplains what it covers very well (ZDNet, September 2014)Table of ContentsForward xiii Preface xv Acknowledgments xix Introduction 1 Big Data Timeline 5 Why This Topic is Relevant Now 8 Is Big Data a Fad? 9 Where Using Big Data Makes a Big Difference 12 Part One The Computing Environment 23 Chapter 1 Hardware 27 Storage (Disk) 27 Central Processing Unit 29 Memory 31 Network 33 Chapter 2 Distributed Systems 35 Database Computing 36 File System Computing 37 Considerations 39 Chapter 3 Analytical Tools 43 Weka 43 Java and JVM Languages 44 R 47 Python 49 SAS 50 Part Two Turning Data into Business Value 53 Chapter 4 Predictive Modeling 55 A Methodology for Building Models 58 sEMMA 61 Binary Classifi cation 64 Multilevel Classifi cation 66 Interval Prediction 66 Assessment of Predictive Models 67 Chapter 5 Common Predictive Modeling Techniques 71 RFM 72 Regression 75 Generalized Linear Models 84 Neural Networks 90 Decision and Regression Trees 101 Support Vector Machines 107 Bayesian Methods Network Classifi cation 113 Ensemble Methods 124 Chapter 6 Segmentation 127 Cluster Analysis 132 Distance Measures (Metrics) 133 Evaluating Clustering 134 Number of Clusters 135 K‐means Algorithm 137 Hierarchical Clustering 138 Profi ling Clusters 138 Chapter 7 Incremental Response Modeling 141 Building the Response Model 142 Measuring the Incremental Response 143 Chapter 8 Time Series Data Mining 149 Reducing Dimensionality 150 Detecting Patterns 151 Time Series Data Mining in Action: Nike+ FuelBand 154 Chapter 9 Recommendation Systems 163 What Are Recommendation Systems? 163 Where Are They Used? 164 How Do They Work? 165 Assessing Recommendation Quality 170 Recommendations in Action: SAS Library 171 Chapter 10 Text Analytics 175 Information Retrieval 176 Content Categorization 177 Text Mining 178 Text Analytics in Action: Let’s Play Jeopardy! 180 Part Three Success Stories of Putting It All Together 193 Chapter 11 Case Study of a Large U.S.‐Based Financial Services Company 197 Traditional Marketing Campaign Process 198 High‐Performance Marketing Solution 202 Value Proposition for Change 203 Chapter 12 Case Study of a Major Health Care Provider 205 CAHPS 207 HEDIS 207 HOS 208 IRE 208 Chapter 13 Case Study of a Technology Manufacturer 215 Finding Defective Devices 215 How They Reduced Cost 216 Chapter 14 Case Study of Online Brand Management 221 Chapter 15 Case Study of Mobile Application Recommendations 225 Chapter 16 Case Study of a High‐Tech Product Manufacturer 229 Handling the Missing Data 230 Application beyond Manufacturing 231 Chapter 17 Looking to the Future 233 Reproducible Research 234 Privacy with Public Data Sets 234 The Internet of Things 236 Software Development in the Future 237 Future Development of Algorithms 238 In Conclusion 241 About the Author 243 Appendix 245 References 247 Index 253

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Book SynopsisOffers practical examples that can guide product engineers through every stage of experimental design: formulating problems, planning experiments, and analysing data. This book discusses both physical and virtual techniques, and includes numerous exercises and solutions. It is suitable for teaching or self-study.Table of ContentsPreface ix 1 What is robust design? 1 1.1 The importance of small variation 1 1.2 Variance reduction 2 1.3 Variation propagation 4 1.4 Discussion 5 1.4.1 Limitations 6 1.4.2 The outline of this book 7 Exercises 8 2 DOE for robust design, part 1 11 2.1 Introduction 11 2.1.1 Noise factors 11 2.1.2 Control factors 12 2.1.3 Control-by-noise interactions 12 2.2 Combined arrays: An example from the packaging industry 13 2.2.1 The experimental array 15 2.2.2 Factor effect plots 15 2.2.3 Analytical analysis and statistical significance 17 2.2.4 Some additional comments on the plotting 20 2.3 Dispersion effects 21 Exercises 23 Reference 25 3 Noise and control factors 27 3.1 Introduction to noise factors 27 3.1.1 Categories of noise 28 3.2 Finding the important noise factors 33 3.2.1 Relating noise to failure modes 33 3.2.2 Reducing the number of noise factors 34 3.3 How to include noise in a designed experiment 40 3.3.1 Compounding of noise factors 40 3.3.2 How to include noise in experimentation 45 3.3.3 Process parameters 48 3.4 Control factors 48 Exercises 49 References 51 4 Response, signal, and P diagrams 53 4.1 The idea of signal and response 53 4.1.1 Two situations 54 4.2 Ideal functions and P diagrams 55 4.2.1 Noise or signal factor 56 4.2.2 Control or signal factor 56 4.2.3 The scope 58 4.3 The signal 63 4.3.1 Including a signal in a designed experiment 64 Exercises 65 5 DOE for robust design, part 2 69 5.1 Combined and crossed arrays 69 5.1.1 Classical DOE versus DOE for robust design 69 5.1.2 The structure of inner and outer arrays 70 5.2 Including a signal in a designed experiment 74 5.2.1 Combined arrays with a signal 74 5.2.2 Inner and outer arrays with a signal 81 5.3 Crossed arrays versus combined arrays 89 5.3.1 Differences in factor aliasing 91 5.4 Crossed arrays and split-plot designs 94 5.4.1 Limits of randomization 94 5.4.2 Split-plot designs 95 Exercises 98 References 99 6 Smaller-the-better and larger-the-better 101 6.1 Different types of responses 101 6.2 Failure modes and smaller-the-better 102 6.2.1 Failure modes 102 6.2.2 STB with inner and outer arrays 103 6.2.3 STB with combined arrays 106 6.3 Larger-the-better 106 6.4 Operating window 108 6.4.1 The window width 110 Exercises 113 References 115 7 Regression for robust design 117 7.1 Graphical techniques 117 7.2 Analytical minimization of (g′(z))2 120 7.3 Regression and crossed arrays 121 7.3.1 Regression terms in the inner array 127 Exercises 128 8 Mathematics of robust design 131 8.1 Notational system 131 8.2 The objective function 132 8.2.1 Multidimensional problems 136 8.2.2 Optimization in the presence of a signal 138 8.2.3 Matrix formulation 139 8.2.4 Pareto optimality 141 8.3 ANOVA for robust design 144 8.3.1 Traditional ANOVA 144 8.3.2 Functional ANOVA 146 8.3.3 Sensitivity indices 149 Exercises 152 References 153 9 Design and analysis of computer experiments 155 9.1 Overview of computer experiments 156 9.1.1 Robust design 157 9.2 Experimental arrays for computer experiments 161 9.2.1 Screening designs 161 9.2.2 Space filling designs 163 9.2.3 Latin hypercubes 165 9.2.4 Latin hypercube designs and alphabetical optimality criteria 166 9.3 Response surfaces 167 9.3.1 Local least squares 168 9.3.2 Kriging 169 9.4 Optimization 171 9.4.1 The objective function 171 9.4.2 Analytical techniques or Monte Carlo 173 Exercises 175 References 176 10 Monte Carlo methods for robust design 177 10.1 Geometry variation 177 10.1.1 Electronic circuits 179 10.2 Geometry variation in two dimensions 179 10.3 Crossed arrays 192 11 Taguchi and his ideas on robust design 195 11.1 History and origin 195 11.2 The experimental arrays 197 11.2.1 The nature of inner arrays 197 11.2.2 Interactions and energy thinking 199 11.2.3 Crossing the arrays 200 11.3 Signal-to-noise ratios 200 11.4 Some other ideas 203 11.4.1 Randomization 203 11.4.2 Science versus engineering 204 11.4.3 Line fitting for dynamic models 204 11.4.4 An aspect on the noise 206 11.4.5 Dynamic models 207 Exercises 208 References 208 Appendix A Loss functions 209 A.1 Why Americans do not buy American television sets 209 A.2 Taguchi’s view on loss function 211 A.3 The average loss and its elements 211 A.4 Loss functions in robust design 214 Exercises 215 References 217 Appendix B Data for chapter 2 219 Appendix C Data for chapter 5 223 Appendix D Data for chapter 6 231 Index 233

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Book SynopsisA broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible, combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is organized around four themes: methods of solution for initial-boundary value problems; applications of partial differential equations; existence and properties of solutions; and the use of software to experiment with graphics and carry out computations. With a primary focus on wave and diffusion processes, Beginning Partial Differential Equations, Third EditionTrade Review“I enjoyed perusing O’Neil’s book. A beginner in the field of PDEs will learn quite a number of juicy facts concerning the flow of heat and the transmission of waves. While a next step will undoubtedly involve more rigor in the use of analytic tools, this first course will catch the attention of those with a curiosity for studying physical processes using differential equations.” (Mathematical Association of America, 15 February 2015) “This book is one of the textbooks that provide an introduction to basic methods and applications of partial differential equations for students of mathematics, physics and engineering.” (Zentralblatt MATH, 1 October 2014) Table of Contents1 First Ideas 1 1.1 Two Partial Differential Equations 11.2 Fourier Series 101.3 Two Eigenvalue Problems 281.4 A Proof of the Fourier Convergence Theorem 302. Solutions of the Heat Equation 392.1 Solutions on an Interval (0, L) 392.2 A Nonhomogeneous Problem 642.3 The Heat Equation in Two space Variables 712.4 The Weak Maximum Principle 753. Solutions of the Wave Equation 813.1 Solutions on Bounded Intervals 813.2 The Cauchy Problem 1093.3 The Wave Equation in Higher Dimensions 1374. Dirichlet and Neumann Problems 1474.1 Laplace’s Equation and Harmonic Functions 1474.2 The Dirichlet Problem for a Rectangle 1534.3 The Dirichlet Problem for a Disk 1584.4 Properties of Harmonic Functions 1654.5 The Neumann Problem 1874.6 Poisson’s Equation 1974.7 Existence Theorem for a Dirichlet Problem 2005. Fourier Integral Methods of Solution 2135.1 The Fourier Integral of a Function 2135.2 The Heat Equation on a Real Line 2205.3 The Debate over the Age of the Earth 2305.4 Burger’s Equation 2335.5 The Cauchy Problem for a Wave Equation 2395.6 Laplace’s Equation on Unbounded Domains 2446. Solutions Using Eigenfunction Expansions 2536.1 A Theory of Eigenfunction Expansions 2536.2 Bessel Functions 2666.3 Applications of Bessel Functions 2796.4 Legendre Polynomials and Applications 2887. Integral Transform Methods of Solution 3077.1 The Fourier Transform 3077.2 Heat and Wave Equations 3187.3 The Telegraph Equation 3327.4 The Laplace Transform 3348 First-Order Equations 3418.1 Linear First-Order Equations 3428.2 The Significance of Characteristics 3498.3 The Quasi-Linear Equation 3549 End Materials 3619.1 Notation 3619.2 Use of MAPLE 3639.3 Answers to Selected Problems 370Index 434

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Book SynopsisPresents a multitude of topics relevant to the quantitative finance community by combining the best of the theory with the usefulness of applications Written by accomplished teachers and researchers in the field, this book presents quantitative finance theory through applications to specific practical problems and comes with accompanying coding techniques in R and MATLAB, and some generic pseudo-algorithms to modern finance. It also offers over 300 examples and exercises that are appropriate for the beginning student as well as the practitioner in the field. The Quantitative Finance book is divided into four parts. Part One begins by providing readers with the theoretical backdrop needed from probability and stochastic processes. We also present some useful finance concepts used throughout the book. In part two of the book we present the classical Black-Scholes-Merton model in a uniquely accessible and understandable way. Implied volatility as well as local volatility surfaces are aTable of ContentsList of Figures xv List of Tables xvii Part I Stochastic Processes and Finance 1 1 Stochastic Processes 3 1.1 Introduction 3 1.2 General Characteristics of Stochastic Processes 4 1.2.1 The Index Set I 4 1.2.2 The State Space S 4 1.2.3 Adaptiveness, Filtration, and Standard Filtration 5 1.2.4 Pathwise Realizations 7 1.2.5 The Finite Dimensional Distribution of Stochastic Processes 8 1.2.6 Independent Components 9 1.2.7 Stationary Process 9 1.2.8 Stationary and Independent Increments 10 1.3 Variation and Quadratic Variation of Stochastic Processes 11 1.4 Other More Specific Properties 13 1.5 Examples of Stochastic Processes 14 1.5.1 The Bernoulli Process (Simple Random Walk) 14 1.5.2 The Brownian Motion (Wiener Process) 17 1.6 Borel—Cantelli Lemmas 19 1.7 Central Limit Theorem 20 1.8 Stochastic Differential Equation 20 1.9 Stochastic Integral 21 1.9.1 Properties of the Stochastic Integral 22 1.10 Maximization and Parameter Calibration of Stochastic Processes 22 1.10.1 Approximation of the Likelihood Function (Pseudo Maximum Likelihood Estimation) 24 1.10.2 Ozaki Method 24 1.10.3 Shoji-Ozaki Method 25 1.10.4 Kessler Method 25 1.11 Quadrature Methods 26 1.11.1 Rectangle Rule: (n = 1) (Darboux Sums) 27 1.11.2 Midpoint Rule 28 1.11.3 Trapezoid Rule 28 1.11.4 Simpson’s Rule 28 1.12 Problems 29 2 Basics of Finance 33 2.1 Introduction 33 2.2 Arbitrage 33 2.3 Options 35 2.3.1 Vanilla Options 35 2.3.2 Put–Call Parity 36 2.4 Hedging 39 2.5 Modeling Return of Stocks 40 2.6 Continuous Time Model 41 2.6.1 Itô’s Lemma 42 2.7 Problems 45 Part II Quantitative Finance in Practice 47 3 Some Models Used in Quantitative Finance 49 3.1 Introduction 49 3.2 Assumptions for the Black–Scholes–Merton Derivation 49 3.3 The B-S Model 50 3.4 Some Remarks on the B-S Model 58 3.4.1 Remark 1 58 3.4.2 Remark 2 58 3.5 Heston Model 60 3.5.1 Heston PDE Derivation 61 3.6 The Cox–Ingersoll–Ross (CIR) Model 63 3.7 Stochastic 𝛼, 𝛽, 𝜌 (SABR) Model 64 3.7.1 SABR Implied Volatility 64 3.8 Methods for Finding Roots of Functions: Implied Volatility 65 3.8.1 Introduction 65 3.8.2 The Bisection Method 65 3.8.3 The Newton’s Method 66 3.8.4 Secant Method 67 3.8.5 Computation of Implied Volatility Using the Newton’s Method 68 3.9 Some Remarks of Implied Volatility (Put–Call Parity) 69 3.10 Hedging Using Volatility 70 3.11 Functional Approximation Methods 73 3.11.1 Local Volatility Model 74 3.11.2 Dupire’s Equation 74 3.11.3 Spline Approximation 77 3.11.4 Numerical Solution Techniques 78 3.11.5 Pricing Surface 79 3.12 Problems 79 4 Solving Partial Differential Equations 83 4.1 Introduction 83 4.2 Useful Definitions and Types of PDEs 83 4.2.1 Types of PDEs (2-D) 83 4.2.2 Boundary Conditions (BC) for PDEs 84 4.3 Functional Spaces Useful for PDEs 85 4.4 Separation of Variables 88 4.5 Moment-Generating Laplace Transform 91 4.5.1 Numeric Inversion for Laplace Transform 92 4.5.2 Fourier Series Approximation Method 93 4.6 Application of the Laplace Transform to the Black–Scholes PDE 96 4.7 Problems 99 5 Wavelets and Fourier Transforms 101 5.1 Introduction 101 5.2 Dynamic Fourier Analysis 101 5.2.1 Tapering 102 5.2.2 Estimation of Spectral Density with Daniell Kernel 103 5.2.3 Discrete Fourier Transform 104 5.2.4 The Fast Fourier Transform (FFT) Method 106 5.3 Wavelets Theory 109 5.3.1 Definition 109 5.3.2 Wavelets and Time Series 110 5.4 Examples of Discrete Wavelets Transforms (DWT) 112 5.4.1 Haar Wavelets 112 5.4.2 Daubechies Wavelets 115 5.5 Application of Wavelets Transform 116 5.5.1 Finance 116 5.5.2 Modeling and Forecasting 117 5.5.3 Image Compression 117 5.5.4 Seismic Signals 117 5.5.5 Damage Detection in Frame Structures 118 5.6 Problems 118 6 Tree Methods 121 6.1 Introduction 121 6.2 Tree Methods: the Binomial Tree 122 6.2.1 One-Step Binomial Tree 122 6.2.2 Using the Tree to Price a European Option 125 6.2.3 Using the Tree to Price an American Option 126 6.2.4 Using the Tree to Price Any Path-Dependent Option 127 6.2.5 Using the Tree for Computing Hedge Sensitivities: the Greeks 128 6.2.6 Further Discussion on the American Option Pricing 128 6.2.7 A Parenthesis: the Brownian Motion as a Limit of Simple Random Walk 132 6.3 Tree Methods for Dividend-Paying Assets 135 6.3.1 Options on Assets Paying a Continuous Dividend 135 6.3.2 Options on Assets Paying a Known Discrete Proportional Dividend 136 6.3.3 Options on Assets Paying a Known Discrete Cash Dividend 136 6.3.4 Tree for Known (Deterministic) Time-Varying Volatility 137 6.4 Pricing Path-Dependent Options: Barrier Options 139 6.5 Trinomial Tree Method and Other Considerations 140 6.6 Markov Process 143 6.6.1 Transition Function 143 6.7 Basic Elements of Operators and Semigroup Theory 146 6.7.1 Infinitesimal Operator of Semigroup 150 6.7.2 Feller Semigroup 151 6.8 General Diffusion Process 152 6.8.1 Example: Derivation of Option Pricing PDE 155 6.9 A General Diffusion Approximation Method 156 6.10 Particle Filter Construction 159 6.11 Quadrinomial Tree Approximation 163 6.11.1 Construction of the One-Period Model 164 6.11.2 Construction of the Multiperiod Model: Option Valuation 170 6.12 Problems 173 7 Approximating PDEs 177 7.1 Introduction 177 7.2 The Explicit Finite Difference Method 179 7.2.1 Stability and Convergence 180 7.3 The Implicit Finite Difference Method 180 7.3.1 Stability and Convergence 182 7.4 The Crank–Nicolson Finite Difference Method 183 7.4.1 Stability and Convergence 183 7.5 A Discussion About the Necessary Number of Nodes in the Schemes 184 7.5.1 Explicit Finite Difference Method 184 7.5.2 Implicit Finite Difference Method 185 7.5.3 Crank–Nicolson Finite Difference Method 185 7.6 Solution of a Tridiagonal System 186 7.6.1 Inverting the Tridiagonal Matrix 186 7.6.2 Algorithm for Solving a Tridiagonal System 187 7.7 Heston PDE 188 7.7.1 Boundary Conditions 189 7.7.2 Derivative Approximation for Nonuniform Grid 190 7.8 Methods for Free Boundary Problems 191 7.8.1 American Option Valuations 192 7.8.2 Free Boundary Problem 192 7.8.3 Linear Complementarity Problem (LCP) 193 7.8.4 The Obstacle Problem 196 7.9 Methods for Pricing American Options 199 7.10 Problems 201 8 Approximating Stochastic Processes 203 8.1 Introduction 203 8.2 Plain Vanilla Monte Carlo Method 203 8.3 Approximation of Integrals Using the Monte Carlo Method 205 8.4 Variance Reduction 205 8.4.1 Antithetic Variates 205 8.4.2 Control Variates 206 8.5 American Option Pricing with Monte Carlo Simulation 208 8.5.1 Introduction 209 8.5.2 Martingale Optimization 210 8.5.3 Least Squares Monte Carlo (LSM) 210 8.6 Nonstandard Monte Carlo Methods 216 8.6.1 Sequential Monte Carlo (SMC) Method 216 8.6.2 Markov Chain Monte Carlo (MCMC) Method 217 8.7 Generating One-Dimensional Random Variables by Inverting the cdf 218 8.8 Generating One-Dimensional Normal Random Variables 220 8.8.1 The Box–Muller Method 221 8.8.2 The Polar Rejection Method 222 8.9 Generating Random Variables: Rejection Sampling Method 224 8.9.1 Marsaglia’s Ziggurat Method 226 8.10 Generating Random Variables: Importance Sampling 236 8.10.1 Sampling Importance Resampling 240 8.10.2 Adaptive Importance Sampling 241 8.11 Problems 242 9 Stochastic Differential Equations 245 9.1 Introduction 245 9.2 The Construction of the Stochastic Integral 246 9.2.1 Itô Integral Construction 249 9.2.2 An Illustrative Example 251 9.3 Properties of the Stochastic Integral 253 9.4 Itô Lemma 254 9.5 Stochastic Differential Equations (SDEs) 257 9.5.1 Solution Methods for SDEs 259 9.6 Examples of Stochastic Differential Equations 260 9.6.1 An Analysis of Cox–Ingersoll–Ross (CIR)-Type Models 263 9.6.2 Moments Calculation for the CIR Model 265 9.6.3 Interpretation of the Formulas for Moments 267 9.6.4 Parameter Estimation for the CIR Model 267 9.7 Linear Systems of SDEs 268 9.8 Some Relationship Between SDEs and Partial Differential Equations (PDEs) 271 9.9 Euler Method for Approximating SDEs 273 9.10 Random Vectors: Moments and Distributions 277 9.10.1 The Dirichlet Distribution 279 9.10.2 Multivariate Normal Distribution 280 9.11 Generating Multivariate (Gaussian) Distributions with Prescribed Covariance Structure 281 9.11.1 Generating Gaussian Vectors 281 9.12 Problems 283 Part III Advanced Models for Underlying Assets 287 10 Stochastic Volatility Models 289 10.1 Introduction 289 10.2 Stochastic Volatility 289 10.3 Types of Continuous Time SV Models 290 10.3.1 Constant Elasticity of Variance (CEV) Models 291 10.3.2 Hull–White Model 292 10.3.3 The Stochastic Alpha Beta Rho (SABR) Model 293 10.3.4 Scott Model 294 10.3.5 Stein and Stein Model 295 10.3.6 Heston Model 295 10.4 Derivation of Formulae Used: Mean-Reverting Processes 296 10.4.1 Moment Analysis for CIR Type Processes 299 10.5 Problems 301 11 Jump Diffusion Models 303 11.1 Introduction 303 11.2 The Poisson Process (Jumps) 303 11.3 The Compound Poisson Process 304 11.4 The Black–Scholes Models with Jumps 305 11.5 Solutions to Partial-Integral Differential Systems 310 11.5.1 Suitability of the Stochastic Model Postulated 311 11.5.2 Regime-Switching Jump Diffusion Model 312 11.5.3 The Option Pricing Problem 313 11.5.4 The General PIDE System 314 11.6 Problems 322 12 General Lévy Processes 325 12.1 Introduction and Definitions 325 12.2 Lévy Processes 325 12.3 Examples of Lévy Processes 329 12.3.1 The Gamma Process 329 12.3.2 Inverse Gaussian Process 330 12.3.3 Exponential Lévy Models 330 12.4 Subordination of Lévy Processes 331 12.5 Rescaled Range Analysis (Hurst Analysis) and Detrended Fluctuation Analysis (DFA) 332 12.5.1 Rescaled Range Analysis (Hurst Analysis) 332 12.5.2 Detrended Fluctuation Analysis 334 12.5.3 Stationarity and Unit Root Test 335 12.6 Problems 336 13 Generalized Lévy Processes, Long Range Correlations, and Memory Effects 337 13.1 Introduction 337 13.1.1 Stable Distributions 337 13.2 The Lévy Flight Models 339 13.2.1 Background 339 13.2.2 Kurtosis 343 13.2.3 Self-Similarity 345 13.2.4 The H - 𝛼 Relationship for the Truncated Lévy Flight 346 13.3 Sum of Lévy Stochastic Variables with Different Parameters 347 13.3.1 Sum of Exponential Random Variables with Different Parameters 348 13.3.2 Sum of Lévy Random Variables with Different Parameters 351 13.4 Examples and Applications 352 13.4.1 Truncated Lévy Models Applied to Financial Indices 352 13.4.2 Detrended Fluctuation Analysis (DFA) and Rescaled Range Analysis Applied to Financial Indices 357 13.5 Problems 362 14 Approximating General Derivative Prices 365 14.1 Introduction 365 14.2 Statement of the Problem 368 14.3 A General Parabolic Integro-Differential Problem 370 14.3.1 Schaefer’s Fixed Point Theorem 371 14.4 Solutions in Bounded Domains 372 14.5 Construction of the Solution in the Whole Domain 385 14.6 Problems 386 15 Solutions to Complex Models Arising in the Pricing of Financial Options 389 15.1 Introduction 389 15.2 Option Pricing with Transaction Costs and Stochastic Volatility 389 15.3 Option Price Valuation in the Geometric Brownian Motion Case with Transaction Costs 390 15.4 Stochastic Volatility Model with Transaction Costs 392 15.5 The PDE Derivation When the Volatility is a Traded Asset 393 15.5.1 The Nonlinear PDE 395 15.5.2 Derivation of the Option Value PDEs in Arbitrage Free and Complete Markets 397 15.6 Problems 400 16 Factor and Copulas Models 403 16.1 Introduction 403 16.2 Factor Models 403 16.2.1 Cross-Sectional Regression 404 16.2.2 Expected Return 406 16.2.3 Macroeconomic Factor Models 407 16.2.4 Fundamental Factor Models 408 16.2.5 Statistical Factor Models 408 16.3 Copula Models 409 16.3.1 Families of Copulas 411 16.4 Problems 412 Part IV Fixed Income Securities and Derivatives 413 17 Models for the Bond Market 415 17.1 Introduction and Notations 415 17.2 Notations 415 17.3 Caps and Swaps 417 17.4 Valuation of Basic Instruments: Zero Coupon and Vanilla Options on Zero Coupon 419 17.4.1 Black Model 419 17.4.2 Short Rate Models 420 17.5 Term Structure Consistent Models 422 17.6 Inverting the Yield Curve 426 17.6.1 Affine Term Structure 427 17.7 Problems 428 18 Exchange Traded Funds (ETFs), Credit Default Swap (CDS), and Securitization 431 18.1 Introduction 431 18.2 Exchange Traded Funds (ETFs) 431 18.2.1 Index ETFs 432 18.2.2 Stock ETFs 433 18.2.3 Bond ETFs 433 18.2.4 Commodity ETFs 433 18.2.5 Currency ETFs 434 18.2.6 Inverse ETFs 435 18.2.7 Leverage ETFs 435 18.3 Credit Default Swap (CDS) 436 18.3.1 Example of Credit Default Swap 437 18.3.2 Valuation 437 18.3.3 Recovery Rate Estimates 439 18.3.4 Binary Credit Default Swaps 439 18.3.5 Basket Credit Default Swaps 439 18.4 Mortgage Backed Securities (MBS) 440 18.5 Collateralized Debt Obligation (CDO) 441 18.5.1 Collateralized Mortgage Obligations (CMO) 441 18.5.2 Collateralized Loan Obligations (CLO) 442 18.5.3 Collateralized Bond Obligations (CBO) 442 18.6 Problems 443 Bibliography 445 Index 459

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