Probability and statistics Books

Book SynopsisAn accessible guide to understanding statistics using simulations, with examples from a range of scientific disciplinesReal-world challenges such as small sample sizes, skewed distributions of data, biased sampling designs, and more predictors than data points are pushing the limits of classical statistical analysis. This textbook provides a new tool for the statistical toolkit: data simulations. It shows that using simulation and data-generating models is an excellent way to validate statistical reasoning and to augment study design and statistical analysis with planning and visualization. Although data simulations are not new to professional statisticians, Statistics by Simulation makes the approach accessible to a broader audience, with examples from many fields. It introduces the reasoning behind data simulation and then shows how to apply it in planning experiments or observational studies, developing analytical workflows, deploying model diagnostics, and

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Book SynopsisPatrick Suppes is a philosopher and scientist whose contributions range over probability and statistics, mathematical and experimental psychology, the foundations of physics, education theory, the philosophy of language, measurement theory, and the philosophy of science.Table of ContentsVolume 1: Introduction; P. Humphreys. Part I: Probability. Some Contributions to Formal Theory of Probability; K. Popper, D. Miller. Elementary Non-Archimedean Representations of Probability for Decision Theory and Games; P.J. Hammond. Random Sequences and Hypotheses Tests; R. Chuaqui. Changing Probability Judgements; I. Levi. Upper and Lower Probability; T.L. Fine. Some Connections between Epistemic Logic and the Theory of Nonadditive Probability; P. Mongin. On the Properties of Conditional Independence; W. Spohn. Qualitative Probabilities Revisited; Z. Domotor. The Monks' Vote: a Dialogue on Unidimensional Probabilistic Geometry; J.-C. Falmagne. Part II: Probabilistic Causality. Probabilistic Causation without Probability; P.W. Holland. Causal Tendency, Necessitivity and Sufficientivity: an Updated Review; I.J. Good. Practical Causal Generalizations; E.W. Adams. In Place of Regression; C. Glymour, P. Spirtes, R. Scheines. Testing Probabilistic Causality; D. Costantini. Psychologistic Aspects of Suppes' Definition of Causality; P. Legrenzi, M. Sonino. Name Index. Subject Index. Volume 2: Part III: Philosophy of Physics. Probability and Quantum Theory; B. Loewer. Schrödinger's Version of EPR, and its Problems; A. Fine. Classical Field Magnitudes; J. Vuillemin. Quantity, Representation and Geometry; B. Mundy. Numerical Experimentation; P. Humphreys. Part IV: Theory Structure. Theories and Theoretical Models; R. Wojcicki. Suppes Predicates and the Construction of Unsolvable Problems in the Axiomatized Sciences; N.C.A. da Costa, F.A. Doria. StructuralExplanation; J.D. Sneed. Part V: Measurement Theory. Fifteen Problems concerning the Representational Theory of Measurement; R.D. Luce, L. Narens. The Meaningfulness of Ordinal Comparisons for General Order Relational Systems; F.S. Roberts, Z.S. Rosenbaum. Theories as Nets: the Case of Combinatorial Measurement Theory; C.U. Moulines, J.A. Díez. Name Index. Subject Index. Volume 3: Part VI: Philosophy of Language and Logic. Patrick Suppes' Contribution to the Philosophy of Language; D. Føllesdal. Open Problems in Relational Grammar; M. Böttner. A Variable-Free Logic for Anaphora; W.C. Purdy. Is Snow White? J. Moravcsik. Can there be Reasons for Putting Limitations on Classical Logic? P. Weingartner. Quantum Logic as a Logic of Identification; J. Hintikka, I. Halonen. Logic and Probability in Quantum Mechanics; M.L. dalla Chiara, R. Giuntini. Part VII: Learning Theory, Action Theory, and Robotics. From Stimulus-Sampling to Array-Similarity Theory; W.K. Estes. Action as Seeing to it that Something is the Case; R. Tuomela, G. Sandu. Command Satisfaction and the Acquisition of Habits; C. Crangle. Part VIII: General Philosophy of Science. Some Observations on Patrick Suppes' Philosophy of Science; M.C. Galavotti. Epilogue. Postscript; P. Suppes. Chronological and Topical Bibliography of Patrick Suppes' Publications. Name Index. Subject Index.

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Book SynopsisStudents will find this book a useful aid to learning the unfamiliar mathematical aspects of stochastic processes while applying them to physical processes that he or she has already encountered.Trade ReviewStudents will love this book. It tells them without fuss how to do simple and useful numerical calculations, with just enough background to understand what they are doing... a refreshingly brief and unconvoluted work. -- Vinay Ambegaokar American Journal of Physics The book is very clearly set out and very easy to read. Undergraduate students and those wishing to learn about stochastic processes for the first time would enjoy the clear pedagogic presentation. -- B.I. Henry The Physicist [ An Introduction to Stochastic Processes in Physics] presents fundamental ideas with admirable clarity and concision. The author presents in about 100 pages enough material for the student to appreciate the very different natures of stochastic and sure processes and to solve simple but important problems involving noise. Any physicist wondering what noise is about would be well advised to pack Lemons' books for their next train journey. -- Professor S.M. Barnett Contemporary Physics Self-contained and provides adequate insight into stochastic processes in physics. It is quite readable and will be useful to students interested in learning about stochastic processes and their relevance in understanding the physical phenomena. It also provides teachers a good approach to communicate the essence of the subject to students. -- Suresh V. Lawande Mathematical ReviewsTable of ContentsContents: Preface and Acknowledgments Chapter 1: Random Variables Chapter 2: Expected Values Chapter 3: Random Steps Chapter 4: Continuous Random Variables Chapter 5: Normal Variable Theorems Chapter 6: Einstein's Brownian Motion Chapter 7: Ornstein-Uhlenbeck Processes Chapter 8: Langevin's Brownian Motion Chapter 9: Other Physical Processes Chapter 10: Fluctuations without Dissipation Appendix A: "On the Theory of Brownian Motion," by Paul Langevin, translated by Anthony Gythiel Appendix B: Kinetic Equations Answers to Problems References Index

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Book SynopsisOffers a comprehensive update of this classic statistics textbook, with careful adherence to the intent, approach, and style of the original authors.Table of ContentsPreface to the Eighth Edition. Preface to the First Edition. Symbols Frequently Used. Introduction. Frequency Distributions. The Mean and Standard Deviation. The Normal Distribution. Tests of Hypotheses. The Comparison of Two Samples. The Binomial Distribution. Shortcut and Nonparametric Methods. Regression. Correlation. Analysis of Frequencies in One-way and Two-way Classifications. One-way Classifications: Analysis of Variance. Analysis of Variance: The Random Effects Model. Two-way Classifications. Failure in the Assumptions. Factorial Experiments. Multiple Linear Regression. Analysis of Covariance. Nonlinear Relations. Two-way Tables with Unequal Numbers and Proportions. Sample Surveys. Appendix. Index.

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Book SynopsisExplores the history of probability, describing the modern concept of randomness and examining ""pre-probabilistic"" ideas of what most people today would characterize as randomness. It documents some historically important early uses of probability, and goes on to explore statistics and the generations of mathematicians and non-mathematicians who began to address problems in statistical analysis.

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Book SynopsisPresents twenty-eight cases, written by teachers describing real situations and actual student thinking in their classrooms, that provide the basis of each session's investigation of specific mathematical concepts and teaching strategies.

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Book SynopsisBasic Concepts of Probability and Statistics provides a mathematically rigorous introduction to the fundamental ideas of modern statistics for readers without a calculus background. It is the only book at this level to introduce readers to modern concepts of hypothesis testing and estimation, covering basic concepts of finite, discrete models of probability and elementary statistical methods. Although published in 1970, it maintains a modern outlook, especially with such topics as models and model building, simple random and stratified survey sampling, experimental design, and nonparametric tests and its discussion of power. The book covers a wide range of applications in manufacturing, biology, and social science, including demographics, political science, and sociology. Each section offers extensive problem sets, with selected answers provided. Among the topics covered that readers may not expect in an elementary text are optimal design and a statement and proof of the fundamental (N

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Book SynopsisThis thorough book collects methods and strategies to analyze proteomics data. It is intended to describe how data obtained by gel-based or gel-free proteomics approaches can be inspected, organized, and interpreted to extrapolate biological information. Organized into four sections, the volume explores strategies to analyze proteomics data obtained by gel-based approaches, different data analysis approaches for gel-free proteomics experiments, bioinformatic tools for the interpretation of proteomics data to obtain biological significant information, as well as methods to integrate proteomics data with other omics datasets including genomics, transcriptomics, metabolomics, and other types of data. Written for the highly successful Methods in Molecular Biology series, chapters include the kind of detailed implementation advice that will ensure high quality results in the lab. Authoritative and practical, Proteomics Data Analysis serves as an ideal Table of ContentsPart I: Data Analysis for Gel-Based Proteomics 1. Two-Dimensional Gel Electrophoresis Image Analysis Elisa Robotti, Elisa Calà, and Emilio Marengo 2. Chemometric Tools for 2D-PAGE Data Analysis Elisa Robotti, Elisa Calà, and Emilio Marengo Part II: Data Analysis for Gel-Free Proteomics 3. Software Options for the Analysis of MS Proteomic Data Avinash Yadav, Federica Marini, Alessandro Cuomo, and Tiziana Bonaldi 4. Analysis of Label-Based Quantitative Proteomics Data Using IsoProt Johannes Griss and Veit Schwämmle 5. Quantification of Changes in Protein Expression Using SWATH Proteomics Clarissa Braccia, Nara Liessi, and Andrea Armirotti 6. Data Processing and Analysis for DIA-Based Phosphoproteomics Using Spectronaut Ana Martinez-Val, Dorte Breinholdt Bekker-Jensen, Alexander Hogrebe, and Jesper Velgaard Olsen 7. Enhanced Glycopeptide Identification Using a GlyConnect Compozitor-Derived Glycan Composition File Julien Mariethoz, Catherine Hayes, and Frédérique Lisacek 8. Elaboration Pipeline for the Management of MALDI-MS Imaging Datasets Andrew Smith, Isabella Piga, Vanna Denti, Clizia Chinello, and Fulvio Magni 9. Features Selection and Extraction in Statistical Analysis of Proteomics Datasets Marta Lualdi and Mauro Fasano Part III: Proteomics Data Interpretation 10. ORA, FCS, and PT Strategies in Functional Enrichment Analysis Marco Fernandes and Holger Husi 11. A Strategy for the Annotation and GO Enrichment Analysis of a List of Differentially Expressed Proteins Using ProteoRE Florence Combes, Valentin Loux, and Yves Vandenbrouck 12. Protein Subcellular Localization Prediction Elettra Barberis, Emilio Marengo, and Marcello Manfredi 13. Protein Secretion Prediction Tools and Extracellular Vesicles Databases Daniela Cecconi, Claudia Di Carlo, and Jessica Brandi 14. Databases for Protein-Protein Interactions Natsu Nakajima, Tatsuya Akutsu, and Ryuichiro Nakato 15. Machine and Deep Learning for Prediction of Subcellular Localization Gaofeng Pan, Chao Sun, Zijun Liao, and Jijun Tang 16. Deep Learning for Protein-Protein Interaction Site Prediction Arian R. Jamasb, Ben Day, Cătălina Cangea, Pietro Liò, and Tom L. Blundell Part IV: Proteomics Data Integration with Other -Omics 17. Integrative Analysis of Incongruous Cancer Genomics and Proteomics Datasets Karla Cervantes-Gracia, Richard Chahwan, and Holger Husi 18. Integration of Proteomics and Other Omics Data Mengyun Wu, Yu Jiang, and Shuangge Ma

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Book SynopsisBasic Notions of Probability Theory.- Calculation of Expectations.- Convexity, Optimization, and Inequalities.- Combinatorics.- Combinatorial Optimization.- Poisson Processes.- Discrete-Time Markov Chains.- Continuous-Time Markov Chains.- Branching Processes.- Martingales.- Diffusion Processes.- Asymptotic Methods.- Numerical Methods.- Poisson Approximation.- Number Theory.- Entropy.- Appendix: Mathematical Review.

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Book SynopsisMethods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods includes updates of established literature from the Wiley Encyclopedia of Clinical Trials as well as original material based on the latest developments in clinical trials. Prepared by a leading expert, the second volume includes numerous contributions from current prominent experts in the field of medical research. In addition, the volume features: Multiple new articles exploring emerging topics, such as evaluation methods with threshold, empirical likelihood methods, nonparametric ROC analysis, over- and under-dispersed models, and multi-armed bandit problems Up-to-date research on the Cox proportional hazard model, frailty models, trial reports, intrarater reliability, conditional power, and the kappa index Key qualitative issues including cost-effectiveness analysis, publication bias, and regulatory issues, which are crucial to the planniTrade Review“This book provides a good overview on most relevant topics for clinical trials.” (Biometrical Journal, 1 October 2015) Table of ContentsContributors xix Preface xxiii 1 Analysis of Over- and Underdispersed Data 1 2 Analysis of Variance (ANOVA) 10 3 Assessment of Health-Related Quality of Life 26 4 Bandit Processes and Response-Adaptive Clinical Trials: The Art of Exploration Versus Exploitation 40 5 Bayesian Dose-Finding Designs in Healthy Volunteers 51 6 Bootstrap 62 7 Conditional Power in Clinical Trial Monitoring 102 8 Cost-Effectiveness Analysis 111 9 Cox-Type Proportional Hazards Models 126 10 Empirical Likelihood Methods in Clinical Experiments 146 11 Frailty Models 166 12 Futility Analysis 174 13 Imaging Science in Medicine I: Overview 187 14 Imaging Science in Medicine, II: Basics of X-Ray Imaging 213 15 Imaging Science in Medicine, III: Digital (21st Century) X-Ray Imaging 264 16 Intention-to-Treat Analysis 313 17 Interim Analyses 323 18 Interrater Reliability 334 19 Intrarater Reliability 340 20 Kaplan-Meier Plot 357 21 Logistic Regression 365 22 Metadata 380 23 Microarray 392 24 Multi-Armed Bandits, Gittins Index, and Its Calculation 416 25 Multiple Comparisons 436 26 Multiple Evaluators 446 27 Noncompartmental Analysis 457 28 Nonparametric ROC Analysis for Diagnostic Trials 483 29 Optimal Biological Dose for Molecularly Targeted Therapies 496 30 Over- and Underdispersion Models 506 31 Permutation Tests in Clinical Trials 527 32 Pharmacoepidemiology, Overview 536 33 Population Pharmacokinetic and Pharmacodynamic Methods 551 34 Proportions: Inferences and Comparisons 570 35 Publication Bias 595 36 Quality of Life 608 37 Relative Risk Modeing 622 38 Sample Size Considerations for Morbidity/Mortality Trials 633 39 Sample Size for Comparing Means 642 40 Sample Size for Comparing Proportions 653 41 Sample Size for Comparing Time-to-Event Data 664 42 Sample Size for Comparing Variabilities 672 43 Screening, Models of 689 44 Screening Trials 721 45 Secondary Efficacy End Points 731 46 Sensitivity, Specificity, and Receiver Operator Characteristic (ROC) Methods 740 47 Software for Genetics/Genomics 752 48 Stability Study Designs 778 49 Subgroup Analysis 793 50 Survival Analysis, Overview 802 51 The FDA and Regulatory Issues 815 52 The Kappa Index 836 53 Treatment Interruption 846 54 Trial Reports: Improving Reporting, Minimizing Bias, and Producing Better Evidence-Based Practice 860 55 U.S. Department of Veterans Affairs Cooperative Studies Program 876 56 Women's Health Initiative: Statistical Aspects and Selected Early Results 901 57 World Health Organization (WHO): Global Health Situation 914 Index 925

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Book SynopsisThis textbook introduces chemistry and chemical engineering students to molecular descriptions of thermodynamics, chemical systems, and biomolecules. Equips students with the ability to apply the method to their own systems, as today''s research is microscopic and molecular and articles are written in that language Provides ample illustrations and tables to describe rather difficult concepts Makes use of plots (charts) to help students understand the mathematics necessary for the contents Includes practice problems and answers Table of ContentsPreface xiii Acknowledgments xvii About the Companion Website xix Symbols and Constants xxi 1 Introduction 1 1.1 Classical Thermodynamics and Statistical Thermodynamics 1 1.2 Examples of Results Obtained from Statistical Thermodynamics 2 1.2.1 Heat Capacity of Gas of Diatomic Molecules 2 1.2.2 Heat Capacity of a Solid 3 1.2.3 Blackbody Radiation 3 1.2.4 Adsorption 4 1.2.5 Helix–Coil Transition 5 1.2.6 Boltzmann Factor 6 1.3 Practices of Notation 6 2 Review of Probability Theory 9 2.1 Probability 9 2.2 Discrete Distributions 11 2.2.1 Binomial Distribution 12 2.2.2 Poisson Distribution 13 2.2.3 Multinomial Distribution 14 2.3 Continuous Distributions 15 2.3.1 Uniform Distribution 19 2.3.2 Exponential Distribution 19 2.3.3 Normal Distribution 21 2.3.4 Distribution of a Dihedral Angle 21 2.4 Means and Variances 22 2.4.1 Discrete Distributions 22 2.4.2 Continuous Distributions 26 2.4.3 Central Limit Theorem 27 2.5 Uncertainty 28 Problems 31 3 Energy and Interactions 35 3.1 Kinetic Energy and Potential Energy of Atoms and Ions 35 3.1.1 Kinetic Energy 35 3.1.2 Gravitational Potential 36 3.1.3 Ion in an Electric Field 36 3.1.4 Total Energy of Atoms and Ions 37 3.2 Kinetic Energy and Potential Energy of Diatomic Molecules 37 3.2.1 Kinetic Energy (Translation, Rotation, Vibration) 37 3.2.2 Dipolar Potential 42 3.2.2.1 Potential of a Permanent Dipole 42 3.2.2.2 Potential of an Induced Dipole 44 3.3 Kinetic Energy of Polyatomic Molecules 46 3.3.1 Linear Polyatomic Molecule 46 3.3.2 Nonlinear Polyatomic Molecule 48 3.4 Interactions Between Molecules 50 3.4.1 Excluded-Volume Interaction 52 3.4.2 Coulomb Interaction 52 3.4.3 Dipole–Dipole Interaction 53 3.4.4 van der Waals Interaction 54 3.4.5 Lennard-Jones Potential 55 3.5 Energy as an Extensive Property 57 3.6 Kinetic Energy of a Gas Molecule in Quantum Mechanics 58 3.6.1 Quantization of Translational Energy 58 3.6.2 Quantization of Rotational Energy 61 3.6.3 Quantization of Vibrational Energy 63 3.6.4 Electronic Energy Levels 65 3.6.5 Comparison of Energy Level Spacings 66 Problems 67 4 Statistical Mechanics 69 4.1 Basic Assumptions, Microcanonical Ensembles, and Canonical Ensembles 69 4.1.1 Basic Assumptions 69 4.1.2 Microcanonical Ensembles 73 4.1.3 Canonical Ensembles 75 4.2 Probability Distribution in Canonical Ensembles and Partition Functions 77 4.2.1 Probability Distribution 77 4.2.2 Partition Function for a System with Discrete States 79 4.2.3 Partition Function for a System with Continuous States 81 4.2.4 Energy Levels and States 83 4.3 Internal Energy 88 4.4 Identification of 𝛽 89 4.5 Equipartition Law 91 4.6 Other Thermodynamic Functions 93 4.7 Another View of Entropy 97 4.8 Fluctuations of Energy 99 4.9 Grand Canonical Ensembles 100 4.10 Cumulants of Energy 107 Problems 110 5 Canonical Ensemble of Gas Molecules 113 5.1 Velocity of Gas Molecules 113 5.2 Heat Capacity of a Classical Gas 116 5.2.1 Point Mass 117 5.2.2 Rigid Dumbbell 117 5.2.3 Elastic Dumbbell 118 5.3 Heat Capacity of a Quantum-Mechanical Gas 120 5.3.1 General Formulas 120 5.3.2 Translation 122 5.3.3 Rotation 124 5.3.4 Vibration 127 5.3.5 Comparison with Classical Models 128 5.4 Distribution of Rotational Energy Levels 129 5.5 Conformations of a Molecule 130 Problems 132 6 Indistinguishable Particles 135 6.1 Distinguishable Particles and Indistinguishable Particles 135 6.2 Partition Function of Indistinguishable Particles 137 6.2.1 System of Distinguishable Particles 137 6.2.2 System of Indistinguishable Particles 137 6.3 Condition of Nondegeneracy 142 6.4 Significance of Division by N! 144 6.4.1 Gas in a Two-Part Box 144 6.4.2 Chemical Potential 145 6.4.3 Mixture of Two Gases 146 6.5 Indistinguishability and Center-of-Mass Movement 147 6.6 Open System of Gas 147 Problems 149 7 Imperfect Gas 153 7.1 Virial Expansion 153 7.2 Molecular Expression of Interaction in the Canonical Ensemble 157 7.3 Second Virial Coefficients in Different Models 164 7.3.1 Hard-Core Repulsion Only 164 7.3.2 Square-well Potential 165 7.3.3 Lennard-Jones Potential 167 7.4 Joule–Thomson Effect 167 Problems 171 8 Rubber Elasticity 175 8.1 Rubber 175 8.2 Polymer Chain in One Dimension 176 8.3 Polymer Chain in Three Dimensions 180 8.4 Network of Springs 184 Problems 185 9 Law of Mass Action 189 9.1 Reaction of Two Monatomic Molecules 190 9.2 Decomposition of Homonuclear Diatomic Molecules 193 9.3 Isomerization 195 9.4 Method of the Steepest Descent 197 Problems 198 10 Adsorption 201 10.1 Adsorption Phenomena 201 10.2 Langmuir Isotherm 202 10.3 BET Isotherm 206 10.4 Dissociative Adsorption 211 10.5 Interaction Between Adsorbed Molecules 213 Problems 213 11 Ising Model 217 11.1 Model 217 11.2 Partition Function 220 11.2.1 One-Dimensional Ising Model 220 11.2.2 Calculating Statistical Averages 221 11.2.2.1 Average Number of Up Spins 222 11.2.2.2 Average of the Number of Spin Alterations (Number of Domains – 1) 222 11.2.2.3 Domain Size 223 11.2.2.4 Size of a Domain of Uniform Spins 223 11.2.3 A Few Examples of 1D Ising Model 223 11.2.3.1 Linear Ising Model, N = 3 223 11.2.3.2 Ring Ising Model, N = 3 225 11.2.3.3 Ring Ising Model, N = 4 225 11.3 Mean-FieldTheories 226 11.3.1 Bragg–Williams (B–W) Approximation 227 11.3.2 Flory–Huggins (F–H) Approximation 231 11.3.3 Approximation by a Mean-Field (MF) Theory 235 11.4 Exact Solution of 1D Ising Model 236 11.4.1 General Formula 236 11.4.2 Large-N Approximation 239 11.4.3 Exact Partition Function for Arbitrary N 241 11.4.4 Ring Ising Model, Arbitrary N 244 11.4.5 Comparison of the Exact Results with Those of Mean-Field Approximations 245 11.5 Variations of the Ising Model 247 11.5.1 System of Uniform Spins 247 11.5.2 Random Local Fields of Opposite Directions 249 11.5.3 Dilute Local Fields 252 Problems 254 12 Helical Polymer 263 12.1 Helix-Forming Polymer 263 12.2 Optical Rotation and Circular Dichroism 266 12.3 Pristine Poly(n-hexyl isocyanate) 267 12.4 Variations to the Helical Polymer 271 12.4.1 Copolymer of Chiral and Achiral Isocyanate Monomers 272 12.4.2 Copolymer of R- and S-Enantiomers of Isocyanate 274 Problems 274 13 Helix–Coil Transition 277 13.1 Historical Background 277 13.2 Polypeptides 281 13.3 Zimm–Bragg Model 283 Problems 289 14 Regular Solutions 291 14.1 Binary Mixture of Equal-Size Molecules 291 14.1.1 Free Energy of Mixing 291 14.1.2 Derivatives of the Free Energy of Mixing 296 14.1.3 Phase Separation 300 14.2 Binary Mixture of Molecules of Different Sizes 304 Problems 312 Appendix A Mathematics 315 A.1 Hyperbolic Functions 315 A.2 Series 317 A.3 Binomial Theorem and Trinomial Theorem 317 A.4 Stirling’s formula 318 A.5 Integrals 318 A.6 Error Functions 318 A.7 Gamma Functions 319 References 321 Index 325

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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 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 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 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 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 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 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 SynopsisHIGHLIGHTS THE USE OF BAYESIAN STATISTICS TO GAIN INSIGHTS FROM EMPIRICAL DATA Featuring an accessible approach, Bayesian Methods for Management and Business: Pragmatic Solutions for Real Problems demonstrates how Bayesian statistics can help to provide insights into important issues facing business and management. The book draws on multidisciplinary applications and examples and utilizes the freely available software WinBUGS and R to illustrate the integration of Bayesian statistics within data-rich environments. Computational issues are discussed and integrated with coverage of linear models, sensitivity analysis, Markov Chain Monte Carlo (MCMC), and model comparison. In addition, more advanced models including hierarchal models, generalized linear models, and latent variable models are presented to further bridge the theory and application in real-world usage. Bayesian Methods for Management and Business: Pragmatic Solutions for Real Problems alTable of ContentsPreface xv 1 Introduction to Bayesian Methods 1 1.1 Bayesian Methods: An Aerial Survey 1 1.1.1 Informal Example 3 1.2 Bayes’ Theorem 4 1.3 Bayes’ Theorem and the Focus Group 6 1.4 The Flavors of Probability 8 1.4.1 Common Ground 9 1.4.2 Frequency-Based Probability 9 1.4.3 Subjective Probability 10 1.5 Summary 11 1.6 Notation Introduced in this Chapter 11 2 A First Look at Bayesian Computation 12 2.1 Getting Started 12 2.2 Selecting the Likelihood Function 13 2.3 Selecting the Functional Form 16 2.4 Selecting the Prior 17 2.5 Finding the Normalizing Constant 18 2.6 Obtaining the Posterior 19 2.7 Communicating Findings 23 2.8 Predicting Future Outcomes 26 2.9 Summary 28 2.10 Exercises 28 2.11 Notation Introduced in this Chapter 29 3 Computer-Assisted Bayesian Computation 30 3.1 Getting Started 30 3.2 Random Number Sequences 31 3.3 Monte Carlo Integration 33 3.4 Monte Carlo Simulation for Inference 36 3.4.1 Testing for a Difference in Proportions 37 3.4.2 Predicting Customer Behavior 38 3.4.3 Predicting Customer Behavior Part 2 40 3.5 The Conjugate Normal Model 40 3.5.1 The Conjugate Normal Model: Mean with Variance Known 40 3.5.2 The Conjugate Normal Model: Variance with Mean Known 42 3.5.3 The Conjugate Normal Model with Mean and Variance Both Unknown 44 3.6 In Practice: Inference for the Conjugate Normal Model 45 3.6.1 Conjugate Normal Mean with Variance Known 46 3.6.2 Conjugate Normal Variance with Mean Known 47 3.6.3 Conjugate Normal Mean and Variance Both Unknown 48 3.7 Count Data and the Conjugate Poisson Model 52 3.7.1 In Detail: Conjugate Poisson Model Development 53 3.7.2 In Practice: Inference for the Conjugate Poisson Model 54 3.8 Summary 56 3.9 Exercises 56 3.10 Notation Introduced in this Chapter 58 3.11 Appendix—In Detail: Finding Posterior Distributions for the Normal Model 58 3.11.1 Analysis of the Normal Mean with Variance Known 59 3.11.2 Analysis of the Normal Variance with Mean Known 61 3.11.3 Analysis of the Conjugate Normal Model with Mean and Variance Both Unknown 62 4 Markov Chain Monte Carlo and Regression Models 64 4.1 Introduction to Markov Chain Monte Carlo 64 4.2 Fundamentals of MCMC 66 4.3 Gibbs Sampling 67 4.3.1 Gibbs Sampling for the Normal Mean 69 4.3.2 Output Analysis 70 4.4 Gibbs Sampling and the Simple Linear Regression Model 73 4.5 In Practice: The Simple Linear Regression Model 76 4.6 The Metropolis Algorithm 79 4.6.1 In Practice: Simulating from a Standard Normal Distribution Using the Metropolis Algorithm 81 4.6.2 In Practice: Regression Analysis Using the Metropolis Algorithm 85 4.7 Hastings’ Extension of the Metropolis Algorithm 87 4.7.1 In Practice: The Metropolis–Hastings Algorithm 89 4.7.2 The Relationship Between the Gibbs Sampler and the Metropolis–Hastings Algorithm 90 4.8 Summary 91 4.9 Exercises 92 5 Estimating Bayesian Models With WinBUGS 93 5.1 An Introduction to WinBUGS 94 5.2 In Practice: A First WinBUGS Model 95 5.3 In Practice: Models for the Mean in WinBUGS 104 5.3.1 Examining the Single-Sample Mean 104 5.3.2 The Two-Sample t-Test 106 5.3.3 An Alternative Parameterization of the Two-Sample t-Test 108 5.4 Examining the Prior’s Influence with Sensitivity Analysis 111 5.4.1 Sensitivity Analysis with Informative Priors 111 5.4.2 Sensitivity Analysis with Noninformative Priors 113 5.4.3 In Practice: Pre-sensitivity Analysis: Graphically Examining a Mean Parameter’s Prior and Posterior Distribution 114 5.4.4 In Practice: Pre-sensitivity Analysis—Graphically Examining a Precision Parameter 117 5.4.5 In Practice: Sensitivity Analysis for a Mean Parameter 118 5.4.6 In Practice: Sensitivity Analysis for a Precision Parameter 118 5.5 In Practice: Examining Proportions in WinBUGS 120 5.5.1 Analyzing Differences in Proportions 121 5.5.2 Predicting Customer Behavior: Part 2 Revisited 124 5.6 Analysis of Variance Models 125 5.6.1 In Practice: One-Way ANOVA 126 5.6.2 In Practice: One-Way ANOVA with Effects Coding 132 5.6.3 In Practice: One-Way ANOVA with Unequal Variances 133 5.6.4 Indexing Parameters by Group Membership Variables 136 5.7 Higher Order ANOVA Models 137 5.7.1 In Practice: Two-Way ANOVA with structure Data 139 5.7.2 Two-Way ANOVA with Group Indicator Variables 140 5.7.3 Using Columnar Data in WinBUGS 143 5.8 Regression and ANCOVA Models in WinBUGS 144 5.8.1 In Practice: Simple Linear Regression Using WinBUGS 145 5.8.2 In Practice: ANCOVA Models Using WinBUGS 147 5.8.3 In Practice: “Undifferenced” ANCOVA Models Using WinBUGS 150 5.9 Summary 152 5.10 Chapter Appendix: Exporting WinBUGS MCMC Output to R 152 5.11 Exercises 153 6 Assessing MCMC Performance inWinBUGS 155 6.1 Convergence Issues in MCMC Modeling 155 6.2 Output Diagnostics in WinBUGS 158 6.2.1 The Quantiles Tool 158 6.2.2 The Autocorrelation Function Tool 159 6.3 Reparameterizing to Improve Convergence 161 6.4 Number and Length of Chains 165 6.4.1 Number of Chains 165 6.4.2 Length of Chains 173 6.5 Metropolis–Hastings Acceptance Rates 175 6.6 Summary 177 6.7 Exercises 178 7 Model Checking and Model Comparison 180 7.1 Graphical Model Checking 180 7.1.1 In Practice: Graphical Fit Plots 181 7.1.2 In Practice: Residual Analysis 183 7.2 Predictive Densities and Checking Model Assumptions 185 7.2.1 The Posterior Predictive p-value 186 7.2.2 In Detail: Comparing Posterior Predictive p-Value Test Statistics 190 7.3 Variable Selection Methods 192 7.3.1 Kuo and Mallick’s Method 192 7.3.2 In Practice: Kuo and Mallick Variable Selection 194 7.3.3 Gibbs Variable Selection 196 7.3.4 In Practice: Gibbs Variable Selection 197 7.3.5 Reversible Jump MCMC 197 7.3.6 In Practice: Reversible Jump MCMC with WinBUGS 198 7.4 Bayes Factors and Bayesian Information Criterion 201 7.4.1 In Practice: Calculating the Marginal Likelihood for a Simple Proportion 204 7.4.2 Bayesian Information Criterion 205 7.5 Deviance Information Criterion 208 7.5.1 AIC and Classical Non-nested Model Selection 208 7.5.2 DIC: A Bayesian Version of AIC 209 7.5.3 In Practice: DIC for Variable Selection 211 7.5.4 In Practice: Likelihood Transformations and DIC 213 7.6 Summary 214 7.7 Exercises 214 8 Hierarchical Models 217 8.1 Fundamentals of Hierarchical Models 218 8.1.1 In Detail: Hierarchical Model Error Terms 222 8.1.2 In Practice: The One-Way Random-Effects ANOVA Model 223 8.1.3 In Practice: Hierarchical Centering 225 8.1.4 In Practice: Examining Alternative Priors for Variance Components 226 8.1.5 In Practice: Longitudinal Modeling 227 8.2 The Random Coefficients Model 228 8.2.1 In Practice: Structuring Data for Hierarchical Models 231 8.2.2 In Practice: The Random Coefficients Model 233 8.2.3 In Practice: Changing Random Coefficients to Be Non-random 236 8.2.4 In Practice: Multiple-Predictor Random Coefficients Models 237 8.3 Hierarchical Models for Variance Terms 238 8.4 Functional Forms at Multiple Hierarchical Levels 242 8.4.1 In Practice: Second-Level Functional Forms 245 8.4.2 In Practice: Interpreting Second-Level Coefficients 247 8.5 In Detail: Modeling Covarying Hierarchical Terms 249 8.5.1 Specifying Priors for the Bivariate Normal 250 8.5.2 In Practice: The Covarying Random Coefficients Model 252 8.5.3 In Practice: Case Studies in the Covarying Random Coefficients Model 254 8.6 Summary 256 8.7 Exercises 256 8.8 Notation Introduced in this Chapter 257 9 Generalized Linear Models 259 9.1 Fundamentals of Generalized Linear Models 259 9.2 Count Data Models: Poisson Regression 262 9.3 Models for Binary Data: Logistic Regression 266 9.4 The Probit Model 271 9.5 In Detail: Multinomial Logistic Regression for Categorical Outcomes 274 9.5.1 In Practice: Multinomial Logit for Contingency Tables 277 9.5.2 In Practice: Multinomial Logit with Continuous Predictors 279 9.6 Hierarchical Models for Count Data 281 9.6.1 The Negative Binomial Regression Model 282 9.6.2 In Practice: Simulating from the Negative Binomial Distribution 282 9.6.3 In Practice: Negative Binomial Regression 285 9.7 Hierarchical Models for Binary Data 287 9.7.1 In Practice: Logistic Regression with Random Intercepts 288 9.8 Summary 290 9.9 Exercises 291 9.10 Notation Introduced in this Chapter 292 10 Models For Difficult Data 294 10.1 Living with Outliers—Robust Regression Models 294 10.1.1 Another Look at the t-Distribution 296 10.1.2 In Practice: Robust Regression with the t-Distribution 297 10.1.3 In Detail: Placing a Prior on 301 10.2 Handling Heteroscedasticity by Modeling Variance Parameters 304 10.2.1 In Practice: Modeling Heteroscedasticity 305 10.3 Dealing with Missing Data 309 10.4 Types of Missing Data 311 10.4.1 Missing Completely at Random Data 311 10.4.2 In Practice: Analyzing MCAR Data 312 10.4.3 Missing at Random Data 314 10.4.4 In Practice: Analyzing MAR Data 315 10.4.5 Missing Not at Random Data 317 10.5 Missing Covariate Data and Non-Normal Missing Data 318 10.6 Summary 319 10.7 Exercises 320 10.8 Notation Introduced in this Chapter 321 11 Introduction To Latent Variable Models 322 11.1 Not Seen but Felt 322 11.2 Latent Variable Models for Binary Data 323 11.2.1 In Practice: The Probit Model Using Latent Variables 325 11.3 Structural Break Models 327 11.3.1 In Practice: Estimating Structural Break Models 329 11.3.2 In Practice: Adding Covariates to Structural Break Models 332 11.3.3 In Detail: Improving Parameter Mixing in Structural Break Models 333 11.4 In Detail: The Ordinal Probit Model 335 11.4.1 Posterior Simulation in the Ordinal Probit Model 336 11.4.2 In Practice: Modeling Credit Ratings with Ordinal Probit 339 11.5 Summary 341 11.6 Exercises 342 AppendixA Common Statistical Distributions 344 References 346 Author Index 357 Subject Index 361

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Book SynopsisThis book provides a comprehensive introduction to multiple-point geostatistics, where spatial continuity is described using training images. Multiple-point geostatistics aims at bridging the gap between physical modelling/realism and spatio-temporal stochastic modelling. The book provides an overview of this new field in three parts. Part I presents a conceptual comparison between traditional random function theory and stochastic modelling based on training images, where random function theory is not always used. Part II covers in detail various algorithms and methodologies starting from basic building blocks in statistical science and computer science. Concepts such as non-stationary and multi-variate modeling, consistency between data and model, the construction of training images and inverse modelling are treated. Part III covers three example application areas, namely, reservoir modelling, mineral resources modelling and climate model downscaling. This book will be an invaluable rTrade Review"I benefited from this book and plan to keep it as a resource on my bookshelf. I recommend Multiple-point Geostatistics: Stochastic Modeling with Training Images to my peers in mathematical geosciences." (Mathematical Geosciences, 2016)Table of ContentsPreface, vii Acknowledgments, xi Part I Concepts I.1 Hiking in the Sierra Nevada, 3 I.2 Spatial estimation based on random function theory, 7 I.3 Universal kriging with training images, 29 I.4 Stochastic simulations based on random function theory, 49 I.5 Stochastic simulation without random function theory, 59 I.6 Returning to the Sierra Nevada, 75 Part II Methods II.1 Introduction, 87 II.2 The algorithmic building blocks, 91 II.3 Multiple-point geostatistics algorithms, 155 II.4 Markov random fields, 173 II.5 Nonstationary modeling with training images, 183 II.6 Multivariate modeling with training images, 199 II.7 Training image construction, 221 II.8 Validation and quality control, 239 II.9 Inverse modeling with training images, 259 II.10 Parallelization, 295 Part III Applications III.1 Reservoir forecasting – the West Coast of Africa (WCA) reservoir, 303 III.2 Geological resources modeling in mining, 329 Coauthored by Cristian P´erez, Julian M. Ortiz, & Alexandre Boucher III.3 Climate modeling application – the case of the Murray–Darling Basin, 345 Index, 361

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Book SynopsisPraise for the First Edition All medical statisticians involved in clinical trials should read this book - Controlled Clinical Trials Featuring a unique combination of the applied aspects of randomization in clinical trials with a nonparametric approach to inference, Randomization in Clinical Trials: Theory and Practice, Second Edition is the go-to guide for biostatisticians and pharmaceutical industry statisticians. Randomization in Clinical Trials: Theory and Practice, Second Edition features: Discussions on current philosophies, controversies, and new developments in the increasingly important role of randomization techniques in clinical trials A new chapter on covariate-adaptive randomization, including minimization techniques and inference New developments in restricted randomization and an increased focus on computation of randomization tests as opposed to the asyTrade Review"Featuring a unique combination of the applied aspects of randomization in clinical trials with a nonparametric approach to inference, the book is the go-to guide for biostatisticians and pharmaceutical industry statisticians." (Zentralblatt MATH 2016)Table of ContentsPreface xi 1 Randomization and the Clinical Trial 1 1.1 Introduction 1 1.2 Causation and Association 2 1.3 Randomized Clinical Trials 6 1.4 Ethics of Randomization 9 1.5 Problems 12 1.6 References 13 2 Issues in the Design of Clinical Trials 15 2.1 Introduction 15 2.2 Study Outcomes 15 2.3 Sources of Bias 18 2.3.1 Selection and ascertainment bias 19 2.3.2 Statistical analysis philosophy 20 2.3.3 Losses to follow-up and noncompliance 21 2.3.4 Covariates 21 2.4 Experimental Design 23 2.5 Recruitment and Follow-Up 25 2.6 Determining the Number of Randomized Subjects 26 2.6.1 Development of the main formula 27 2.6.2 Example 29 2.6.3 Survival trials 29 2.6.4 Adjustment for noncompliance 32 2.6.5 Additional considerations 32 2.7 Problems 33 2.8 References 34 3 Randomization for Balancing Treatment Assignments 37 3.1 Introduction 37 3.2 Complete Randomization 38 3.3 Forced Balance Procedures 40 3.3.1 Random allocation rule 40 3.3.2 Truncated binomial design 42 3.3.3 Hadamard randomization 44 3.3.4 Maximal procedure 46 3.4 Forced Balance Randomization Within Blocks 46 3.4.1 Permuted block design 46 3.4.2 Random block design 47 3.5 Efron’s Biased Coin Design 48 3.6 Other Biased Coin Designs and Generalizations 51 3.7 Wei’s Urn Design 52 3.8 Other urn Models and Generalizations 54 3.9 Comparison of Balancing Properties 55 3.10 Restricted Randomization for Unbalanced Allocation 58 3.11 K > 2 Treatments 61 3.12 Problems 62 3.13 References 64 3.14 Appendix 66 4 The Effects of Unobserved Covariates 67 4.1 Introduction 67 4.2 A Bound on the Probability of a Covariate Imbalance 68 4.3 Simulation Results 70 4.4 Accidental Bias 71 4.5 Maximum Eigenvalue of 𝚺T 73 4.6 Accidental Bias for Biased Coin Designs 74 4.7 Chronological Bias 75 4.8 Problems 76 4.9 References 76 4.10 Appendix 77 5 Selection Bias 79 5.1 Introduction 79 5.2 The Blackwell–Hodges Model 81 5.3 Predictability of a Randomization Sequence 83 5.4 Selection Bias for the Random Allocation Rule and Truncated Binomial Design 84 5.5 Selection Bias in a Permuted Block Design 87 5.5.1 Permuted blocks using the random allocation rule 87 5.5.2 Permuted blocks with truncated binomial randomization 87 5.5.3 Random block design 87 5.5.4 Conclusions 89 5.6 Selection Bias for Other Restricted Randomization Procedures 90 5.6.1 Efron’s biased coin design 90 5.6.2 Wei’s urn design 90 5.6.3 Smith’s design 91 5.7 Simulation Results 91 5.8 Controlling and Testing for Selection Bias in Practice 93 5.9 Problems 94 5.10 References 94 5.11 Appendix 95 6 Randomization as a Basis for Inference 97 6.1 Introduction 97 6.2 The Population Model 97 6.3 The Randomization Model 100 6.4 Randomization Tests 103 6.5 Linear Rank Tests 105 6.6 Variance of the Linear Rank Test 108 6.7 Optimal Rank Scores 110 6.8 Exact and Large-Sample Randomization Tests 111 6.8.1 Computation of exact tests 112 6.8.2 Large sample randomization tests 113 6.9 Monte Carlo Re-Randomization Tests 115 6.9.1 Unconditional tests 115 6.9.2 Example 116 6.9.3 Conditional tests 117 6.10 Preservation of Error Rates 118 6.11 Regression Modeling 120 6.12 Analyses with Missing Data 121 6.13 Sample Size Considerations for Random Sample Fractions 122 6.14 Group Sequential Monitoring 123 6.14.1 Establishing a stopping boundary 124 6.14.2 Information fraction 125 6.15 Problems 126 6.16 References 127 6.17 Appendix A 129 6.18 Appendix B 131 7 Stratification 133 7.1 Introduction 133 7.2 Stratified Randomization 134 7.3 Is Stratification Necessary? 135 7.4 Treatment Imbalances in Stratified Trials 136 7.5 Stratified Analysis Using Randomization Tests 138 7.6 Efficiency of Stratified Randomization in a Stratified Analysis 140 7.7 Conclusions 144 7.8 Problems 144 7.9 References 145 8 Restricted Randomization in Practice 147 8.1 Introduction 147 8.2 Stratification 148 8.3 Characteristics of Randomization Procedures 149 8.3.1 Consideration of selection bias 149 8.3.2 Implications for analysis 151 8.4 Selecting a Randomization Procedure 151 8.4.1 Choosing parameter values 152 8.4.2 Comparing procedures 153 8.4.3 Conclusions 156 8.5 Generation of Sequences 156 8.6 Implementation 157 8.6.1 Packaging and labeling 158 8.6.2 The actual randomization 159 8.7 Special Situations 160 8.8 Some Examples 163 8.8.1 The optic neuritis treatment trial 163 8.8.2 Vesnarinone in congestive heart failure 163 8.8.3 The diabetes control and complications trial 163 8.8.4 Captopril in diabetic nephropathy 164 8.8.5 The diabetes prevention program 164 8.8.6 Scleral buckling versus primary vitrectomy in retinal detachment (The SPR Study) 164 8.9 Problems 165 8.10 References 166 9 Covariate-Adaptive Randomization 169 9.1 Early Work 169 9.1.1 Zelen’s rule 170 9.1.2 The Pocock–Simon procedure 170 9.1.3 Example: Adjuvant chemotherapy for locally invasive bladder cancer 171 9.1.4 Wei’s marginal urn design 171 9.1.5 Is marginal balance sufficient? 171 9.1.6 Is randomization necessary? 172 9.2 More Recent Covariate-Adaptive Randomization Procedures 173 9.2.1 Balancing within strata 173 9.2.2 Balancing with respect to continuous covariates 174 9.3 Optimal Design Based on a Linear Model 175 9.4 The Trade-Off Among Balance, Efficiency, and Ethics 177 9.5 Inference for Covariate-Adaptive Randomization 179 9.5.1 Model-based inference 179 9.5.2 Randomization-based inference 180 9.6 Conclusions 181 9.7 Problems 182 9.8 References 185 10 Response-Adaptive Randomization 189 10.1 Introduction 189 10.2 Historical Notes 190 10.2.1 Roots in bandit problems 190 10.2.2 Roots in sequential stopping problems 191 10.2.3 Roots in randomization 192 10.3 Optimal Allocation 193 10.4 Response-Adaptive Randomization to Target R∗ 196 10.4.1 Sequential maximum likelihood procedure 196 10.4.2 Doubly adaptive biased coin design 198 10.4.3 Example 200 10.4.4 Efficient randomized-adaptive design 201 10.5 Urn Models 201 10.5.1 The generalized Friedman’s urn model 201 10.5.2 The randomized play-the-winner rule 202 10.5.3 Designs to target any allocation 205 10.5.4 Ternary urn models 206 10.5.5 Klein urn 207 10.6 Treatment Effect Mappings 207 10.7 Covariate-Adjusted Response-Adaptive Randomization 208 10.8 Problems 209 10.9 References 211 10.10 Appendix 214 11 Inference for Response-Adaptive Randomization 217 11.1 Introduction 217 11.2 Population-Based Inference 217 11.2.1 The likelihood 217 11.2.2 Sufficiency 220 11.2.3 Bias of the maximum likelihood estimators 220 11.2.4 Confidence interval procedures 222 11.3 Power 223 11.3.1 The relationship between power and the variability of the design 223 11.3.2 Asymptotically best procedures 225 11.3.3 Response-adaptive randomization and sequential monitoring 226 11.4 Randomization-Based Inference 226 11.5 Problems 228 11.6 References 228 12 Response-Adaptive Randomization in Practice 231 12.1 Basic Assumptions 231 12.2 Bias, Masking, and Consent 232 12.3 Logistical Issues 233 12.4 Selection of A Procedure 234 12.5 Benefits of Response-Adaptive Randomization 236 12.6 Some Examples 237 12.6.1 The extracorporeal membrane oxygenation trial 237 12.6.2 The fluoxetine trial 238 12.7 Conclusions 239 12.8 Problems 240 12.9 References 240 Author Index 243 Subject Index 249

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Book SynopsisA comprehensive guide to implementing SAE methods for poverty studies and poverty mapping There is an increasingly urgent demand for poverty and living conditions data, in relation to local areas and/or subpopulations.Table of ContentsForeword xv Preface xvii Acknowledgements xxiii About the Editor xxv List of Contributors xxvii 1 Introduction on Measuring Poverty at Local Level Using Small Area Estimation Methods 1Monica Pratesi and Nicola Salvati 1.1 Introduction 1 1.2 Target Parameters 2 1.2.1 Definition of the Main Poverty Indicators 2 1.2.2 Direct and Indirect Estimate of Poverty Indicators at Small Area Level 3 1.3 Data-related and Estimation-related Problems for the Estimation of Poverty Indicators 5 1.4 Model-assisted and Model-based Methods Used for the Estimation of Poverty Indicators: a Short Review 7 1.4.1 Model-assisted Methods 7 1.4.2 Model-based Methods 12 References 15 Part I DEFINITION OF INDICATORS AND DATA COLLECTION AND INTEGRATION METHODS 2 Regional and Local Poverty Measures 21Achille Lemmi and Tomasz Panek 2.1 Introduction 21 2.2 Poverty – Dilemmas of Definition 22 2.3 Appropriate Indicators of Poverty and Social Exclusion at Regional and Local Levels 23 2.3.1 Adaptation to the Regional Level 23 2.4 Multidimensional Measures of Poverty 25 2.4.1 Multidimensional Fuzzy Approach to Poverty Measurement 25 2.4.2 Fuzzy Monetary Depth Indicators 26 2.5 Co-incidence of Risks of Monetary Poverty and Material Deprivation 30 2.6 Comparative Analysis of Poverty in EU Regions in 2010 31 2.6.1 Data Source 31 2.6.2 Object of Interest 31 2.6.3 Scope and Assumptions of the Empirical Analysis 32 2.6.4 Risk of Monetary Poverty 32 2.6.5 Risk of Material Deprivation 33 2.6.6 Risk of Manifest Poverty 37 2.7 Conclusions 38 References 39 3 Administrative and Survey Data Collection and Integration 41Alessandra Coli, Paolo Consolini and Marcello D’Orazio 3.1 Introduction 41 3.2 Methods to Integrate Data from Different Data Sources: Objectives and Main Issues 43 3.2.1 Record Linkage 43 3.2.2 Statistical Matching 46 3.3 Administrative and Survey Data Integration: Some Examples of Application in Well-being and Poverty Studies 50 3.3.1 Data Integration for Measuring Disparities in Economic Well-being at the Macro Level 51 3.3.2 Collection and Integration of Data at the Local Level 53 3.4 Concluding Remarks 56 References 57 4 Small Area Methods and Administrative Data Integration 61Li-Chun Zhang and Caterina Giusti 4.1 Introduction 61 4.2 Register-based Small Area Estimation 63 4.2.1 Sampling Error: A Study of Local Area Life Expectancy 63 4.2.2 Measurement Error due to Progressive Administrative Data 65 4.3 Administrative and Survey Data Integration 68 4.3.1 Coverage Error and Finite-population Bias 68 4.3.2 Relevance Error and Benchmarked Synthetic Small Area Estimation 70 4.3.3 Probability Linkage Error 75 4.4 Concluding Remarks 80 References 81 Part II IMPACT OF SAMPLING DESIGN, WEIGHTING AND VARIANCE ESTIMATION 5 Impact of Sampling Designs in Small Area Estimation with Applications to Poverty Measurement 85Jan Pablo Burgard, Ralf Münnich and Thomas Zimmermann 5.1 Introduction 85 5.2 Sampling Designs in our Study 87 5.3 Estimation of Poverty Indicators 90 5.3.1 Design-based Approaches 90 5.3.2 Model-based Estimators 92 5.4 Monte Carlo Comparison of Estimation Methods and Designs 96 5.5 Summary and Outlook 105 Acknowledgements 106 References 106 6 Model-assisted Methods for Small Area Estimation of Poverty Indicators 109Risto Lehtonen and Ari Veijanen 6.1 Introduction 109 6.1.1 General 109 6.1.2 Concepts and Notation 110 6.2 Design-based Estimation of Gini Index for Domains 111 6.2.1 Estimators 111 6.2.2 Simulation Experiments 114 6.2.3 Empirical Application 116 6.3 Model-assisted Estimation of At-risk-of Poverty Rate 117 6.3.1 Assisting Models in GREG and Model Calibration 117 6.3.2 Generalized Regression Estimation 119 6.3.3 Model Calibration Estimation 120 6.3.4 Simulation Experiments 122 6.3.5 Empirical Example 123 6.4 Discussion 124 6.4.1 Empirical Results 124 6.4.2 Inferential Framework 125 6.4.3 Data Infrastructure 125 References 126 7 Variance Estimation for Cumulative and Longitudinal Poverty Indicators from Panel Data at Regional Level 129Gianni Betti, Francesca Gagliardi and Vijay Verma 7.1 Introduction 129 7.2 Cumulative vs. Longitudinal Measures of Poverty 130 7.2.1 Cumulative Measures 130 7.2.2 Longitudinal Measures 131 7.3 Principle Methods for Cross-sectional Variance Estimation 131 7.4 Extension to Cumulation and Longitudinal Measures 133 7.5 Practical Aspects: Specification of Sample Structure Variables 134 7.6 Practical Aspects: Design Effects and Correlation 136 7.6.1 Components of the Design Effect 136 7.6.2 Estimating the Components of Design Effect 138 7.6.3 Estimating other Components using Random Grouping of Elements 139 7.7 Cumulative Measures and Measures of Net Change 140 7.7.1 Estimation of the Measures 140 7.7.2 Variance Estimation 141 7.8 An Application to Three Years’ Averages 141 7.8.1 Computation Given Limited Information on Sample Structure in EU-SILC 141 7.8.2 Direct Computation 144 7.8.3 Empirical Results 145 7.9 Concluding Remarks 146 References 147 Part III SMALL AREA ESTIMATION MODELING AND ROBUSTNESS 8 Models in Small Area Estimation when Covariates are Measured with Error 151Serena Arima, Gauri S. Datta and Brunero Liseo 8.1 Introduction 151 8.2 Functional Measurement Error Approach for Area-level Models 153 8.2.1 Frequentist Method for Functional Measurement Error Models 154 8.2.2 Bayesian Method for Functional Measurement Error Models 156 8.3 Small Area Prediction with a Unit-level Model when an Auxiliary Variable is Measured with Error 156 8.3.1 Functional Measurement Error Approach for Unit-level Models 157 8.3.2 Structural Measurement Error Approach for Unit-level Models 160 8.4 Data Analysis 162 8.4.1 Example 1: Median Income Data 162 8.4.2 Example 2: SAIPE Data 165 8.5 Discussion and Possible Extensions 169 Acknowledgements 169 Disclaimer 170 References 170 9 Robust Domain Estimation of Income-based Inequality Indicators 171Nikos Tzavidis and Stefano Marchetti 9.1 Introduction 171 9.2 Definition of Income-based Inequality Measures 172 9.3 Robust Small Area Estimation of Inequality Measures with M-quantile Regression 173 9.4 Mean Squared Error Estimation 176 9.5 Empirical Evaluations 176 9.6 Estimating the Gini Coefficient and the Quintile Share Ratio for Unplanned Domains in Tuscany 180 9.7 Conclusions 183 References 185 10 Nonparametric Regression Methods for Small Area Estimation 187M. Giovanna Ranalli, F. Jay Breidt and Jean D. Opsomer 10.1 Introduction 187 10.2 Nonparametric Methods in Small Area Estimation 188 10.2.1 Nested Error Nonparametric Unit Level Model Using Penalized Splines 189 10.2.2 Nested Error Nonparametric Unit Level Model Using Kernel Methods 191 10.2.3 Generalized Responses 192 10.2.4 Robust Approaches 192 10.3 A Comparison for the Estimation of the Household Per-capita Consumption Expenditure in Albania 195 10.4 Concluding Remarks 202 References 202 Part IV SPATIO-TEMPORAL MODELING OF POVERTY 11 Area-level Spatio-temporal Small Area Estimation Models 207María Dolores Esteban, Domingo Morales and Agustín Pérez 11.1 Introduction 207 11.2 Extensions of the Fay–Herriot Model 209 11.3 An Area-level Model with MA(1) Time Correlation 212 11.4 EBLUP and MSE 214 11.5 EBLUP of Poverty Proportions 215 11.6 Simulations 216 11.6.1 Simulation 1 216 11.6.2 Simulation 2 217 11.7 R Codes 220 11.8 Concluding Remarks 220 Appendix 11.A: MSE Components 221 11.A.1 Calculation of g1(𝜽) 221 11.A.2 Calculation of g2(𝜽) 221 11.A.3 Calculation of g3(𝜽) 222 Acknowledgements 224 References 224 12 Unit Level Spatio-temporal Models 227Maria Chiara Pagliarella and Renato Salvatore 12.1 Unit Level Models 230 12.2 Spatio-temporal Time-varying Effects Models 232 12.3 State Space Models with Spatial Structure 234 12.4 The Italian EU-SILC Data: an Application with the Spatio-temporal Unit Level Models 236 12.5 Concluding Remarks 239 Appendix 12.A: Restricted Maximum Likelihood Estimation 240 Appendix 12.B: Mean Squared Error Estimation of the Unit Level State Space Model 241 References 242 13 Spatial Information and Geoadditive Small Area Models 245Chiara Bocci and Alessandra Petrucci 13.1 Introduction 245 13.2 Geoadditive Models 247 13.3 Geoadditive Small Area Model for Skewed Data 248 13.4 Small Area Mean Estimators 250 13.5 Estimation of the Household Per-capita Consumption Expenditure in Albania 251 13.5.1 Data 251 13.5.2 Results 253 13.6 Concluding Remarks and Open Questions 258 Acknowledgement 259 References 259 Part V SMALL AREA ESTIMATION OF THE DISTRIBUTION FUNCTION OF INCOME AND INEQUALITIES 14 Model-based Direct Estimation of a Small Area Distribution Function 263Hukum Chandra, Nicola Salvati and Ray Chambers 14.1 Introduction 263 14.2 Estimation of the Small Area Distribution Function 264 14.3 Model-based Direct Estimator for the Estimation of the Distribution Function of Equivalized Income in the Toscana, Lombardia and Campania Provinces of Italy 268 14.4 Final Remarks 275 References 276 15 Small Area Estimation for Lognormal Data 279Emily Berg, Hukum Chandra and Ray Chambers 15.1 Introduction 279 15.2 Literature on Small Area Estimation for Skewed Data 280 15.3 Small Area Predictors for a Unit-Level Lognormal Model 282 15.3.1 The Linear Unit-Level Mixed Model 282 15.3.2 A Synthetic Estimator 283 15.3.3 A Model-Based Direct Estimator 285 15.3.4 An Empirical Bayes Predictor 286 15.4 Simulations 287 15.4.1 Comparison of Synthetic, TrMBDE, and EB Predictors 287 15.4.2 Bias and Robustness of the EB Predictor 291 15.4.3 Comparison of Lognormal and Gamma Distributions 291 15.5 Concluding Remarks 294 Appendix 15.A: Mean Squared Error Estimation for the Empirical Best Predictor 295 References 296 16 Bayesian Beta Regression Models for the Estimation of Poverty and Inequality Parameters in Small Areas 299Enrico Fabrizi, Maria Rosaria Ferrante and Carlo Trivisano 16.1 Introduction 299 16.2 Direct Estimation 300 16.3 Small Area Estimation of the At-risk-of-poverty Rate 302 16.3.1 The Model 302 16.3.2 Data Analysis 304 16.4 Small Area Estimation of the Material Deprivation Rates 305 16.4.1 The Model 305 16.4.2 Data Analysis 306 16.5 Joint Estimation of the At-risk-of-poverty Rate and the Gini Coefficient 308 16.5.1 The Models 308 16.5.2 Data Analysis 310 16.6 A Short Description of Markov Chain Monte Carlo Algorithms and R Software Codes 312 16.7 Concluding Remarks 312 References 313 17 Empirical Bayes and Hierarchical Bayes Estimation of Poverty Measures for Small Areas 315John N. K. Rao and Isabel Molina 17.1 Introduction 315 17.2 Poverty Measures 316 17.3 Fay–Herriot Area Level Model 317 17.4 Unit Level Nested Error Linear Regression Model 319 17.4.1 ELL/World Bank Method 319 17.4.2 Empirical Bayes Method 321 17.4.3 Hierarchical Bayes Method 322 17.5 Application 323 17.6 Concluding Remarks 324 References 324 Part VI DATA ANALYSIS AND APPLICATIONS 18 Small Area Estimation Using Both Survey and Census Unit Record Data 327Stephen J. Haslett 18.1 Introduction 327 18.2 The ELL Implementation Process and Methodology 329 18.2.1 ELL: Implementation Process 329 18.2.2 ELL Methodology: Survey Regression, Contextual Effects, Clustering, and the Bootstrap 331 18.2.3 Fitting Survey-based Models 334 18.2.4 Residuals and the Bootstrap 335 18.2.5 ELL: Linkages to Other Related Methods 338 18.3 ELL – Advantages, Criticisms and Disadvantages 339 18.4 Conclusions 344 References 346 19 An Overview of the U.S. Census Bureau’s Small Area Income and Poverty Estimates Program 349William R. Bell, Wesley W. Basel and Jerry J. Maples 19.1 Introduction 349 19.2 U.S. Poverty Measure and Poverty Data Sources 351 19.2.1 Poverty Measure and Survey Data Sources 351 19.2.2 Administrative Data Sources Used for Covariate Information 354 19.3 SAIPE Poverty Models and Estimation Procedures 356 19.3.1 State Poverty Models 357 19.3.2 County Poverty Models 363 19.3.3 School District Poverty Estimation 368 19.3.4 Major Changes Made in SAIPE Models and Estimation Procedures 372 19.4 Current Challenges and Recent SAIPE Research 374 19.5 Conclusions 375 References 376 20 Poverty Mapping for the Chilean Comunas 379Carolina Casas-Cordero Valencia, Jenny Encina and Partha Lahiri 20.1 Introduction 379 20.2 Chilean Poverty Measures and Casen 381 20.2.1 The Poverty Measure Used in Chile 381 20.2.2 The Casen Survey 382 20.3 Data Preparation 383 20.3.1 Comuna Level Data Derived from Casen 2009 383 20.3.2 Comuna Level Administrative Data 387 20.4 Description of the Small Area Estimation Method Implemented in Chile 391 20.4.1 Modeling 394 20.4.2 Estimation of A and 𝛽 395 20.4.3 Empirical Bayes Estimator of 𝜃i 395 20.4.4 Limited Translation Empirical Bayes Estimator of 𝜃i 395 20.4.5 Back-transformation and raking 396 20.4.6 Confidence intervals for the poverty rates 396 20.5 Data Analysis 397 20.6 Discussion 399 Acknowledgements 401 References 402 21 Appendix on Software and Codes Used in the Book 405Antonella D’Agostino, Francesca Gagliardi and Laura Neri 21.1 Introduction 405 21.2 R and SAS Software: a Brief Note 406 21.3 Getting Started: EU-SILC Data 409 21.4 A Quick Guide to the Scripts 410 21.4.1 Basics of the Scripts 410 21.4.2 A Quick guide to Chapter 5 (Impact of Sampling Designs in Small Area Estimation with Applications to Poverty Measurement) 412 21.4.3 A Quick guide to Chapter 6 (Model-assisted Methods for Small Area Estimation of Poverty Indicators) 412 21.4.4 A Quick Guide to Chapter 7 (Variance Estimation for Cumulative and Longitudinal Poverty Indicators from Panel Data at Regional Level) 414 21.4.5 A Quick Guide to Chapter 8 (Models in Small Area Estimation when Covariates are Measured with Error) 415 21.4.6 A Quick Guide to Chapter 9 (Robust Domain Estimation of Income-based Inequality Indicators) 416 21.4.7 A Quick Guide to Chapter 10 (Nonparametric Regression Methods for Small Area Estimation) 417 21.4.8 A Quick Guide to Chapter 11 (Area-level Spatio-temporal Small Area Estimation Models) 418 21.4.9 A Quick Guide to Chapter 12 (Unit Level Spatio-temporal Models) 419 21.4.10 A Quick Guide to Chapter 13 (Spatial Information and Geoadditive Small Area Models) 420 21.4.11 A Quick guide to Chapter 14 (Model-based Direct Estimation of a Small Area Distribution Function) 422 21.4.12 A Quick Guide to Chapter 16 (Bayesian Beta Regression Models for the Estimation of Poverty and Inequality Parameters in Small Areas) 423 21.4.13 A Quick Guide to Chapter 17 (Empirical Bayes and Hierarchical Bayes Estimation of Poverty Measures for Small Areas) 424 21.4.14 A Quick Guide to Chapter 18 - (Small Area Estimation Using Both Survey and Census Unit Record Data: Links, Alternatives, and the Central Roles of Regression and Contextual Variables) 425 References 426 Author Index 427 Subject Index 431

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Book SynopsisAn introduction to the mathematical theory and financial models developed and used on Wall Street Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models. The authors promote a problem-solving approach when applying mathematics in real-wTable of ContentsPreface xvii Financial Glossary xxii Part I Measure Theory 1 Sets and Sequences 3 2 Measures 15 3 Extension of Measures 29 4 Lebesgue-Stieltjes Measures 37 5 Measurable Functions 47 6 Lebesgue Integration 57 7 The Radon-Nikodym Theorem 77 8 LP Spaces 85 9 Convergence 97 10 Product Measures 113 Part II Probability Theory 11 Events and Random Variables 127 12 Independence 141 13 Expectation 161 14 Conditional Expectation 173 15 Inequalities 189 16 Law of Large Numbers 199 17 Characteristic Functions 217 18 Discrete Distributions 227 19 Continuous Distributions 239 20 Central Limit Theorems 257 Part III Stochastic Processes 21 Stochastic Processes 271 22 Martingales 291 23 Stopping Times 301 24 Martingale Inequalities 321 25 Martingale Convergence Theorems 333 26 Random Walks 343 27 Poisson Processes 357 28 Brownian Motion 373 29 Markov Processes 389 30 Lévy Processes 401 Part IV Stochastic Calculus 31 The Wiener Integral 421 32 The Itô Integral 431 33 Extension of the Itô Integral 453 34 Martingale Stochastic Integrals 463 35 The Itô Formula 477 36 Martingale Representation Theorem 495 37 Change of Measure 503 38 Stochastic Differential Equations 515 39 Diffusion 531 40 The Feynman-Kac Formula 547 Part V Stochastic Financial Models 41 Discrete-Time Models 561 42 Black-Scholes Option Pricing Models 579 43 Path-Dependent Options 593 44 American Options 609 45 Short Rate Models 629 46 Instantaneous Forward Rate Models 647 47 LIBOR Market Models 667 References 687 List of Symbols 703 Subject Index 707

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Book SynopsisADVANCES IN HEAVY TAILED RISK MODELING A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes. A companion with Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the handbook provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed forTable of Contents1 Motivation for Heavy-Tailed Models 1 2 Fundamentals of Extreme Value Theory for OpRisk 17 3 Heavy-Tailed Model Class Characterizations for LDA 105 4 Flexible Heavy-Tailed Severity Models: α-Stable Family 139 5 Flexible Heavy-Tailed Severity Models: Tempered Stable and Quantile Transforms 227 6 Families of Closed-Form Single Risk LDA Models 279 7 Single Risk Closed-Form Approximations of Asymptotic Tail Behaviour 353 8 Single Loss Closed-Form Approximations of Risk Measures 433 9 Recursions for Distributions of LDA Models 517 A Miscellaneous Definitions and List of Distributions 587

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Book SynopsisEssential Statistics for the Pharmaceutical Sciences is targeted at all those involved in research in pharmacology, pharmacy or other areas of pharmaceutical science; everybody from undergraduate project students to experienced researchers should find the material they need. This book will guide all those who are not specialist statisticians in using sound statistical principles throughout the whole journey of a research project - designing the work, selecting appropriate statistical methodology and correctly interpreting the results. It deliberately avoids detailed calculation methodology. Its key features are friendliness and clarity. All methods are illustrated with realistic examples from within pharmaceutical science. This edition now includes expanded coverage of some of the topics included in the first edition and adds some new topics relevant to pharmaceutical research. a clear, accessible introduction to the key statistical techniques used Table of ContentsPreface xiii Statistical packages xix About the Website xxi PART 1: PRESENTING DATA 1 1 Data types 3 1.1 Does it really matter? 3 1.2 Interval scale data 4 1.3 Ordinal scale data 4 1.4 Nominal scale data 5 1.5 Structure of this book 6 1.6 Chapter summary 6 2 Data presentation 7 2.1 Numerical tables 8 2.2 Bar charts and histograms 9 2.3 Pie charts 14 2.4 Scatter plots 16 2.5 Pictorial symbols 21 2.6 Chapter summary 22 PART 2: INTERVAL-SCALE DATA 23 3 Descriptive statistics for interval scale data 25 3.1 Summarising data sets 25 3.2 Indicators of central tendency: Mean, median and mode 26 3.3 Describing variability – Standard deviation and coefficient of variation 33 3.4 Quartiles – Another way to describe data 36 3.5 Describing ordinal data 40 3.6 Using computer packages to generate descriptive statistics 43 3.7 Chapter summary 45 4 The normal distribution 47 4.1 What is a normal distribution? 47 4.2 Identifying data that are not normally distributed 48 4.3 Proportions of individuals within 1SD or 2SD of the mean 52 4.4 Skewness and kurtosis 54 4.5 Chapter summary 57 4.6 Appendix: Power, sample size and the problem of attempting to test for a normal distribution 58 5 Sampling from populations. The standard error of the mean 63 5.1 Samples and populations 63 5.2 From sample to population 65 5.3 Types of sampling error 65 5.4 What factors control the extent of random sampling error when estimating a population mean? 68 5.5 Estimating likely sampling error – The SEM 70 5.6 Offsetting sample size against SD 74 5.7 Chapter summary 75 6 95% Confidence Interval for the Mean and Data Transformation 77 6.1 What is a confidence interval? 78 6.2 How wide should the interval be? 78 6.3 What do we mean by ‘95%’ confidence? 79 6.4 Calculating the interval width 80 6.5 A long series of samples and 95% C.I.s 81 6.6 How sensitive is the width of the C.I. to changes in the SD, the sample size or the required level of confidence? 82 6.7 Two statements 85 6.8 One-sided 95% C.I.s 85 6.9 The 95% C.I. for the difference between two treatments 88 6.10 The need for data to follow a normal distribution and data transformation 90 6.11 Chapter summary 94 7 The two-sample t-test (1): Introducing hypothesis tests 95 7.1 The two-sample t-test – an example of an hypothesis test 96 7.2 Significance 103 7.3 The risk of a false positive finding 104 7.4 What aspects of the data will influence whether or not we obtain a significant outcome? 106 7.5 Requirements for applying a two-sample t-test 108 7.6 Performing and reporting the test 109 7.7 Chapter summary 110 8 The two]sample t-test (2): The dreaded P value 111 8.1 Measuring how significant a result is 111 8.2 P values 112 8.3 Two ways to define significance? 113 8.4 Obtaining the P value 113 8.5 P values or 95% confidence intervals? 114 8.6 Chapter summary 115 9 The two-sample t-test (3): False negatives, power and necessary sample sizes 117 9.1 What else could possibly go wrong? 118 9.2 Power 119 9.3 Calculating necessary sample size 122 9.4 Chapter summary 130 10 The two-sample t-test (4): Statistical significance, practical significance and equivalence 131 10.1 Practical significance – Is the difference big enough to matter? 131 10.2 Equivalence testing 135 10.3 Non-inferiority testing 139 10.4 P values are less informative and can be positively misleading 141 10.5 Setting equivalence limits prior to experimentation 143 10.6 Chapter summary 144 11 The two-sample t-test (5): One-sided testing 145 11.1 Looking for a change in a specified direction 146 11.2 Protection against false positives 148 11.3 Temptation! 149 11.4 Using a computer package to carry out a one-sided test 153 11.5 Chapter summary 153 12 What does a statistically significant result really tell us? 155 12.1 Interpreting statistical significance 155 12.2 Starting from extreme scepticism 159 12.3 Bayesian statistics 160 12.4 Chapter summary 161 13 The paired t-test: Comparing two related sets of measurements 163 13.1 Paired data 163 13.2 We could analyse the data by a two-sample t]test 165 13.3 Using a paired t-test instead 165 13.4 Performing a paired t-test 166 13.5 What determines whether a paired t-test will be significant? 169 13.6 Greater power of the paired t-test 170 13.7 Applicability of the test 170 13.8 Choice of experimental design 171 13.9 Requirement for applying a paired t-test 172 13.10 Sample sizes, practical significance and one-sided tests 173 13.11 Summarising the differences between paired and two-sample t-tests 175 13.12 Chapter summary 175 14 Analyses of variance: Going beyond t-tests 177 14.1 Extending the complexity of experimental designs 177 14.2 One-way analysis of variance 178 14.3 Two-way analysis of variance 188 14.4 Fixed and random factors 198 14.5 Multi-factorial experiments 204 14.6 Chapter summary 204 15 Correlation and regression – Relationships between measured values 207 15.1 Correlation analysis 208 15.2 Regression analysis 218 15.3 Multiple regression 225 15.4 Chapter summary 235 16 Analysis of Covariance 237 16.1 A clinical trial where ANCOVA would be appropriate 238 16.2 General interpretation of ANCOVA results 239 16.3 Analysis of the COPD trial results 241 16.4 Advantages of ANCOVA over a simple two]sample t]test 244 16.5 Chapter summary 249 PART 3: NOMINAL-SCALE DATA 251 17 Describing categorised data and the goodness of fit chi-square test 253 17.1 Descriptive statistics 254 17.2 Testing whether the population proportion might credibly be some pre-determined figure 258 17.3 Chapter summary 264 18 Contingency chi-square, Fisher’s and McNemar’s tests 265 18.1 Using the contingency chi]square test to compare observed proportions 266 18.2 Extent of change in proportion with an expulsion – Clinically significant? 270 18.3 Larger tables – Attendance at diabetic clinics 270 18.4 Planning experimental size 273 18.5 Fisher’s exact test 275 18.6 McNemar’s test 277 18.7 Chapter summary 279 18.8 Appendix 280 19 Relative Risk, Odds Ratio and Number Needed to Treat 283 19.1 Measures of treatment effect – Relative Risk, Odds Ratio and Number Needed to Treat 283 19.2 Similarity between Relative Risk and Odds Ratio 287 19.3 Interpreting the various measures 288 19.4 95% confidence intervals for measures of effect size 289 19.5 Chapter summary 293 20 Logistic regression 295 20.1 Modelling a binary outcome 295 20.2 Additional predictors and the problem of confounding 304 20.3 Analysis by computer package 307 20.4 Extending logistic regression beyond dichotomous outcomes 308 20.5 Chapter summary 309 20.6 Appendix 309 PART 4: ORDINAL-SCALE DATA 311 21 Ordinal and non-normally distributed data. Transformations and non-parametric tests 313 21.1 Transforming data to a normal distribution 314 21.2 The Mann–Whitney test – a non]parametric method 318 21.3 Dealing with ordinal data 323 21.4 Other non-parametric methods 325 21.5 Chapter summary 333 21.6 Appendix 334 PART 5: OTHER TOPICS 337 22 Measures of agreement 339 22.1 Answers to several questions 340 22.2 Several answers to one question – do they agree? 344 22.3 Chapter summary 358 23 Survival analysis 361 23.1 What special problems arise with survival data? 362 23.2 Kaplan–Meier survival estimation 363 23.3 Declining sample sizes in survival studies 369 23.4 Precision of sampling estimates of survival 369 23.5 Indicators of survival 371 23.6 Testing for differences in survival 374 23.7 Chapter summary 383 24 Multiple testing 385 24.1 What is it and why is it a problem? 385 24.2 Where does multiple testing arise? 386 24.3 Methods to avoid false positives 388 24.4 The role of scientific journals 392 24.5 Chapter summary 393 25 Questionnaires 395 25.1 Types of questions 396 25.2 Sample sizes and low return rates 398 25.3 Analysing the results 399 25.4 Problem number two: Confounded questionnaire data 401 25.5 Problem number three: Multiple testing with questionnaire data 401 25.6 Chapter summary 403 Index 000

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Book SynopsisPraise for the Third Edition: This new third edition has been substantially rewritten and updated with new topics and material, new examples and exercises, and to more fully illustrate modern applications of RSM. - Zentralblatt Math Featuring a substantial revision, the Fourth Edition of Response Surface Methodology: Process and Product Optimization Using Designed Experiments presents updated coverage on the underlying theory and applications of response surface methodology (RSM). Providing the assumptions and conditions necessary to successfully apply RSM in modern applications, the new edition covers classical and modern response surface designs in order to present a clear connection between the designs and analyses in RSM. With multiple revised sections with new topics and expanded coverage, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Fourth EditionTable of ContentsPreface xiii 1 Introduction 1 1.1 Response Surface Methodology, 1 1.1.1 Approximating Response Functions, 2 1.1.2 The Sequential Nature of RSM, 7 1.1.3 Objectives and Typical Applications of RSM, 9 1.1.4 RSM and the Philosophy of Quality Improvement, 11 1.2 Product Design and Formulation (Mixture Problems), 11 1.3 Robust Design and Process Robustness Studies, 12 1.4 Useful References on RSM, 12 2 Building Empirical Models 13 2.1 Linear Regression Models, 13 2.2 Estimation of the Parameters in Linear Regression Models, 14 2.3 Properties of the Least Squares Estimators and Estimation of 𝜎2, 22 2.4 Hypothesis Testing in Multiple Regression, 24 2.4.1 Test for Significance of Regression, 24 2.4.2 Tests on Individual Regression Coefficients and Groups of Coefficients, 27 2.5 Confidence Intervals in Multiple Regression, 31 2.5.1 Confidence Intervals on the Individual Regression Coefficients β, 32 2.5.2 A Joint Confidence Region on the Regression Coefficients β, 32 2.5.3 Confidence Interval on the Mean Response, 33 2.6 Prediction of New Response Observations, 35 2.7 Model Adequacy Checking, 36 2.7.1 Residual Analysis, 36 2.7.2 Scaling Residuals, 38 2.7.3 Influence Diagnostics, 42 2.7.4 Testing for Lack of Fit, 43 2.8 Fitting a Second-Order Model, 47 2.9 Qualitative Regressor Variables, 55 2.10 Transformation of the Response Variable, 61 Exercises, 66 3 Two-Level Factorial Designs 81 3.1 Introduction, 81 3.2 The 22 Design, 82 3.3 The 23 Design, 94 3.4 The General 2k Design, 103 3.5 A Single Replicate of the 2k Design, 108 3.6 2k Designs are Optimal Designs, 125 3.7 The Addition of Center Points to the 2k Design, 130 3.8 Blocking in the 2k Factorial Design, 135 3.8.1 Blocking in the Replicated Design, 135 3.8.2 Confounding in the 2k Design, 137 3.9 Split-Plot Designs, 141 Exercises, 146 4 Two-Level Fractional Factorial Designs 161 4.1 Introduction, 161 4.2 The One-Half Fraction of the 2k Design, 162 4.3 The One-Quarter Fraction of the 2k Design, 174 4.4 The General 2k−p Fractional Factorial Design, 184 4.5 Resolution III Designs, 188 4.6 Resolution IV and V Designs, 197 4.7 Alias Structures in Fractional Factorial and Other Designs, 198 4.8 Nonregular Fractional Factorial Designs, 200 4.8.1 Nonregular Fractional Factorial Designs for 6, 7, and 8 Factors in 16 Runs, 203 4.8.2 Nonregular Fractional Factorial Designs for 9 Through 14 Factors in 16 Runs, 209 4.8.3 Analysis of Nonregular Fractional Factorial Designs, 213 4.9 Fractional Factorial Split-Plot Designs, 216 4.10 Summary, 219 Exercises, 220 5 Process Improvement with Steepest Ascent 233 5.1 Determining the Path of Steepest Ascent, 234 5.1.1 Development of the Procedure, 234 5.1.2 Practical Application of the Method of Steepest Ascent, 237 5.2 Consideration of Interaction and Curvature, 241 5.2.1 What About a Second Phase?, 244 5.2.2 What Happens Following Steepest Ascent?, 244 5.3 Effect of Scale (Choosing Range of Factors), 245 5.4 Confidence Region for Direction of Steepest Ascent, 247 5.5 Steepest Ascent Subject to a Linear Constraint, 250 5.6 Steepest Ascent in a Split-Plot Experiment, 254 Exercises, 262 6 The Analysis of Second-Order Response Surfaces 273 6.1 Second-Order Response Surface, 273 6.2 Second-Order Approximating Function, 274 6.2.1 The Nature of the Second-Order Function and Second-Order Surface, 274 6.2.2 Illustration of Second-Order Response Surfaces, 276 6.3 A Formal Analytical Approach to the Second-Order Model, 277 6.3.1 Location of the Stationary Point, 278 6.3.2 Nature of the Stationary Point (Canonical Analysis), 278 6.3.3 Ridge Systems, 282 6.3.4 Role of Contour Plots, 286 6.4 Ridge Analysis of the Response Surface, 289 6.4.1 Benefits of Ridge Analysis, 290 6.4.2 Mathematical Development of Ridge Analysis, 291 6.5 Sampling Properties of Response Surface Results, 296 6.5.1 Standard Error of Predicted Response, 296 6.5.2 Confidence Region on the Location of the Stationary Point, 299 6.5.3 Use and Computation of the Confidence Region on the Location of the Stationary Point, 300 6.5.4 Confidence Intervals on Eigenvalues in Canonical Analysis, 304 6.6 Further Comments Concerning Response Surface Analysis, 307 Exercises, 307 7 Multiple Response Optimization 325 7.1 Balancing Multiple Objectives, 325 7.2 Strategies for Multiple Response Optimization, 338 7.2.1 Overlaying Contour Plots, 339 7.2.2 Constrained Optimization, 340 7.2.3 Desirability Functions, 341 7.2.4 Pareto Front Optimization, 343 7.2.5 Other Options for Optimization, 349 7.3 A Sequential Process for Optimization—DMRCS, 350 7.4 Incorporating Uncertainty of Response Predictions into Optimization, 352 Exercises, 357 8 Design of Experiments for Fitting Response Surfaces—I 369 8.1 Desirable Properties of Response Surface Designs, 369 8.2 Operability Region, Region of Interest, and Metrics for Desirable Properties, 371 8.2.1 Metrics for Desirable Properties, 372 8.2.2 Model Inadequacy and Model Bias, 373 8.3 Design of Experiments for First-Order Models and First-Order Models with Interactions, 375 8.3.1 The First-Order Orthogonal Design, 376 8.3.2 Orthogonal Designs for Models Containing Interaction, 378 8.3.3 Other First-Order Orthogonal Designs—The Simplex Design, 381 8.3.4 Definitive Screening Designs, 385 8.3.5 Another Variance Property—Prediction Variance, 389 8.4 Designs for Fitting Second-Order Models, 393 8.4.1 The Class of Central Composite Designs, 393 8.4.2 Design Moments and Property of Rotatability, 399 8.4.3 Rotatability and the CCD, 403 8.4.4 More on Prediction Variance—Scaled, Unscaled, and Estimated, 406 8.4.5 The Face-Centered Cube in Cuboidal Regions, 408 8.4.6 Choosing between Spherical and Cuboidal Regions, 411 8.4.7 The Box–Behnken Design, 413 8.4.8 Definitive Screening Designs for Fitting Second-Order Models, 417 8.4.9 Orthogonal Blocking in Second-Order Designs, 422 Exercises, 434 9 Experimental Designs for Fitting Response Surfaces—II 451 9.1 Designs that Require a Relatively Small Run Size, 452 9.1.1 The Hoke Designs, 452 9.1.2 Koshal Design, 454 9.1.3 Hybrid Designs, 455 9.1.4 The Small Composite Design, 458 9.1.5 Some Saturated or Near-Saturated Cuboidal Designs, 462 9.1.6 Equiradial Designs, 463 9.2 General Criteria for Constructing, Evaluating, and Comparing Designed Experiments, 465 9.2.1 Practical Design Optimality, 467 9.2.2 Use of Design Efficiencies for Comparison of Standard Second-Order Designs, 474 9.2.3 Graphical Procedure for Evaluating the Prediction Capability of an RSM Design, 477 9.3 Computer-Generated Designs in RSM, 488 9.3.1 Important Relationship Between Prediction Variance and Design Augmentation for D-Optimality, 491 9.3.2 Algorithms for Computer-Generated Designs, 494 9.3.3 Comparison of D-, G-, and I-Optimal Designs, 497 9.3.4 Illustrations Involving Computer-Generated Design, 499 9.3.5 Computer-Generated Designs Involving Qualitative Variables, 508 9.4 Multiple Objective Computer-Generated Designs for RSM, 517 9.4.1 Pareto Front Optimization for Selecting a Design, 518 9.4.2 Pareto Aggregating Point Exchange Algorithm, 519 9.4.3 Using DMRCS for Design Optimization, 520 9.5 Some Final Comments Concerning Design Optimality and Computer-Generated Design, 525 Exercises, 527 10 Advanced Topics in Response Surface Methodology 543 10.1 Effects of Model Bias on the Fitted Model and Design, 543 10.2 A Design Criterion Involving Bias and Variance, 547 10.2.1 The Case of a First-Order Fitted Model and Cuboidal Region, 550 10.2.2 Minimum Bias Designs for a Spherical Region of Interest, 556 10.2.3 Simultaneous Consideration of Bias and Variance, 558 10.2.4 How Important Is Bias?, 558 10.3 Errors in Control of Design Levels, 560 10.4 Experiments with Computer Models, 563 10.4.1 Design for Computer Experiments, 567 10.4.2 Analysis for Computer Experiments, 570 10.4.3 Combining Information from Physical and Computer Experiments, 574 10.5 Minimum Bias Estimation of Response Surface Models, 575 10.6 Neural Networks, 579 10.7 Split-Plot Designs for Second-Order Models, 581 10.8 RSM for Non-Normal Responses—Generalized Linear Models, 591 10.8.1 Model Framework: The Link Function, 592 10.8.2 The Canonical Link Function, 593 10.8.3 Estimation of Model Coefficients, 593 10.8.4 Properties of Model Coefficients, 595 10.8.5 Model Deviance, 595 10.8.6 Overdispersion, 597 10.8.7 Examples, 598 10.8.8 Diagnostic Plots and Other Aspects of the GLM, 605 Exercises, 609 11 Robust Parameter Design and Process Robustness Studies 619 11.1 Introduction, 619 11.2 What is Parameter Design?, 619 11.2.1 Examples of Noise Variables, 620 11.2.2 An Example of Robust Product Design, 621 11.3 The Taguchi Approach, 622 11.3.1 Crossed Array Designs and Signal-to-Noise Ratios, 622 11.3.2 Analysis Methods, 625 11.3.3 Further Comments, 630 11.4 The Response Surface Approach, 631 11.4.1 The Role of the Control × Noise Interaction, 631 11.4.2 A Model Containing Both Control and Noise Variables, 635 11.4.3 Generalization of Mean and Variance Modeling, 638 11.4.4 Analysis Procedures Associated with the Two Response Surfaces, 642 11.4.5 Estimation of the Process Variance, 651 11.4.6 Direct Variance Modeling, 655 11.4.7 Use of Generalized Linear Models, 657 11.5 Experimental Designs For RPD and Process Robustness Studies, 661 11.5.1 Combined Array Designs, 661 11.5.2 Second-Order Designs, 663 11.5.3 Other Aspects of Design, 665 11.6 Dispersion Effects in Highly Fractionated Designs, 672 11.6.1 The Use of Residuals, 673 11.6.2 Further Diagnostic Information from Residuals, 674 11.6.3 Further Comments Concerning Variance Modeling, 680 Exercises, 684 12 Experiments with Mixtures 693 12.1 Introduction, 693 12.2 Simplex Designs and Canonical Mixture Polynomials, 696 12.2.1 Simplex Lattice Designs, 696 12.2.2 The Simplex-Centroid Design and Its Associated Polynomial, 704 12.2.3 Augmentation of Simplex Designs with Axial Runs, 707 12.3 Response Trace Plots, 716 12.4 Reparameterizing Canonical Mixture Models to Contain A Constant Term (𝛽0), 716 Exercises, 720 13 Other Mixture Design and Analysis Techniques 731 13.1 Constraints on the Component Proportions, 731 13.1.1 Lower-Bound Constraints on the Component Proportions, 732 13.1.2 Upper-Bound Constraints on the Component Proportions, 743 13.1.3 Active Upper- and Lower-Bound Constraints, 747 13.1.4 Multicomponent Constraints, 758 13.2 Mixture Experiments Using Ratios of Components, 759 13.3 Process Variables in Mixture Experiments, 763 13.3.1 Mixture-Process Model and Design Basics, 763 13.3.2 Split-Plot Designs for Mixture-Process Experiments, 767 13.3.3 Robust Parameter Designs for Mixture-Process Experiments, 778 13.4 Screening Mixture Components, 783 Exercises, 785 Appendix 1 Moment Matrix of a Rotatable Design 797 Appendix 2 Rotatability of a Second-Order Equiradial Design 803 References 807 Index 821

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Book SynopsisCategorical Statistics for CommunicationResearch presents scholars with a discipline-specific guide to categorical data analysis. The text blends necessary background information and formulas for statistical procedures with data analyses illustrating techniques such as log- linear modeling and logistic regression analysis.Table of ContentsDetailed Contents ix Preface xiii Acknowledgments xix About the Companion Website xx 1. Introduction to Categorical Statistics 1 2. Univariate Goodness of Fit and Contingency Tables in Two Dimensions 12 3. Contingency Tables in Three Dimensions 41 4. Log-linear Analysis 58 5. Logit Log-linear Analysis 90 6. Binary Logistic Regression 119 7. Multinomial Logistic Regression 153 8. Ordinal Logistic Regression 171 9. Probit Analysis 198 10. Poisson and Negative Binomial Regression 216 11. Interrater Agreement Measures for Nominal and Ordinal Data 232 12. Concluding Communication 255 Appendix A: Chi]Square Table 259 Appendix B: SPSS Code for Selected Procedures 261 Index 266

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Book SynopsisAn up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors Additional problems and chapter-end practice exercises at the end of each chapter Table of ContentsPreface xi About the Companion Website xv 1 A Review of Elementary Matrix Algebra 1 1.1 Introduction 1 1.2 Definitions and Notation 1 1.3 Matrix Addition and Multiplication 2 1.4 The Transpose 3 1.5 The Trace 4 1.6 The Determinant 5 1.7 The Inverse 9 1.8 Partitioned Matrices 12 1.9 The Rank of a Matrix 14 1.10 Orthogonal Matrices 15 1.11 Quadratic Forms 16 1.12 Complex Matrices 18 1.13 Random Vectors and Some Related Statistical Concepts 19 Problems 29 2 Vector Spaces 35 2.1 Introduction 35 2.2 Definitions 35 2.3 Linear Independence and Dependence 42 2.4 Matrix Rank and Linear Independence 45 2.5 Bases and Dimension 49 2.6 Orthonormal Bases and Projections 53 2.7 Projection Matrices 58 2.8 Linear Transformations and Systems of Linear Equations 65 2.9 The Intersection and Sum of Vector Spaces 73 2.10 Oblique Projections 76 2.11 Convex Sets 80 Problems 85 3 Eigenvalues and Eigenvectors 95 3.1 Introduction 95 3.2 Eigenvalues, Eigenvectors, and Eigenspaces 95 3.3 Some Basic Properties of Eigenvalues and Eigenvectors 99 3.4 Symmetric Matrices 106 3.5 Continuity of Eigenvalues and Eigenprojections 114 3.6 Extremal Properties of Eigenvalues 116 3.7 Additional Results Concerning Eigenvalues Of Symmetric Matrices 123 3.8 Nonnegative Definite Matrices 129 3.9 Antieigenvalues and Antieigenvectors 141 Problems 144 4 Matrix Factorizations and Matrix Norms 155 4.1 Introduction 155 4.2 The Singular Value Decomposition 155 4.3 The Spectral Decomposition of a Symmetric Matrix 162 4.4 The Diagonalization of a Square Matrix 169 4.5 The Jordan Decomposition 173 4.6 The Schur Decomposition 175 4.7 The Simultaneous Diagonalization of Two Symmetric Matrices 178 4.8 Matrix Norms 184 Problems 191 5 Generalized Inverses 201 5.1 Introduction 201 5.2 The Moore–Penrose Generalized Inverse 202 5.3 Some Basic Properties of the Moore–Penrose Inverse 205 5.4 The Moore–Penrose Inverse of a Matrix Product 211 5.5 The Moore–Penrose Inverse of Partitioned Matrices 215 5.6 The Moore–Penrose Inverse of a Sum 219 5.7 The Continuity of the Moore–Penrose Inverse 222 5.8 Some Other Generalized Inverses 224 5.9 Computing Generalized Inverses 232 Problems 238 6 Systems of Linear Equations 247 6.1 Introduction 247 6.2 Consistency of a System of Equations 247 6.3 Solutions to a Consistent System of Equations 251 6.4 Homogeneous Systems of Equations 258 6.5 Least Squares Solutions to a System of Linear Equations 260 6.6 Least Squares Estimation For Less Than Full Rank Models 266 6.7 Systems of Linear Equations and The Singular Value Decomposition 271 6.8 Sparse Linear Systems of Equations 273 Problems 278 7 Partitioned Matrices 285 7.1 Introduction 285 7.2 The Inverse 285 7.3 The Determinant 288 7.4 Rank 296 7.5 Generalized Inverses 298 7.6 Eigenvalues 302 Problems 307 8 Special Matrices and Matrix Operations 315 8.1 Introduction 315 8.2 The Kronecker Product 315 8.3 The Direct Sum 323 8.4 The Vec Operator 323 8.5 The Hadamard Product 329 8.6 The Commutation Matrix 339 8.7 Some Other Matrices Associated With the Vec Operator 346 8.8 Nonnegative Matrices 351 8.9 Circulant and Toeplitz Matrices 363 8.10 Hadamard and Vandermonde Matrices 369 Problems 373 9 Matrix Derivatives and Related Topics 387 9.1 Introduction 387 9.2 Multivariable Differential Calculus 387 9.3 Vector and Matrix Functions 390 9.4 Some Useful Matrix Derivatives 396 9.5 Derivatives of Functions of Patterned Matrices 400 9.6 The Perturbation Method 402 9.7 Maxima and Minima 409 9.8 Convex and Concave Functions 413 9.9 The Method of Lagrange Multipliers 417 Problems 423 10 Inequalities 433 10.1 Introduction 433 10.2 Majorization 433 10.3 Cauchy-Schwarz Inequalities 444 10.4 H¨older’s Inequality 446 10.5 Minkowski’s Inequality 450 10.6 The Arithmetic-Geometric Mean Inequality 452 Problems 453 11 Some Special Topics Related to Quadratic Forms 457 11.1 Introduction 457 11.2 Some Results on Idempotent Matrices 457 11.3 Cochran’s Theorem 462 11.4 Distribution of Quadratic Forms in Normal Variates 465 11.5 Independence of Quadratic Forms 471 11.6 Expected Values of Quadratic Forms 477 11.7 The Wishart Distribution 485 Problems 496 References 507 Index 513

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Book SynopsisReflects the developments and new directions in the field since the publication of the first successful edition and contains a complete set of problems and solutions This revised and expanded edition reflects the developments and new directions in the field since the publication of the first edition. In particular, sections on nonstationary panel data analysis and a discussion on the distinction between deterministic and stochastic trends have been added. Three new chapters on long-memory discrete-time and continuous-time processes have also been created, whereas some chapters have been merged and some sections deleted. The first eleven chapters of the first edition have been compressed into ten chapters, with a chapter on nonstationary panel added and located under Part I: Analysis of Non-fractional Time Series. Chapters 12 to 14 have been newly written under Part II: Analysis of Fractional Time Series. Chapter 12 discusses the basic theory of long-memory processes byTable of ContentsPreface to the Second Edition xi Preface to the First Edition xiii Part I Analysis of Non Fractional Time Series 1 1 Models for Nonstationarity and Noninvertibility 3 1.1 Statistics from the One-Dimensional Random Walk 3 1.1.1 Eigenvalue Approach 4 1.1.2 Stochastic Process Approach 11 1.1.3 The Fredholm Approach 12 1.1.4 An Overview of the Three Approaches 14 1.2 A Test Statistic from a Noninvertible Moving Average Model 16 1.3 The AR Unit Root Distribution 23 1.4 Various Statistics from the Two-Dimensional Random Walk 29 1.5 Statistics from the Cointegrated Process 41 1.6 Panel Unit Root Tests 47 2 Brownian Motion and Functional Central Limit Theorems 51 2.1 The Space L2 of Stochastic Processes 51 2.2 The Brownian Motion 55 2.3 Mean Square Integration 58 2.3.1 The Mean Square Riemann Integral 59 2.3.2 The Mean Square Riemann–Stieltjes Integral 62 2.3.3 The Mean Square Ito Integral 66 2.4 The Ito Calculus 72 2.5 Weak Convergence of Stochastic Processes 77 2.6 The Functional Central Limit Theorem 81 2.7 FCLT for Linear Processes 87 2.8 FCLT for Martingale Differences 91 2.9 Weak Convergence to the Integrated Brownian Motion 99 2.10 Weak Convergence to the Ornstein–Uhlenbeck Process 103 2.11 Weak Convergence of Vector-Valued Stochastic Processes 109 2.11.1 Space Cq 109 2.11.2 Basic FCLT for Vector Processes 110 2.11.3 FCLT for Martingale Differences 112 2.11.4 FCLT for the Vector-Valued Integrated Brownian Motion 115 2.12 Weak Convergence to the Ito Integral 118 3 The Stochastic Process Approach 127 3.1 Girsanov’s Theorem: O-U Processes 127 3.2 Girsanov’s Theorem: Integrated Brownian Motion 137 3.3 Girsanov’s Theorem: Vector-Valued Brownian Motion 142 3.4 The Cameron–Martin Formula 145 3.5 Advantages and Disadvantages of the Present Approach 147 4 The Fredholm Approach 149 4.1 Motivating Examples 149 4.2 The Fredholm Theory: The Homogeneous Case 155 4.3 The c.f. of the Quadratic Brownian Functional 161 4.4 Various Fredholm Determinants 171 4.5 The Fredholm Theory: The Nonhomogeneous Case 190 4.5.1 Computation of the Resolvent – Case 1 192 4.5.2 Computation of the Resolvent – Case 2 199 4.6 Weak Convergence of Quadratic Forms 203 5 Numerical Integration 213 5.1 Introduction 213 5.2 Numerical Integration: The Nonnegative Case 214 5.3 Numerical Integration: The Oscillating Case 220 5.4 Numerical Integration: The General Case 228 5.5 Computation of Percent Points 236 5.6 The Saddlepoint Approximation 240 6 Estimation Problems in Nonstationary Autoregressive Models 245 6.1 Nonstationary Autoregressive Models 245 6.2 Convergence in Distribution of LSEs 250 6.2.1 Model A 251 6.2.2 Model B 253 6.2.3 Model C 255 6.2.4 Model D 257 6.3 The c.f.s for the Limiting Distributions of LSEs 260 6.3.1 The Fixed Initial Value Case 261 6.3.2 The Stationary Case 265 6.4 Tables and Figures of Limiting Distributions 267 6.5 Approximations to the Distributions of the LSEs 276 6.6 Nearly Nonstationary Seasonal AR Models 281 6.7 Continuous Record Asymptotics 289 6.8 Complex Roots on the Unit Circle 292 6.9 Autoregressive Models with Multiple Unit Roots 300 7 Estimation Problems in Noninvertible Moving Average Models 311 7.1 Noninvertible Moving Average Models 311 7.2 The Local MLE in the Stationary Case 314 7.3 The Local MLE in the Conditional Case 325 7.4 Noninvertible Seasonal Models 330 7.4.1 The Stationary Case 331 7.4.2 The Conditional Case 333 7.4.3 Continuous Record Asymptotics 335 7.5 The Pseudolocal MLE 337 7.5.1 The Stationary Case 337 7.5.2 The Conditional Case 339 7.6 Probability of the Local MLE at Unity 341 7.7 The Relationship with the State Space Model 343 8 Unit Root Tests in Autoregressive Models 349 8.1 Introduction 349 8.2 Optimal Tests 350 8.2.1 The LBI Test 352 8.2.2 The LBIU Test 353 8.3 Equivalence of the LM Test with the LBI or LBIU Test 356 8.3.1 Equivalence with the LBI Test 356 8.3.2 Equivalence with the LBIU Test 358 8.4 Various Unit Root Tests 360 8.5 Integral Expressions for the Limiting Powers 362 8.5.1 Model A 363 8.5.2 Model B 364 8.5.3 Model C 365 8.5.4 Model D 367 8.6 Limiting Power Envelopes and Point Optimal Tests 369 8.7 Computation of the Limiting Powers 372 8.8 Seasonal Unit Root Tests 382 8.9 Unit Root Tests in the Dependent Case 389 8.10 The Unit Root Testing Problem Revisited 395 8.11 Unit Root Tests with Structural Breaks 398 8.12 Stochastic Trends Versus Deterministic Trends 402 8.12.1 Case of Integrated Processes 403 8.12.2 Case of Near-Integrated Processes 406 8.12.3 Some Simulations 409 9 Unit Root Tests in Moving Average Models 415 9.1 Introduction 415 9.2 The LBI and LBIU Tests 416 9.2.1 The Conditional Case 417 9.2.2 The Stationary Case 419 9.3 The Relationship with the Test Statistics in Differenced Form 424 9.4 Performance of the LBI and LBIU Tests 427 9.4.1 The Conditional Case 427 9.4.2 The Stationary Case 430 9.5 Seasonal Unit Root Tests 434 9.5.1 The Conditional Case 434 9.5.2 The Stationary Case 436 9.5.3 Power Properties 438 9.6 Unit Root Tests in the Dependent Case 444 9.6.1 The Conditional Case 444 9.6.2 The Stationary Case 446 9.7 The Relationship with Testing in the State Space Model 447 9.7.1 Case (I) 449 9.7.2 Case (II) 450 9.7.3 Case (III) 452 9.7.4 The Case of the Initial Value Known 454 10 Asymptotic Properties of Nonstationary Panel Unit Root Tests 459 10.1 Introduction 459 10.2 Panel Autoregressive Models 461 10.2.1 Tests Based on the OLSE 463 10.2.2 Tests Based on the GLSE 471 10.2.3 Some Other Tests 475 10.2.4 Limiting Power Envelopes 480 10.2.5 Graphical Comparison 485 10.3 Panel Moving Average Models 488 10.3.1 Conditional Case 490 10.3.2 Stationary Case 494 10.3.3 Power Envelope 499 10.3.4 Graphical Comparison 502 10.4 Panel Stationarity Tests 507 10.4.1 Limiting Local Powers 508 10.4.2 Power Envelope 512 10.4.3 Graphical Comparison 514 10.5 Concluding Remarks 515 11 Statistical Analysis of Cointegration 517 11.1 Introduction 517 11.2 Case of No Cointegration 519 11.3 Cointegration Distributions: The Independent Case 524 11.4 Cointegration Distributions: The Dependent Case 532 11.5 The Sampling Behavior of Cointegration Distributions 537 11.6 Testing for Cointegration 544 11.6.1 Tests for the Null of No Cointegration 544 11.6.2 Tests for the Null of Cointegration 547 11.7 Determination of the Cointegration Rank 552 11.8 Higher Order Cointegration 556 11.8.1 Cointegration in the I(d) Case 556 11.8.2 Seasonal Cointegration 559 Part II Analysis of Fractional Time Series 567 12 ARFIMA Models and the Fractional Brownian Motion 569 12.1 Nonstationary Fractional Time Series 569 12.1.1 Case of d = ½ 570 12.1.2 Case of d > ½ 572 12.2 Testing for the Fractional Integration Order 575 12.2.1 i.i.d. Case 575 12.2.2 Dependent Case 581 12.3 Estimation for the Fractional Integration Order 584 12.3.1 i.i.d. Case 584 12.3.2 Dependent Case 586 12.4 Stationary Long-Memory Processes 591 12.5 The Fractional Brownian Motion 597 12.6 FCLT for Long-Memory Processes 603 12.7 Fractional Cointegration 608 12.7.1 Spurious Regression in the Fractional Case 609 12.7.2 Cointegrating Regression in the Fractional Case 610 12.7.3 Testing for Fractional Cointegration 614 12.8 The Wavelet Method for ARFIMA Models and the fBm 614 12.8.1 Basic Theory of the Wavelet Transform 615 12.8.2 Some Advantages of the Wavelet Transform 618 12.8.3 Some Applications of the Wavelet Analysis 625 13 Statistical Inference Associated with the Fractional Brownian Motion 629 13.1 Introduction 629 13.2 A Simple Continuous-Time Model Driven by the fBm 632 13.3 Quadratic Functionals of the Brownian Motion 641 13.4 Derivation of the c.f. 645 13.4.1 Stochastic Process Approach via Girsanov’s Theorem 645 13.4.2 Fredholm Approach via the Fredholm Determinant 647 13.5 Martingale Approximation to the fBm 651 13.6 The Fractional Unit Root Distribution 659 13.6.1 The FD Associated with the Approximate Distribution 659 13.6.2 An Interesting Moment Property 664 13.7 The Unit Root Test Under the fBm Error 669 14 Maximum Likelihood Estimation for the Fractional Ornstein–Uhlenbeck Process 673 14.1 Introduction 673 14.2 Estimation of the Drift: Ergodic Case 677 14.2.1 Asymptotic Properties of the OLSEs 677 14.2.2 The MLE and MCE 679 14.3 Estimation of the Drift: Non-ergodic Case 687 14.3.1 Asymptotic Properties of the OLSE 687 14.3.2 The MLE 687 14.4 Estimation of the Drift: Boundary Case 692 14.4.1 Asymptotic Properties of the OLSEs 692 14.4.2 The MLE and MCE 693 14.5 Computation of Distributions and Moments of the MLE and MCE 695 14.6 The MLE-based Unit Root Test Under the fBm Error 703 14.7 Concluding Remarks 707 15 Solutions to Problems 709 References 865 Author Index 879 Subject Index 883

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Book SynopsisThis book addresses the difficulties experienced by wet lab researchers with the statistical analysis of molecular biology related data. The authors explain how to use R and Bioconductor for the analysis of experimental data in the field of molecular biology.Table of ContentsForeword, xiii Preface, xv Acknowledgements, xix About the Companion Website, xxi 1 Introduction to R statistical environment, 1 Why R?, 1 Installing R, 2 Interacting with R, 2 Graphical interfaces and integrated development environment (IDE) integration, 3 Scripting and sourcing, 3 The R history and the R environment file, 4 Packages and package repositories, 4 Comprehensive R Archive Network, 5 Bioconductor, 6 Working with data, 7 Basic operations in R, 8 Some basics of graphics in R, 10 Getting help in R, 12 Files for practicing, 13 Study exercises and questions, 14 References, 14 Webliography, 15 2 Simple sequence analysis, 17 Sequence files, 17 FASTA sequence format, 18 GenBank flat file format, 19 Reading sequence files into R, 20 Obtaining sequences from remote databases, 21 Seqinr package, 21 Ape package, 22 Descriptive statistics of nucleotide sequences, 24 Descriptive statistics of proteins, 28 Aligned sequences, 31 Visualization of genes and transcripts in a professional way, 34 Files for practicing, 37 Study exercises and questions, 38 References, 38 Webliography, 39 Packages, 40 3 Annotating gene groups, 41 Enrichment analysis: an overview, 41 Overview of two different methods, 41 Enrichment analysis results, 42 Common aspects of the two different approaches, 43 Overrepresentation analysis, 46 Hypergeometric test using GOstats, 47 ORA analysis using topGO, 48 Enrichment analysis of microarray sets with topGO, 51 Gene set enrichment analysis, 52 GSEA with R, 56 Files for practicing, 61 Study exercises and questions, 61 References, 62 Webliography, 62 Packages, 63 4 Next-generation sequencing: introduction and genomic applications, 65 High-throughput sequencing background, 65 Experimental background, 66 Single-end and paired-end sequencing reads, 67 Assemble reads, 69 How many reads? Depth of coverage, 71 Storing data in files, 72 FASTQ, 72 SAM and BAM files, 76 Variant call format files, 77 General data analysis workflow, 77 Data processing considerations, 78 Quality checking and screening read sequences, 80 Quality checking for one file, 82 Quality inspection for multiple files in a project, 82 Quality filtering of FASTQ files, 83 Handling alignment files and genomic variants, 84 Alignment and variation visualization, 88 Simple handling of VCF files, 89 Genomic applications: low- and medium-depth sequencing, 91 Aneuploidity sequencing and copy number variation identification, 92 SNP identification and validation, 92 Exome sequencing, 93 Genomic region resequencing, 93 Full genome and metagenome sequencing, 94 Files for practicing, 94 Study exercises and questions, 94 References, 95 Webliography, 97 Packages, 97 5 Quantitative transcriptomics: qRT-PCR, 99 Transcriptome, 99 Polymerase chain reaction, 100 Standards for qPCR, 102 R packages, 104 Understanding delta Ct, 104 Calculation of delta Ct, 105 Requirements for real delta Ct calculations, 107 Absolute quantification, 110 Value prediction, the professional way, 114 Relative quantification using the ddCt method, 115 Comparison of two conditions, 116 Comparison of multiple experimental conditions, 118 Quality control with melting curve, 121 Files for practicing, 123 Study exercises and questions, 123 References, 123 Webliography, 124 Packages, 124 6 Advanced transcriptomics: gene expression microarrays, 125 Microarray analysis: probes and samples, 125 Experimental background, 126 Archiving and publishing microarray data, 128 Minimum information standard, 128 Data preprocessing, 128 Accessing data from CEL files, 129 Quality control, 131 Normalization, 132 Differential gene expression, 133 Annotating results, 136 Creating normalized expression set from Illumina data, 138 Automated data access from GEO, 140 Files for practicing, 142 Study exercises and questions, 142 References, 143 Webliography, 144 Packages, 144 7 Next-generation sequencing in transcriptomics: RNA-seq experiments, 145 High-throughput RNA sequencing background, 145 Experimental background, 145 RNA-seq applications, 146 Differential expression with different resolutions, 147 Preparing count tables, 148 Alignment files to read counts, 148 Differential expression in simple comparison, 151 A naive t-test approach, 151 Single factor analysis with edgeR, 153 Differential expression with DESeq, 156 Complex experimental arrangements, 159 Experimental factors and design matrix, 160 GLM with edgeR, 161 GLMs with DESeq, 162 Heatmap visualization, 163 Files for practicing, 164 Study exercises and questions, 164 References, 165 Webliography, 166 Packages, 166 8 Deciphering the regulome: from ChIP to ChIP-seq, 167 Chromatin immunoprecipitation, 167 Experimental background, 168 Fragment analysis, 168 ChIP data in ENCODE, 169 ChIP with tiling microarrays, 169 High-throughput sequencing of ChIP fragments, 176 Connecting annotation to peaks, 181 Analysis of binding site motifs, 182 Files for practicing, 186 Study exercises and questions, 187 References, 187 Webliography, 188 Packages, 189 9 Inferring regulatory and other networks from gene expression data, 191 Gene regulatory networks, 191 Data for gene network inference, 192 Reconstruction of co-expression networks, 193 Gene regulatory network inference focusing of master regulators, 201 Integrated interpretation of genes with GeneAnswers, 207 Files for practicing, 211 Study exercises and questions, 212 References, 213 Packages, 214 10 Analysis of biological networks, 215 A gentle introduction to networks, 215 Networks and their components and features, 215 Random networks, 220 Biological networks, 221 Files for storing network information, 223 Important network metrics in biology, 227 Distance-based measures, 228 Degree and related measures, 230 Vulnerability, 231 Community structure of a network, 234 Graph visualization, 236 Cytoscape, 240 Files for practicing, 241 Study exercises and questions, 241 References, 242 Webliography, 243 Packages, 243 11 Proteomics: mass spectrometry, 245 Mass spectrometry and proteomics: why and how?, 245 File formats for MS data, 246 Accessing the raw data of published studies, 247 Identification of peptides in the samples, 249 Peptide mass fingerprinting, 249 Peptide identification by using MS/MS spectra, 250 Quantitative proteomics, 254 Getting protein-specific annotation, 258 Files for practicing, 259 Study exercises and questions, 259 References, 259 Webliography, 260 Packages, 260 12 Measuring protein abundance with ELISA, 261 Enzyme-linked immunosorbent assays, 261 Accessing ELISA data, 264 Concentration calculation with a standard curve, 264 Preparing reference data, 267 Fitting linear model, 268 Fitting of a logistic model, 269 Concentration calculations by employing models, 270 Comparative calculations using concentrations, 271 Files for practicing, 277 Study exercises and questions, 277 References, 277 Packages, 278 13 Flow cytometry: counting and sorting stained cells, 279 Theoretical aspects of flow cytometry, 279 Experiment types: diagnosis versus discovery, 280 Measurement arrangements, 281 Fluorescent dyes, 281 Tubes versus plates, 285 Instruments, 285 What about data?, 287 Files, 287 Workflows, 288 Data preprocessing, 289 Handling all samples together, 290 Compensation, 292 Quality assurance, 292 Using workflow objects and transformation, 296 Normalization, 298 Cell population identification, 299 Manual gating, 300 Automatic gating, 304 Relating cell populations to external variables, 305 Reporting results, 307 MIFlowCyt, 307 FlowRepository.org, 308 Files for practicing, 308 Study exercises and questions, 309 References, 309 Webliography, 310 Packages, 310 Glossary, 311 Index, 323

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Book SynopsisPresents information sources and methodologies for modeling and simulating banking system stability Combining both academic and institutional knowledge and experience, Banking Systems Simulation: Theory, Practice, and Application of Modeling Shocks, Losses, and Contagion presents banking system risk modeling clearly within a theoretical framework. Written from the global financial perspective, the book explores single bank risk, common bank exposures, and contagion, and how these apply on a systemic level. Zedda approaches these simulation methods logically by providing the basic building blocks of modeling and simulation, and then delving further into the individual techniques that make up a systems model. In addition, the author provides clear and detailed explanations of the foundational research into the mathematical and legal concepts used to analyze banking risk problems, measures and data for representing the main banking risk sources, and the majoTable of ContentsForeword xi Introduction xv 1 Banking Risk 1 1.1 Single Bank Risk 4 1.2 The Basel Committee on Banking Supervision Approach to Regulation 14 1.3 Banking Risk Modeling and Stress Testing 33 1.4 Contagion 36 1.5 System Modeling 41 2 Simulation Models 45 2.1 Simulating Shocks: Idiosyncratic Shocks, or Exogenous Failure of Individual Banks 49 2.2 Simulating Shocks: Stress Testing 54 2.3 Simulating Shocks: Systematic Common Shocks 56 2.4 Simulating Shocks: Common Shocks 58 2.5 Estimation of Losses Variability and Assets Riskiness 70 2.6 Simulating Shocks: Correlated Risk Factors 82 2.7 Simulating Shocks: Combining Idiosyncratic and Common Shocks 87 2.8 Correlation 89 2.9 The Interbank Matrix 98 2.10 Loss Given Default 127 2.11 Interbank Losses Attribution 132 2.12 Contagion Simulation Methods 133 2.13 Data and Applied Problems 140 3 Real Economy, Sovereign Risk, and Banking Systems Linkages 149 3.1 Effects of Bank Riskiness on Sovereign Risk 150 3.2 Effects of Sovereign Risk on Bank Riskiness 153 3.3 Linkages to the Real Economy 154 3.4 Modeling 156 3.5 Implementation 159 4 Applications 163 4.1 Testing for Banks–Public Finances Contagion Risk 163 4.2 Banking Systems Regulation What-If Tests 164 4.3 Banks’ Minimum Capital Requirements: Cost–Benefit Analysis 169 4.4 Deposits Guarantee Schemes (DGS)/Resolution Funds Dimensioning 174 4.5 Computing Capital Coverage from Assets PD and Bank PD 178 4.6 Computing Banks Probability to Default from Capital Coverage and Assets PD 180 4.7 Risk Contributions and SiFis 182 4.8 The Regulator’s Dilemma 202 Appendix: Software References and Tools 205 References 223 Index 235

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Book SynopsisBRIDGES THE GAP BETWEEN SAS AND R, ALLOWING USERS TRAINED IN ONE LANGUAGE TO EASILY LEARN THE OTHER SAS and R are widely-used, very different software environments. Prized for its statistical and graphical tools, R is an open-source programming language that is popular with statisticians and data miners who develop statistical software and analyze data. SAS (Statistical Analysis System) is the leading corporate software in analytics thanks to its faster data handling and smaller learning curve. SAS for R Users enables entry-level data scientists to take advantage of the best aspects of both tools by providing a cross-functional framework for users who already know R but may need to work with SAS. Those with knowledge of both R and SAS are of far greater value to employers, particularly in corporate settings. Using a clear, step-by-step approach, this book presents an analytics workflow that mirrors that of the everyday data scientist. This up-to-date guide is coTable of ContentsPreface Scope Chapter 1 About SAS and R Chapter 2 Data Input, Import and Print Chapter 3 Data Inspection and Cleaning Chapter 4 Handling Dates, Strings, Numbers Chapter 5 Numerical Summary and Group by Analysis Chapter 6 Frequency Distributions and Cross Tabulations Chapter 7 Using SQL with SAS and R Chapter 8 Functions, Loops, Arrays, Macros Chapter 9 Data Visualization Chapter 10 Data Output Chapter 11 Statistics for Data Scientists Citations

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Book SynopsisNONPARAMETRIC STATISTICS WITH APPLICATIONS TO SCIENCE AND ENGINEERING WITH R Introduction to the methods and techniques of traditional and modern nonparametric statistics, incorporating R code Nonparametric Statistics with Applications to Science and Engineering with R presents modern nonparametric statistics from a practical point of view, with the newly revised edition including custom R functions implementing nonparametric methods to explain how to compute them and make them more comprehensible. Relevant built-in functions and packages on CRAN are also provided with a sample code. R codes in the new edition not only enable readers to perform nonparametric analysis easily, but also to visualize and explore data using R's powerful graphic systems, such as ggplot2 package and R base graphic system. The new edition includes useful tables at the end of each chapter that help the reader find data sets, files, functions, and packages that are used and relevant to the respective chapter. Table of ContentsPreface xi 1 Introduction 1 1.1 Efficiency of Nonparametric Methods 2 1.2 Overconfidence Bias 4 1.3 Computing with R 5 1.4 Exercises 6 References 7 2 Probability Basics 9 2.1 Helpful Functions 10 2.2 Events, Probabilities and Random Variables 12 2.3 Numerical Characteristics of Random Variables 13 2.4 Discrete Distributions 14 2.5 Continuous Distributions 18 2.6 Mixture Distributions 24 2.7 Exponential Family of Distributions 26 2.8 Stochastic Inequalities 26 2.9 Convergence of Random Variables 28 2.10 Exercises 32 References 34 3 Statistics Basics 35 3.1 Estimation 36 3.2 Empirical Distribution Function 36 3.3 Statistical Tests 38 3.4 Confidence Intervals 41 3.5 Likelihood 45 3.6 Exercises 49 References 51 4 Bayesian Statistics 53 4.1 The Bayesian Paradigm 53 4.2 Ingredients for Bayesian Inference 54 4.3 Point Estimation 58 4.4 Interval Estimation: Credible Sets 60 4.5 Bayesian Testing 62 4.6 Bayesian Prediction 65 4.7 Bayesian Computation and Use of WinBUGS 67 4.8 Exercises 69 References 73 5 Order Statistics 75 5.1 Joint Distributions of Order Statistics 77 5.2 Sample Quantiles 79 5.3 Tolerance Intervals 79 5.4 Asymptotic Distributions of Order Statistics 81 5.5 Extreme Value Theory 82 5.6 Ranked Set Sampling 83 5.7 Exercises 84 References 87 6 Goodness of Fit 89 6.1 KolmogorovSmirnov Test Statistic 90 6.2 Smirnov Test to Compare Two Distributions 96 6.3 Specialized Tests 99 6.4 Probability Plotting 106 6.5 Runs Test 112 6.6 Meta Analysis 117 6.7 Exercises 121 References 125 7 Rank Tests 127 7.1 Properties of Ranks 128 7.2 Sign Test 130 7.3 Spearman Coefficient of Rank Correlation 135 7.4 Wilcoxon Signed Rank Test 139 7.5 Wilcoxon (TwoSample) Sum Rank Test 142 7.6 MannWhitney U Test 144 7.7 Test of Variances 146 7.8 Walsh Test for Outliers 147 7.9 Exercises 148 References 153 8 Designed Experiments 155 8.1 KruskalWallis Test 156 8.2 Friedman Test 160 8.3 Variance Test for Several Populations 165 8.4 Exercises 166 References 169 9 Categorical Data 171 9.1 ChiSquare and GoodnessofFit 172 9.2 Contingency Tables 178 9.3 Fisher Exact Test 183 9.4 Mc Nemar Test 184 9.5 Cochran’s Test 186 9.6 MantelHaenszel Test 188 9.7 CLT for Multinomial Probabilities 190 9.8 Simpson’s Paradox 191 9.9 Exercises 193 References 200 10 Estimating Distribution Functions 203 10.1 Introduction 203 10.2 Nonparametric Maximum Likelihood 204 10.3 KaplanMeier Estimator 205 10.4 Confidence Interval for F 213 10.5 Plugin Principle 214 10.6 SemiParametric Inference 215 10.7 Empirical Processes 217 10.8 Empirical Likelihood 218 10.9 Exercises 221 References 223 11 Density Estimation 225 11.1 Histogram 226 11.2 Kernel and Bandwidth 228 11.3 Exercises 235 References 236 12 Beyond Linear Regression 237 12.1 Least Squares Regression 238 12.2 Rank Regression 239 12.3 Robust Regression 243 12.4 Isotonic Regression 249 12.5 Generalized Linear Models 252 12.6 Exercises 259 References 261 13 Curve Fitting Techniques 263 13.1 Kernel Estimators 265 13.2 Nearest Neighbor Methods 269 13.3 Variance Estimation 272 13.4 Splines 273 13.5 Summary 279 13.6 Exercises 279 References 282 14 Wavelets 285 14.1 Introduction to Wavelets 285 14.2 How Do the Wavelets Work? 288 14.3 Wavelet Shrinkage 295 14.4 Exercises 304 References 305 15 Bootstrap 307 15.1 Bootstrap Sampling 307 15.2 Nonparametric Bootstrap 309 15.3 Bias Correction for Nonparametric Intervals 315 15.4 The Jackknife 317 15.5 Bayesian Bootstrap 318 15.6 Permutation Tests 320 15.7 More on the Bootstrap 324 15.8 Exercises 325 References 327 16 EM Algorithm 329 16.1 Fisher’s Example 331 16.2 Mixtures 333 16.3 EM and Order Statistics 338 16.4 MAP via EM 339 16.5 Infection Pattern Estimation 341 16.6 Exercises 342 References 343 17 Statistical Learning 345 17.1 Discriminant Analysis 346 17.2 Linear Classification Models 349 17.3 Nearest Neighbor Classification 353 17.4 Neural Networks 355 17.5 Binary Classification Trees 361 17.6 Exercises 368 References 369 18 Nonparametric Bayes 371 18.1 Dirichlet Processes 372 18.2 Bayesian Categorical Models 380 18.3 Infinitely Dimensional Problems 383 18.4 Exercises 387 References 389 A WinBUGS 392 A.1 Using WinBUGS 393 A.2 Builtin Functions 396 B R Coding 400 B.1 Programming in R 400 B.2 Basics of R 402 B.3 R Commands 403 B.4 R for Statistics 405 R Index 411 Author Index 414 Subject Index 418

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Book SynopsisIndividual Participant Data Meta-Analysis: A Handbook for Healthcare Research provides a comprehensive introduction to the fundamental principles and methods that healthcare researchers need when considering, conducting or using individual participant data (IPD) meta-analysis projects. Written and edited by researchers with substantial experience in the field, the book details key concepts and practical guidance for each stage of an IPD meta-analysis project, alongside illustrated examples and summary learning points. Split into five parts, the book chapters take the reader through the journey from initiating and planning IPD projects to obtaining, checking, and meta-analysing IPD, and appraising and reporting findings. The book initially focuses on the synthesis of IPD from randomised trials to evaluate treatment effects, including the evaluation of participant-level effect modifiers (treatment-covariate interactions). Detailed extension is then made to specialist topTable of ContentsAcknowledgements xxiii 1 Individual Participant Data Meta-analysis for Healthcare Research 1Richard D. Riley, Lesley A. Stewart, and Jayne F. Tierney 1.1 Introduction 1 1.2 What Is IPD and How Does It Differ from Aggregate Data? 1 1.3 IPD Meta-analysis: A New Era for Evidence Synthesis 2 1.4 Scope of This Book and Intended Audience 2 Part I Rationale, Planning, and Conduct 7 2 Rationale for Embarking on an IPD Meta-analysis Project 9Jayne F. Tierney, Richard D. Riley, Catrin Tudur Smith, Mike Clarke, and Lesley A. Stewart 2.1 Introduction 9 2.2 How Does the Research Process Differ for IPD and Aggregate Data Meta-analysis Projects? 10 2.3 What Are the Potential Advantages of an IPD Meta-analysis Project? 11 2.4 What Are the Potential Challenges of an IPD Meta-Analysis Project? 14 2.5 Empirical Evidence of Differences between Results of IPD and Aggregate Data Metaanalysis Projects 14 2.6 Guidance for Deciding When IPD Meta-analysis Projects Are Needed to Evaluate Treatment Effects from Randomised Trials 15 2.7 Concluding Remarks 19 3 Planning and Initiating an IPD Meta-analysis Project 21Lesley A. Stewart, Richard D. Riley, and Jayne F. Tierney 3.1 Introduction 22 3.2 Organisational Approach 22 3.3 Developing a Project Scope 26 3.4 Assessing Feasibility and ‘In Principle’ Support and Collaboration 26 3.5 Establishing a Team with the Right Skills 29 3.6 Advisory and Governance Functions 30 3.7 Estimating How Long the Project Will Take 31 3.8 Estimating the Resources Required 33 3.9 Obtaining Funding 38 3.10 Obtaining Ethical Approval 39 3.11 Data-sharing Agreement 41 3.12 Additional Planning for Prospective Meta-analysis Projects 41 3.13 Concluding Remarks 43 4 Running an IPD Meta-analysis Project: From Developing the Protocol to Preparing Data for Meta-analysis 45Jayne F. Tierney, Richard D. Riley, Larysa H.M. Rydzewska, and Lesley A. Stewart 4.1 Introduction 46 4.2 Preparing to Collect IPD 46 4.3 Initiating and Maintaining Collaboration 57 4.4 Obtaining IPD 59 4.5 Checking and Harmonising Incoming IPD 62 4.6 Checking the IPD to Inform Risk of Bias Assessments 66 4.7 Assessing and Presenting the Overall Quality of a Trial 76 4.8 Verification of Finalised Trial IPD 77 4.9 Merging IPD Ready for Meta-analysis 77 4.10 Concluding Remarks 80 Part I References 81 Part II Fundamental Statistical Methods and Principles 87 5 The Two-stage Approach to IPD Meta-analysis 89Richard D. Riley, Thomas P.A. Debray, Tim P. Morris, and Dan Jackson 5.1 Introduction 90 5.2 First Stage of a Two-stage IPD Meta-analysis 90 5.3 Second Stage of a Two-stage IPD Meta-analysis 106 5.4 Meta-regression and Subgroup Analyses 120 5.5 The ipdmetan Software Package 121 5.6 Combining IPD with Aggregate Data from non-IPD Trials 124 5.7 Concluding Remarks 125 6 The One-stage Approach to IPD Meta-analysis 127Richard D. Riley and Thomas P.A. Debray 127 6.1 Introduction 128 6.2 One-stage IPD Meta-analysis Models Using Generalised Linear Mixed Models 129 6.3 One-stage Models for Time-to-event Outcomes 152 6.4 One-stage Models Combining Different Sources of Evidence 159 6.5 Reporting of One-stage Models in Protocols and Publications 162 6.6 Concluding Remarks 162 7 Using IPD Meta-analysis to Examine Interactions between Treatment Effect and Participant-level Covariates 163Richard D. Riley and David J. Fisher 7.1 Introduction 164 7.2 Meta-regression and Its Limitations 166 7.3 Two-stage IPD Meta-analysis to Estimate Treatment-covariate Interactions 168 7.4 The One-stage Approach 174 7.5 Combining IPD and non-IPD Trials 181 7.6 Handling of Continuous Covariates 184 7.7 Handling of Categorical or Ordinal Covariates 191 7.8 Misconceptions and Cautions 191 7.9 Is My Identified Treatment-covariate Interaction Genuine? 195 7.10 Reporting of Analyses of Treatment-covariate Interactions 196 7.11 Can We Predict a New Patient’s Treatment Effect? 196 7.11.1 Linking Predictions to Clinical Decision Making 198 7.12 Concluding Remarks 198 8 One-stage versus Two-stage Approach to IPD Meta-analysis: Differences and Recommendations 199Richard D. Riley, Danielle L. Burke, and Tim Morris 8.1 Introduction 200 8.2 One-stage and Two-stage Approaches Usually Give Similar Results 200 8.3 Ten Key Reasons Why One-stage and Two-stage Approaches May Give Different Results 203 8.4 Recommendations and Guidance 216 8.5 Concluding Remarks 217 Part II References 219 Part III Critical Appraisal and Dissemination 237 9 Examining the Potential for Bias in IPD Meta-analysis Results 239Richard D. Riley, Jayne F. Tierney, and Lesley A. Stewart 9.1 Introduction 240 9.2 Publication and Reporting Biases of Trials 240 9.3 Biased Availability of the IPD from Trials 244 9.4 Trial Quality (risk of bias) 247 9.5 Other Potential Biases Affecting IPD Meta-analysis Results 248 9.6 Concluding Remarks 251 10 Reporting and Dissemination of IPD Meta-analyses 253Lesley A. Stewart, Richard D. Riley, and Jayne F. Tierney 10.1 Introduction 253 10.2 Reporting IPD Meta-analysis Projects in Academic Reports 254 10.3 Additional Means of Disseminating Findings 266 10.4 Concluding Remarks 270 11 A Tool for the Critical Appraisal of IPD Meta-analysis Projects (CheckMAP) 271Jayne F. Tierney, Lesley A. Stewart, Claire L. Vale, and Richard D. Riley 11.1 Introduction 271 11.2 The CheckMAP Tool 272 11.3 Was the IPD Meta-analysis Project Done within a Systematic Review Framework? 272 11.4 Were the IPD Meta-analysis Project Methods Pre-specified in a Publicly Available Protocol? 274 11.5 Did the IPD Meta-analysis Project Have a Clear Research Question Qualified by Explicit Eligibility Criteria? 276 11.6 Did the IPD Meta-analysis Project Have a Systematic and Comprehensive Search Strategy? 276 11.7 Was the Approach to Data Collection Consistent and Thorough? 277 11.8 Were IPD Obtained from Most Eligible Trials and Their Participants? 277 11.9 Was the Validity of the IPD Checked for Each Trial? 278 11.10 Was the Risk of Bias Assessed for Each Trial and Its Associated IPD? 27811.10.1 Was the Randomisation Process Checked Based on IPD? 278 11.11 Were the Methods of Meta-analysis Appropriate? 280 11.12 Concluding Remarks 283 Part III References 285 Part IV Special Topics in Statistics 291 12 Power Calculations for Planning an IPD Meta-analysis 293Richard D. Riley and Joie Ensor 12.1 Introduction 294 12.2 Motivating Example: Power of a Planned IPD Meta-analysis of Trials of Interventions to Reduce Weight Gain in Pregnant Women 295 12.3 The Contribution of Individual Trials Toward Power 301 12.4 The Impact of Model Assumptions on Power 302 12.5 Extensions 305 12.6 Concluding Remarks 309 13 Multivariate Meta-analysis Using IPD 311Richard D. Riley, Dan Jackson, and Ian R. White 13.1 Introduction 312 13.2 General Two-stage Approach for Multivariate IPD Meta-analysis 314 13.3 Application to an IPD Meta-analysis of Anti-hypertensive Trials 329 13.4 Extension to Multivariate Meta-regression 333 13.5 Potential Limitations of Multivariate Meta-analysis 334 13.6 One-stage Multivariate IPD Meta-analysis Applications 337 13.7 Special Applications of Multivariate Meta-analysis 340 13.8 Concluding Remarks 346 14 Network Meta-analysis Using IPD 347Richard D. Riley, David M. Phillippo, and Sofia Dias 14.1 Introduction 348 14.2 Rationale and Assumptions for Network Meta-analysis 348 14.3 Network Meta-analysis Models Assuming Consistency 350 14.4 Ranking Treatments 357 14.5 How Do We Examine Inconsistency between Direct and Indirect Evidence? 359 14.6 Benefits of IPD for Network Meta-analysis 361 14.7 Combining IPD and Aggregate Data in Network Meta-analysis 365 14.8 Further Topics 370 14.9 Concluding Remarks 372 Part IV References 375 Part V Diagnosis, Prognosis and Prediction 387 15 IPD Meta-analysis for Test Accuracy Research 389Richard D. Riley, Brooke Levis, and Yemisi Takwoingi 389 15.1 Introduction 390 15.2 Motivating Example: Diagnosis of Fever in Children Using Ear Temperature 394 15.3 Key Steps Involved in an IPD Meta-analysis of Test Accuracy Studies 397 15.4 IPD Meta-analysis of Test Accuracy at Multiple Thresholds 410 15.5 IPD Meta-analysis for Examining a Test’s Clinical Utility 414 15.6 Comparing Tests 418 15.7 Concluding Remarks 420 16 IPD Meta-analysis for Prognostic Factor Research 421Richard D. Riley, Karel G.M. Moons, and Thomas P.A. Debray 16.1 Introduction 422 16.2 Potential Advantages of an IPD Meta-analysis 424 16.3 Key Steps Involved in an IPD Meta-analysis of Prognostic Factor Studies 427 16.4 Software 444 16.5 Concluding Remarks 444 17 IPD Meta-analysis for Clinical Prediction Model Research 447Richard D. Riley, Kym I.E. Snell, Laure Wynants, Valentijn M.T. de Jong, Karel G.M. Moons, and Thomas P.A. Debray 17.1 Introduction 448 17.2 IPD Meta-analysis for Prediction Model Research 448 17.3 External Validation of an Existing Prediction Model Using IPD Meta-analysis 455 17.4 Updating and Tailoring of a Prediction Model Using IPD Meta-analysis 470 17.5 Comparison of Multiple Existing Prediction Models Using IPD Meta-analysis 472 17.6 Using IPD Meta-analysis to Examine the Added Value of a New Predictor to an Existing Prediction Model 478 17.7 Developing a New Prediction Model Using IPD Meta-analysis 479 17.8 Examining the Utility of a Prediction Model Using IPD Meta-analysis 491 17.9 Software 494 17.10 Reporting 495 17.11 Concluding Remarks 495 18 Dealing with Missing Data in an IPD Meta-analysis 499Thomas Debray, Kym I.E. Snell, Matteo Quartagno, Shahab Jolani, Karel G.M. Moons, and Richard D. Riley 499 18.1 Introduction 500 18.2 Motivating Example: IPD Meta-analysis Validating Prediction Models for Risk of Preeclampsia in Pregnancy 500 18.3 Types of Missing Data in an IPD Meta-analysis 502 18.4 Recovering Actual Values of Missing Data within IPD 502 18.5 Mechanisms and Patterns of Missing Data in an IPD Meta-analysis 502 18.6 Multiple Imputation to Deal with Missing Data in a Single Study 506 18.7 Ensuring Congeniality of Imputation and Analysis Models 509 18.8 Dealing with Sporadically Missing Data in an IPD Meta-analysis by Applying Multiple Imputation for Each Study Separately 509 18.9 Dealing with Systematically Missing Data in an IPD Meta-analysis Using a Bivariate Metaanalysis of Partially and Fully Adjusted Results 511 18.10 Dealing with Both Sporadically and Systematically Missing Data in an IPD Meta-analysis Using Multilevel Modelling 514 18.11 Comparison of Methods and Recommendations 521 18.12 Software 523 18.13 Concluding Remarks 524 Part V References 525 Index 000

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Book SynopsisExplores mathematical statistics in its entiretyfrom the fundamentals to modern methods This book introduces readers to point estimation, confidence intervals, and statistical tests. Based on the general theory of linear models, it provides an in-depth overview of the following: analysis of variance (ANOVA) for models with fixed, random, and mixed effects; regression analysis is also first presented for linear models with fixed, random, and mixed effects before being expanded to nonlinear models; statistical multi-decision problems like statistical selection procedures (Bechhofer and Gupta) and sequential tests; and design of experiments from a mathematical-statistical point of view. Most analysis methods have been supplemented by formulae for minimal sample sizes. The chapters also contain exercises with hints for solutions. Translated from the successful German text, Mathematical Statistics requires knowledge of probability theory (combinatorics, probability distributions, functioTable of ContentsPreface xiii 1 Basic Ideas of Mathematical Statistics 1 1.1 Statistical Population and Samples 2 1.1.1 Concrete Samples and Statistical Populations 2 1.1.2 Sampling Procedures 4 1.2 Mathematical Models for Population and Sample 8 1.3 Sufficiency and Completeness 9 1.4 The Notion of Information in Statistics 20 1.5 Statistical Decision Theory 28 1.6 Exercises 32 References 37 2 Point Estimation 39 2.1 Optimal Unbiased Estimators 41 2.2 Variance-Invariant Estimation 53 2.3 Methods for Construction and Improvement of Estimators 57 2.3.1 Maximum Likelihood Method 57 2.3.2 Least Squares Method 60 2.3.3 Minimum Chi-Squared Method 61 2.3.4 Method of Moments 62 2.3.5 Jackknife Estimators 63 2.3.6 Estimators Based on Order Statistics 64 2.3.6.1 Order and Rank Statistics 64 2.3.6.2 L-Estimators 66 2.3.6.3 M-Estimators 67 2.3.6.4 R-Estimators 68 2.4 Properties of Estimators 68 2.4.1 Small Samples 69 2.4.2 Asymptotic Properties 71 2.5 Exercises 75 References 78 3 Statistical Tests and Confidence Estimations 79 3.1 Basic Ideas of Test Theory 79 3.2 The Neyman–Pearson Lemma 87 3.3 Tests for Composite Alternative Hypotheses and One-Parametric Distribution Families 96 3.3.1 Distributions with Monotone Likelihood Ratio and Uniformly Most Powerful Tests for One-Sided Hypotheses 96 3.3.2 UMPU-Tests for Two-Sided Alternative Hypotheses 105 3.4 Tests for Multi-Parametric Distribution Families 110 3.4.1 General Theory 111 3.4.2 The Two-Sample Problem: Properties of Various Tests and Robustness 124 3.4.2.1 Comparison of Two Expectations 125 3.4.3 Comparison of Two Variances 137 3.4.4 Table for Sample Sizes 138 3.5 Confidence Estimation 139 3.5.1 One-Sided Confidence Intervals in One-Parametric Distribution Families 140 3.5.2 Two-Sided Confidence Intervals in One-Parametric and Confidence Intervals in Multi-Parametric Distribution Families 143 3.5.3 Table for Sample Sizes 146 3.6 Sequential Tests 147 3.6.1 Introduction 147 3.6.2 Wald’s Sequential Likelihood Ratio Test for One-Parametric Exponential Families 149 3.6.3 Test about Mean Values for Unknown Variances 153 3.6.4 Approximate Tests for the Two-Sample Problem 158 3.6.5 Sequential Triangular Tests 160 3.6.6 A Sequential Triangular Test for the Correlation Coefficient 162 3.7 Remarks about Interpretation 169 3.8 Exercises 170 References 176 4 Linear Models: General Theory 179 4.1 Linear Models with Fixed Effects 179 4.1.1 Least Squares Method 180 4.1.2 Maximum Likelihood Method 184 4.1.3 Tests of Hypotheses 185 4.1.4 Construction of Confidence Regions 190 4.1.5 Special Linear Models 191 4.1.6 The Generalised Least Squares Method (GLSM) 198 4.2 Linear Models with Random Effects: Mixed Models 199 4.2.1 Best Linear Unbiased Prediction (BLUP) 200 4.2.2 Estimation of Variance Components 202 4.3 Exercises 203 References 204 5 Analysis of Variance (ANOVA): Fixed Effects Models (Model I of Analysis of Variance) 207 5.1 Introduction 207 5.2 Analysis of Variance with One Factor (Simple- or One-Way Analysis of Variance) 215 5.2.1 The Model and the Analysis 215 5.2.2 Planning the Size of an Experiment 228 5.2.2.1 General Description for All Sections of This Chapter 228 5.2.2.2 The Experimental Size for the One-Way Classification 231 5.3 Two-Way Analysis of Variance 232 5.3.1 Cross-Classification (A × B) 233 5.3.1.1 Parameter Estimation 236 5.3.1.2 Testing Hypotheses 244 5.3.2 Nested Classification (A B) 260 5.4 Three-Way Classification 272 5.4.1 Complete Cross-Classification (A × B × C) 272 5.4.2 Nested Classification (C≺B≺A) 279 5.4.3 Mixed Classification 282 5.4.3.1 Cross-Classification between Two Factors Where One of Them Is Subordinated to a Third Factor B≺A × C 282 5.4.3.2 Cross-Classification of Two Factors in Which a Third Factor Is Nested C≺ A× B 288 5.5 Exercises 291 References 291 6 Analysis of Variance: Estimation of Variance Components (Model II of the Analysis of Variance) 293 6.1 Introduction: Linear Models with Random Effects 293 6.2 One-Way Classification 297 6.2.1 Estimation of Variance Components 300 6.2.1.1 Analysis of Variance Method 300 6.2.1.2 Estimators in Case of Normally Distributed Y 302 6.2.1.3 REML: Estimation 304 6.2.1.4 Matrix Norm Minimising Quadratic Estimation 305 6.2.1.5 Comparison of Several Estimators 306 6.2.2 Tests of Hypotheses and Confidence Intervals 308 6.2.3 Variances and Properties of the Estimators of the Variance Components 310 6.3 Estimators of Variance Components in the Two-Way and Three-Way Classification 315 6.3.1 General Description for Equal and Unequal Subclass Numbers 315 6.3.2 Two-Way Cross-Classification 319 6.3.3 Two-Way Nested Classification 324 6.3.4 Three-Way Cross-Classification with Equal Subclass Numbers 326 6.3.5 Three-Way Nested Classification 334 6.3.6 Three-Way Mixed Classification 334 6.4 Planning Experiments 336 6.5 Exercises 338 References 339 7 Analysis of Variance: Models with Finite Level Populations and Mixed Models 341 7.1 Introduction: Models with Finite Level Populations 341 7.2 Rules for the Derivation of SS, df, MS and E(MS) in Balanced ANOVA Models 343 7.3 Variance Component Estimators in Mixed Models 348 7.3.1 An Example for the Balanced Case 349 7.3.2 The Unbalanced Case 351 7.4 Tests for Fixed Effects and Variance Components 353 7.5 Variance Component Estimation and Tests of Hypotheses in Special Mixed Models 354 7.5.1 Two-Way Cross-Classification 355 7.5.2 Two-Way Nested Classification B ≺ A 358 7.5.2.1 Levels of A Random 360 7.5.2.2 Levels of B Random 361 7.5.3 Three-Way Cross-Classification 362 7.5.4 Three-Way Nested Classification 365 7.5.5 Three-Way Mixed Classification 369 7.5.5.1 The Type (B ≺ A) × C 369 7.5.5.2 The Type C ≺ AB 374 7.6 Exercises 376 References 376 8 Regression Analysis: Linear Models with Non-random Regressors (Model I of Regression Analysis) and with Random Regressors (Model II of Regression Analysis) 377 8.1 Introduction 377 8.2 Parameter Estimation 380 8.2.1 Least Squares Method 380 8.2.2 Optimal Experimental Design 394 8.3 Testing Hypotheses 397 8.4 Confidence Regions 406 8.5 Models with Random Regressors 410 8.5.1 Analysis 410 8.5.2 Experimental Designs 415 8.6 Mixed Models 416 8.7 Concluding Remarks about Models of Regression Analysis 417 8.8 Exercises 419 References 419 9 Regression Analysis: Intrinsically Non-linear Model I 421 9.1 Estimating by the Least Squares Method 424 9.1.1 Gauß–Newton Method 425 9.1.2 Internal Regression 431 9.1.3 Determining Initial Values for Iteration Methods 433 9.2 Geometrical Properties 434 9.2.1 Expectation Surface and Tangent Plane 434 9.2.2 Curvature Measures 440 9.3 Asymptotic Properties and the Bias of LS Estimators 443 9.4 Confidence Estimations and Tests 447 9.4.1 Introduction 447 9.4.2 Tests and Confidence Estimations Based on the Asymptotic Covariance Matrix 451 9.4.3 Simulation Experiments to Check Asymptotic Tests and Confidence Estimations 452 9.5 Optimal Experimental Design 454 9.6 Special Regression Functions 458 9.6.1 Exponential Regression 458 9.6.1.1 Point Estimator 458 9.6.1.2 Confidence Estimations and Tests 460 9.6.1.3 Results of Simulation Experiments 463 9.6.1.4 Experimental Designs 466 9.6.2 The Bertalanffy Function 468 9.6.3 The Logistic (Three-Parametric Hyperbolic Tangent) Function 473 9.6.4 The Gompertz Function 476 9.6.5 The Hyperbolic Tangent Function with Four Parameters 479 9.6.6 The arc tangent Function with Four Parameters 484 9.6.7 The Richards Function 487 9.6.8 Summarising the Results of Sections 9.6.1–9.6.7 487 9.6.9 Problems of Model Choice 488 9.7 Exercises 489 References 490 10 Analysis of Covariance (ANCOVA) 495 10.1 Introduction 495 10.2 General Model I–I of the Analysis of Covariance 496 10.3 Special Models of the Analysis of Covariance for the Simple Classification 503 10.3.1 One Covariable with Constant γ 504 10.3.2 A Covariable with Regression Coefficients γi Depending on the Levels of the Classification Factor 506 10.3.3 A Numerical Example 507 10.4 Exercises 510 References 511 11 Multiple Decision Problems 513 11.1 Selection Procedures 514 11.1.1 Basic Ideas 514 11.1.2 Indifference Zone Formulation for Expectations 516 11.1.2.1 Selection of Populations with Normal Distribution 517 11.1.2.2 Approximate Solutions for Non-normal Distributions and t = 1 529 11.1.3 Selection of a Subset Containing the Best Population with Given Probability 530 11.1.3.1 Selection of the Normal Distribution with the Largest Expectation 534 11.1.3.2 Selection of the Normal Distribution with Smallest Variance 535 11.2 Multiple Comparisons 536 11.2.1 Confidence Intervals for All Contrasts: Scheffé’s Method 542 11.2.2 Confidence Intervals for Given Contrast: Bonferroni’s and Dunn’s Method 547 11.2.3 Confidence Intervals for All Contrasts for ni = n: Tukey’s Method 550 11.2.4 Confidence Intervals for All Contrast: Generalised Tukey’s Method 553 11.2.5 Confidence Intervals for the Differences of Treatments with a Control: Dunnett’s Method 555 11.2.6 Multiple Comparisons and Confidence Intervals 556 11.2.7 Which Multiple Comparisons Shall Be Used? 559 11.3 A Numerical Example 560 11.4 Exercises 564 References 564 12 Experimental Designs 567 12.1 Introduction 568 12.2 Block Designs 571 12.2.1 Completely Balanced Incomplete Block Designs (BIBD) 574 12.2.2 Construction Methods of BIBD 582 12.2.3 Partially Balanced Incomplete Block Designs 596 12.3 Row–Column Designs 600 12.4 Factorial Designs 603 12.5 Programs for Construction of Experimental Designs 604 12.6 Exercises 604 References 605 Appendix A: Symbolism 609 Appendix B: Abbreviations 611 Appendix C: Probability and Density Functions 613 Appendix D: Tables 615 Solutions and Hints for Exercises 627 Index 659

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Book SynopsisAn Introduction to Machine Learning in Finance, With Mathematical Background, Data Visualization, and R Nonparametric function estimation is an important part of machine learning, which is becoming increasingly important in quantitative finance. Nonparametric Finance provides graduate students and finance professionals with a foundation in nonparametric function estimation and the underlying mathematics. Combining practical applications, mathematically rigorous presentation, and statistical data analysis into a single volume, this book presents detailed instruction in discrete chapters that allow readers to dip in as needed without reading from beginning to end. Coverage includes statistical finance, risk management, portfolio management, and securities pricing to provide a practical knowledge base, and the introductory chapter introduces basic finance concepts for readers with a strictly mathematical background. Economic significance is emphasized over statistical significance throTable of ContentsPreface xxiii 1 Introduction 1 1.1 Statistical Finance 2 1.2 Risk Management 3 1.3 Portfolio Management 5 1.4 Pricing of Securities 6 Part I Statistical Finance 11 2 Financial Instruments 13 2.1 Stocks 13 2.2 Fixed Income Instruments 19 2.3 Derivatives 23 2.4 Data Sets 27 3 Univariate Data Analysis 33 3.1 Univariate Statistics 34 3.2 Univariate Graphical Tools 42 3.3 Univariate ParametricModels 55 3.4 Tail Modeling 61 3.5 Asymptotic Distributions 83 3.6 Univariate Stylized Facts 91 4 Multivariate Data Analysis 95 4.1 Measures of Dependence 95 4.2 Multivariate Graphical Tools 103 4.3 Multivariate ParametricModels 107 4.4 Copulas 111 5 Time Series Analysis 121 5.1 Stationarity and Autocorrelation 122 5.2 Model Free Estimation 128 5.3 Univariate Time Series Models 135 5.4 Multivariate Time Series Models 157 5.5 Time Series Stylized Facts 160 6 Prediction 163 6.1 Methods of Prediction 164 6.2 Forecast Evaluation 170 6.3 Predictive Variables 175 6.4 Asset Return Prediction 182 Part II Risk Management 193 7 Volatility Prediction 195 7.1 Applications of Volatility Prediction 197 7.2 Performance Measures for Volatility Predictors 199 7.3 Conditional Heteroskedasticity Models 200 7.4 Moving Average Methods 205 7.5 State Space Predictors 211 8 Quantiles and Value-at-Risk 219 8.1 Definitions of Quantiles 220 8.2 Applications of Quantiles 223 8.3 Performance Measures for Quantile Estimators 227 8.4 Nonparametric Estimators of Quantiles 233 8.5 Volatility Based Quantile Estimation 240 8.6 Excess Distributions in Quantile Estimation 258 8.7 Extreme ValueTheory in Quantile Estimation 288 8.8 Expected Shortfall 292 Part III Portfolio Management 297 9 Some Basic Concepts of Portfolio Theory 299 9.1 Portfolios and Their Returns 300 9.2 Comparison of Return andWealth Distributions 312 9.3 Multiperiod Portfolio Selection 326 10 Performance Measurement 337 10.1 The Sharpe Ratio 338 10.2 Certainty Equivalent 346 10.3 Drawdown 347 10.4 Alpha and Conditional Alpha 348 10.5 Graphical Tools of Performance Measurement 356 11 Markowitz Portfolios 367 11.1 Variance Penalized Expected Return 369 11.2 Minimizing Variance under a Sufficient Expected Return 372 11.3 Markowitz Bullets 375 11.4 Further Topics in Markowitz Portfolio Selection 381 11.5 Examples of Markowitz Portfolio Selection 383 12 Dynamic Portfolio Selection 385 12.1 Prediction in Dynamic Portfolio Selection 387 12.2 Backtesting Trading Strategies 393 12.3 One Risky Asset 394 12.4 Two Risky Assets 405 Part IV Pricing of Securities 419 13 Principles of Asset Pricing 421 13.1 Introduction to Asset Pricing 422 13.2 Fundamental Theorems of Asset Pricing 430 13.3 Evaluation of Pricing and Hedging Methods 456 14 Pricing by Arbitrage 459 14.1 Futures and the Put–Call Parity 460 14.2 Pricing in Binary Models 466 14.3 Black–Scholes Pricing 485 14.4 Black–Scholes Hedging 505 14.5 Black–Scholes Hedging and Volatility Estimation 515 15 Pricing in IncompleteModels 521 15.1 Quadratic Hedging and Pricing 522 15.2 Utility Maximization 523 15.3 Absolutely Continuous Changes of Measures 530 15.4 GARCH Market Models 534 15.5 Nonparametric Pricing Using Historical Simulation 545 15.6 Estimation of the Risk-Neutral Density 551 15.7 Quantile Hedging 555 16 Quadratic and Local Quadratic Hedging 557 16.1 Quadratic Hedging 558 16.2 Local Quadratic Hedging 583 16.3 Implementations of Local Quadratic Hedging 595 17 Option Strategies 615 17.1 Option Strategies 616 17.2 Profitability of Option Strategies 625 18 Interest Rate Derivatives 649 18.1 Basic Concepts of Interest Rate Derivatives 650 18.2 Interest Rate Forwards 659 18.3 Interest Rate Options 666 18.4 Modeling Interest Rate Markets 669 References 673 Index 681

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Book SynopsisPresents a useful guide for applications of SEM whilst systematically demonstrating various SEM models using Mplus Focusing on the conceptual and practical aspects of Structural Equation Modeling (SEM), this book demonstrates basic concepts and examples of various SEM models, along with updates on many advanced methods, including confirmatory factor analysis (CFA) with categorical items, bifactor model, Bayesian CFA model, item response theory (IRT) model, graded response model (GRM), multiple imputation (MI) of missing values, plausible values of latent variables, moderated mediation model, Bayesian SEM, latent growth modeling (LGM) with individually varying times of observations, dynamic structural equation modeling (DSEM), residual dynamic structural equation modeling (RDSEM), testing measurement invariance of instrument with categorical variables, longitudinal latent class analysis (LLCA), latent transition analysis (LTA), growth mixture modeling (GMM) with Table of ContentsPreface ix 1 Introduction to structural equation modeling 1 1.1 Introduction 1 1.2 Model formulation 3 1.2.1 Measurement models 4 1.2.2 Structural models 6 1.2.3 Model formulation in equations 7 1.3 Model identification 11 1.4 Model estimation 14 1.4.1 Bayes estimator 17 1.5 Model fit evaluation 19 1.5.1 The model 𝜒2 statistic 20 1.5.2 Comparative fit index (CFI) 20 1.5.3 Tucker Lewis index (TLI) or non-normed fit index (NNFI) 21 1.5.4 Root mean square error of approximation (RMSEA) 22 1.5.5 Root mean-square residual (RMR), standardized RMR (SRMR), and weighted RMR (WRMR) 22 1.5.6 Information criteria indices 24 1.5.7 Model fit evaluation with Bayes estimator 25 1.5.8 Model comparison 26 1.6 Model modification 27 1.7 Computer programs for SEM 28 Appendix 1.A Expressing variances and covariances among observed variables as functions of model parameters 30 Appendix 1.B Maximum likelihood function for SEM 32 2 Confirmatory factor analysis 33 2.1 Introduction 33 2.2 Basics of CFA models 34 2.2.1 Latent variables/factors 39 2.2.2 Indicator variables 39 2.2.3 Item parceling 40 2.2.4 Factor loadings 42 2.2.5 Measurement errors 42 2.2.6 Item reliability 44 2.2.7 Scale reliability 44 2.3 CFA models with continuous indicators 45 2.3.1 Alternative methods for factor scaling 52 2.3.2 Model estimated item reliability 57 2.3.3 Model modification based on modification indices 57 2.3.4 Model estimated scale reliability 58 2.3.5 Item parceling 60 2.4 CFA models with non-normal and censored continuous indicators 61 2.4.1 Testing non-normality 61 2.4.2 CFA models with non-normal indicators 62 2.4.3 CFA models with censored data 67 2.5 CFA models with categorical indicators 70 2.5.1 CFA models with binary indicators 72 2.5.2 CFA models with ordinal categorical indicators 76 2.6 The item response theory (IRT) model and the graded response model (GRM) 77 2.6.1 The item response theory (IRT) model 77 2.6.2 The graded response model (GRM) 86 2.7 Higher-order CFA models 91 2.8 Bifactor models 96 2.9 Bayesian CFA models 102 2.10 Plausible values of latent variables 110 Appendix 2.A BSI-18 instrument 113 Appendix 2.B Item reliability 114 Appendix 2.C Cronbach’s alpha coefficient 116 Appendix 2.D Calculating probabilities using probit regression coefficients 117 3 Structural equation models 119 3.1 Introduction 119 3.2 Multiple indicators, multiple causes (MIMIC) model 120 3.2.1 Interaction effects between covariates 126 3.2.2 Differential item functioning (DIF) 127 3.3 General structural equation models 137 3.3.1 Testing indirect effects 141 3.4 Correcting for measurement error in single indicator variables 144 3.5 Testing interactions involving latent variables 150 3.6 Moderated mediating effect models 153 3.6.1 Bootstrap confidence intervals 159 3.6.2 Estimating counterfactual-based causal effects in Mplus 160 3.7 Using plausible values of latent variables in secondary analysis 164 3.8 Bayesian structural equation modeling (BSEM) 167 Appendix 3.A Influence of measurement errors 173 Appendix 3.B Fraction of missing information (FMI) 175 4 Latent growth modeling (LGM) for longitudinal data analysis 177 4.1 Introduction 177 4.2 Linear LGM 178 4.2.1 Unconditional linear LGM 178 4.2.2 LGM with time-invariant covariates 184 4.2.3 LGM with time-invariant and time-varying covariates 189 4.3 Nonlinear LGM 192 4.3.1 LGM with polynomial time functions 192 4.3.2 Piecewise LGM 203 4.3.3 Free time scores 210 4.3.4 LGM with distal outcomes 211 4.4 Multiprocess LGM 216 4.5 Two-part LGM 221 4.6 LGM with categorical outcomes 229 4.7 LGM with individually varying times of observation 238 4.8 Dynamic structural equation modeling (DSEM) 241 4.8.1 DSEM using observed centering for covariates 241 4.8.2 Residual DSEM (RDSEM) using observed centering for covariates 245 4.8.3 Residual DSEM (RDSEM) using latent variable centering for covariates 248 5 Multigroup modeling 253 5.1 Introduction 253 5.2 Multigroup CFA models 254 5.2.1 Multigroup first-order CFA 258 5.2.2 Multigroup second-order CFA 289 5.2.3 Multigroup CFA with categorical indicators 306 5.3 Multigroup SEM 316 5.3.1 Testing invariance of structural path coefficients across groups 322 5.3.2 Testing invariance of indirect effects across groups 326 5.4 Multigroup latent growth modeling (LGM) 327 5.4.1 Testing invariance of the growth function 332 5.4.2 Testing invariance of latent growth factor means 335 6 Mixture modeling 339 6.1 Introduction 339 6.2 Latent class analysis (LCA) modeling 340 6.2.1 Description of LCA models 341 6.2.2 Defining the latent classes 347 6.2.3 Predicting class membership 347 6.2.4 Unconditional LCA 348 6.2.5 Directly including covariates into LCA models 360 6.2.6 Approaches for auxiliary variables in LCA models 363 6.2.7 Implementing the PC, three-step, Lanza’s, and BCH methods 365 6.2.8 LCA with residual covariances 370 6.3 Extending LCA to longitudinal data analysis 373 6.3.1 Longitudinal latent class analysis (LLCA) 373 6.3.2 Latent transition analysis (LTA) models 375 6.4 Growth mixture modeling (GMM) 392 6.4.1 Unconditional growth mixture modeling (GMM) 394 6.4.2 GMM with covariates and a distal outcome 402 6.5 Factor mixture modeling (FMM) 411 6.5.1 LCFA models 417 Appendix 6.A Including covariates in LTA model 418 Appendix 6.B Manually implementing three-step mixture modeling 434 7 Sample size for structural equation modeling 443 7.1 Introduction 443 7.2 The rules of thumb for sample size in SEM 444 7.3 The Satorra-Saris method for estimating sample size 445 7.3.1 Application of The Satorra-Saris method to CFA models 446 7.3.2 Application of the Satorra-Saris’s method to latent growth models 454 7.4 Monte Carlo simulation for estimating sample sizes 458 7.4.1 Application of a Monte Carlo simulation to CFA models 459 7.4.2 Application of a Monte Carlo simulation to latent growth models 463 7.4.3 Application of a Monte Carlo simulation to latent growth models with covariates 467 7.4.4 Application of a Monte Carlo simulation to latent growth models with missing values 469 7.5 Estimate sample size for SEM based on model fit indexes 473 7.5.1 Application of the MacCallum–Browne–Sugawara’s method 474 7.5.2 Application of Kim’s method 477 7.6 Estimate sample sizes for latent class analysis (LCA) model 479 References 483 Index 507

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Book SynopsisFor years, organizations have struggled to make sense out of their data. IT projects designed to provide employees with dashboards, KPIs, and business-intelligence tools often take a year or more to reach the finish line...if they get there at all. This has always been a problem. Today, though, it''s downright unacceptable. The world changes faster than ever. Speed has never been more important. By adhering to antiquated methods, firms lose the ability to see nascent trendsand act upon them until it''s too late. But what if the process of turning raw data into meaningful insights didn''t have to be so painful, time-consuming, and frustrating? What if there were a better way to do analytics? Fortunately, you''re in luck... Analytics: The Agile Way is the eighth book from award-winning author and Arizona State University professor Phil Simon. Analytics: The Agile Waydemonstrates how progressive organizations such as Google, NextdTable of ContentsPreface: The Power of Dynamic Data xvii List of Figures and Tables xxvii Introduction: It Didn’t Used to Be This Way 1 A Little History Lesson 2 Analytics and the Need for Speed 5 Book Scope, Approach, and Style 9 Intended Audience 12 Plan of Attack 13 Next 14 Notes 14 Part One Background and Trends 17 Chapter 1 Signs of the Times: Why Data and Analytics Are Dominating Our World 19 The Moneyball Effect 20 Digitization and the Great Unbundling 22 Amazon Web Services and Cloud Computing 24 Not Your Father’s Data Storage 26 Moore’s Law 28 The Smartphone Revolution 28 The Democratization of Data 29 The Primacy of Privacy 29 The Internet of Things 31 The Rise of the Data-Savvy Employee 31 The Burgeoning Importance of Data Analytics 32 Data-Related Challenges 40 Companies Left Behind 41 The Growth of Analytics Programs 42 Next 43 Notes 43 Chapter 2 The Fundamentals of Contemporary Data: A Primer on What It Is, Why It Matters, and How to Get It 45 Types of Data 46 Getting the Data 52 Data in Motion 61 Next 63 Notes 63 Chapter 3 The Fundamentals of Analytics: Peeling Back the Onion 65 Defining Analytics 66 Types of Analytics 69 Streaming Data Revisited 72 A Final Word on Analytics 74 Next 75 Notes 75 Part Two Agile Methods and Analytics 77 Chapter 4 A Better Way to Work: The Benefits and Core Values of Agile Development 79 The Case against Traditional Analytics Projects 80 Proving the Superiority of Agile Methods 82 The Case for Guidelines over Rules 84 Next 88 Notes 88 Chapter 5 Introducing Scrum: Looking at One of Today’s Most Popular Agile Methods 89 A Very Brief History 90 Scrum Teams 91 User Stories 94 Backlogs 97 Sprints and Meetings 98 Releases 101 Estimation Techniques 102 Other Scrum Artifacts, Tools, and Concepts 109 Next 112 Chapter 6 A Framework for Agile Analytics: A Simple Model for Gathering Insights 113 Perform Business Discovery 115 Perform Data Discovery 117 Prepare the Data 118 Model the Data 120 Score and Deploy 127 Evaluate and Improve 128 Next 130 Notes 130 Part Three Analytics in Action 131 Chapter 7 University Tutoring Center: An In-Depth Case Study on Agile Analytics 133 The UTC and Project Background 134 Project Goals and Kickoff 136 Iteration One 139 Iteration Two 140 Iteration Three 145 Iteration Four 146 Results 147 Lessons 148 Next 148 Chapter 8 People Analytics at Google/Alphabet: Not Your Father’s HR Department 149 The Value of Business Experiments 150 PiLab’s Adventures in Analytics 151 A Better Approach to Hiring 153 Staffing 156 The Value of Perks 158 Results and Lessons 162 Next 162 Notes 163 Chapter 9 The Anti-Google: Beneke Pharmaceuticals 165 Project Background 166 Business and Data Discovery 167 The Friction Begins 168 Astonishing Results 169 Developing Options 171 The Grand Finale 172 Results and Lessons 173 Next 174 Chapter 10 Ice Station Zebra Medical: How Agile Methods Solved a Messy Health-Care Data Problem 175 Paying Nurses 176 Enter the Consultant 178 User Stories 179 Agile: The Better Way 182 Results 183 Lessons 183 Next 184 Chapter 11 Racial Profiling at Nextdoor: Using Data to Build a Better App and Combat a PR Disaster 185 Unintended but Familiar Consequences 187 Evaluating the Problem 188 Results and Lessons 193 Next 195 Notes 195 Part Four Making the Most Out of Agile Analytics ..........197 Chapter 12 The Benefits of Agile Analytics: The Upsides of Small Batches 199 Life at IAC 200 Life at RDC 203 Comparing the Two 206 Next 206 Chapter 13 No Free Lunch: The Impediments to—and Limitations of—Agile Analytics 209 People Issues 210 Data Issues 212 The Limitations of Agile Analytics 216 Next 219 Chapter 14 The Importance of Designing for Data: Lessons from the Upstarts 221 The Genes of Music 222 The Tension between Data and Design 226 Next 229 Notes 229 Part Five Conclusions and Next Steps 231 Chapter 15 What Now?: A Look Forward 233 A Tale of Two Retailers 234 The Blurry Futures of Data, Analytics, and Related Issues 239 Final Thoughts and Next Steps 242 Notes 243 Afterword 245 Acknowledgments 247 Selected Bibliography 249 Books 249 Articles and Essays 251 About the Author 253 Index 255

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Book SynopsisA timely update of a highly popular handbook on statistical genomics This new, two-volume edition of a classic text provides a thorough introduction to statistical genomics, a vital resource for advanced graduate students, early-career researchers and new entrants to the field. It introduces new and updated information on developments that have occurred since the 3rd edition. Widely regarded as the reference work in the field, it features new chapters focusing on statistical aspects of data generated by new sequencing technologies, including sequence-based functional assays. It expands on previous coverage of the many processes between genotype and phenotype, including gene expression and epigenetics, as well as metabolomics. It also examines population genetics and evolutionary models and inference, with new chapters on the multi-species coalescent, admixture and ancient DNA, as well as genetic association studies including causal analyses and variant interpretTable of ContentsVolume 1 List of Contributors xxiii Editors’ Preface to the Fourth Edition xxvii Glossary xxix Abbreviations and Acronyms xxxix 1 Statistical Modeling and Inference in Genetics 1Daniel Wegmann and Christoph Leuenberger 2 Linkage Disequilibrium, Recombination and Haplotype Structure 51Gil McVean and Jerome Kelleher 3 Haplotype Estimation and Genotype Imputation 87Jonathan Marchini 4 Mathematical Models in Population Genetics 115Nick Barton and Alison Etheridge 5 Coalescent Theory 145Magnus Nordborg 6 Phylogeny Estimation Using Likelihood-Based Methods 177John P. Huelsenbeck 7 The Multispecies Coalescent 219Laura Kubatko 8 Population Structure, Demography and Recent Admixture 247G. Hellenthal 9 Statistical Methods to Detect Archaic Admixture and Identify Introgressed Sequences 275Liming Li and Joshua M. Akey 10 Population Genomic Analyses of DNA from Ancient Remains 295Torsten Gunther and Mattias Jakobsson 11 Sequence Covariation Analysis in Biological Polymers 325William R. Taylor, Shaun Kandathil, and David T. Jones 12 Probabilistic Models for the Study of Protein Evolution 347Umberto Perron, Iain H. Moal, Jeffrey L. Thorne, and Nick Goldman 13 Adaptive Molecular Evolution 369Ziheng Yang 14 Detecting Natural Selection 397Aaron J. Stern and Rasmus Nielsen 15 Evolutionary Quantitative Genetics 421Bruce Walsh and Michael B. Morrissey 16 Conservation Genetics 457Mark Beaumont and Jinliang Wang 17 Statistical Methods for Plant Breeding 501Ian Mackay, Hans-Peter Piepho, and Antonio Augusto Franco Garcia 18 Forensic Genetics 531B.S.Weir Volume 2 19 Ethical Issues in Statistical Genetics 551Susan E. Wallace and Richard Ashcroft 20 Descent-Based Gene Mapping in Pedigrees and Populations 573E.A. Thompson 21 Genome-Wide Association Studies 597Andrew P. Morris and Lon R. Cardon 22 Replication and Meta-analysis of Genome-Wide Association Studies 631Frank Dudbridge and Paul Newcombe 23 Inferring Causal Relationships between Risk Factors and Outcomes Using Genetic Variation 651Stephen Burgess, Christopher N. Foley, and Verena Zuber 24 Improving Genetic Association Analysis through Integration of Functional Annotations of the Human Genome 679Qiongshi Lu and Hongyu Zhao 25 Inferring Causal Associations between Genes and Disease via the Mapping of Expression Quantitative Trait Loci 697Solveig K. Sieberts and Eric E. Schadt 26 Statistical Methods for Single-Cell RNA-Sequencing 735Tallulah S. Andrews, Vladimir Yu. Kiselev, and Martin Hemberg 27 Variant Interpretation and Genomic Medicine 761K. Carss, D. Goldstein, V. Aggarwal, and S. Petrovski 28 Prediction of Phenotype from DNA Variants 799M.E. Goddard, T.H.E. Meuwissen, and H.D. Daetwyler 29 Disease Risk Models 815Allison Meisner and Nilanjan Chatterjee 30 Bayesian Methods for Gene Expression Analysis 843Alex Lewin, Leonardo Bottolo, and Sylvia Richardson 31 Modelling Gene Expression Dynamics with Gaussian Process Inference 879Magnus Rattray, Jing Yang, Sumon Ahmed, and Alexis Boukouvalas 32 Modelling Non-homogeneous Dynamic Bayesian Networks with Piecewise Linear Regression Models 899Marco Grzegorczyk and Dirk Husmeier 33 DNA Methylation 933Kasper D. Hansen, Kimberly D. Siegmund, and Shili Lin 34 Statistical Methods in Metabolomics 949Timothy M.D. Ebbels, Maria De Iorio, and David A. Stephens 35 Statistical and Computational Methods in Microbiome and Metagenomics 977Hongzhe Li 36 Bacterial Population Genomics 997Jukka Corander, Nicholas J. Croucher, Simon R. Harris, John A. Lees, and Gerry Tonkin-Hill Reference Author Index 1021 Subject Index 1109

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Book SynopsisLearn how to apply the principles of machine learning totime series modeling with thisindispensableresource Machine Learning for Time Series Forecasting with Pythonis an incisive and straightforward examination of one of the most crucial elements of decision-makingin finance,marketing,education, and healthcare:time series modeling. Despitethe centrality of time series forecasting, few business analysts are familiar with the power or utility of applying machine learning to time series modeling. Author Francesca Lazzeri, a distinguishedmachine learning scientistandeconomist,corrects that deficiency by providing readers withcomprehensiveand approachableexplanation andtreatment of the applicationof machine learning to time series forecasting. Written for readers who have little to no experience in time seriesforecastingor machine learning, the book comprehensively coversall the topics necessary to: Understand time series forecasting concepts, such asstationarity,horizon,trend,and seasonalityPrepare time series dataformodelingEvaluatetime series forecasting models'performance and accuracyUnderstand when to use neural networks instead of traditional time series models in time series forecasting Machine Learning for Time Series Forecasting with Pythonis fullreal-world examples, resourcesand concrete strategies to help readers explore and transform data and develop usable, practical time series forecasts. Perfect for entry-level data scientists, business analysts,developers, and researchers, this book is an invaluable and indispensable guide to the fundamental and advanced concepts of machine learning applied to time series modeling. Table of ContentsAcknowledgments vii Introduction xv Chapter 1 Overview of Time Series Forecasting 1 Flavors of Machine Learning for Time Series Forecasting 3 Supervised Learning for Time Series Forecasting 14 Python for Time Series Forecasting 21 Experimental Setup for Time Series Forecasting 24 Conclusion 26 Chapter 2 How to Design an End-to-End Time Series Forecasting Solution on the Cloud 29 Time Series Forecasting Template 31 Business Understanding and Performance Metrics 33 Data Ingestion 36 Data Exploration and Understanding 39 Data Pre-processing and Feature Engineering 40 Modeling Building and Selection 42 An Overview of Demand Forecasting Modeling Techniques 44 Model Evaluation 46 Model Deployment 48 Forecasting Solution Acceptance 53 Use Case: Demand Forecasting 54 Conclusion 58 Chapter 3 Time Series Data Preparation 61 Python for Time Series Data 62 Common Data Preparation Operations for Time Series 65 Time stamps vs. Periods 66 Converting to Timestamps 69 Providing a Format Argument 70 Indexing 71 Time/Date Components 76 Frequency Conversion 78 Time Series Exploration and Understanding 79 How to Get Started with Time Series Data Analysis 79 Data Cleaning of Missing Values in the Time Series 84 Time Series Data Normalization and Standardization 86 Time Series Feature Engineering 89 Date Time Features 90 Lag Features and Window Features 92 Rolling Window Statistics 95 Expanding Window Statistics 97 Conclusion 98 Chapter 4 Introduction to Autoregressive and Automated Methods for Time Series Forecasting 101 Autoregression 102 Moving Average 119 Autoregressive Moving Average 120 Autoregressive Integrated Moving Average 122 Automated Machine Learning 129 Conclusion 136 Chapter 5 Introduction to Neural Networks for Time Series Forecasting 137 Reasons to Add Deep Learning to Your Time Series Toolkit 138 Deep Learning Neural Networks Are Capable of Automatically Learning and Extracting Features from Raw and Imperfect Data 140 Deep Learning Supports Multiple Inputs and Outputs 142 Recurrent Neural Networks Are Good at Extracting Patterns from Input Data 143 Recurrent Neural Networks for Time Series Forecasting 144 Recurrent Neural Networks 145 Long Short-Term Memory 147 Gated Recurrent Unit 148 How to Prepare Time Series Data for LSTMs and GRUs 150 How to Develop GRUs and LSTMs for Time Series Forecasting 154 Keras 155 TensorFlow 156 Univariate Models 156 Multivariate Models 160 Conclusion 164 Chapter 6 Model Deployment for Time Series Forecasting 167 Experimental Set Up and Introduction to Azure Machine Learning SDK for Python 168 Workspace 169 Experiment 169 Run 169 Model 170 Compute Target, RunConfiguration, and ScriptRun Config 171 Image and Webservice 172 Machine Learning Model Deployment 173 How to Select the Right Tools to Succeed with Model Deployment 175 Solution Architecture for Time Series Forecasting with Deployment Examples 177 Train and Deploy an ARIMA Model 179 Configure the Workspace 182 Create an Experiment 183 Create or Attach a Compute Cluster 184 Upload the Data to Azure 184 Create an Estimator 188 Submit the Job to the Remote Cluster 188 Register the Model 189 Deployment 189 Define Your Entry Script and Dependencies 190 Automatic Schema Generation 191 Conclusion 196 References 197 Index 199

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Book SynopsisAgent-based Models and Causal Inference Scholars of causal inference have given little credence to the possibility that ABMs could be an important tool in warranting causal claims. Manzo's book makes a convincing case that this is a mistake. The book starts by describing the impressive progress that ABMs have made as a credible methodology in the last several decades. It then goes on to compare the inferential threats to ABMs versus the traditional methods of RCTs, regression, and instrumental variables showing that they have a common vulnerability of being based on untestable assumptions. The book concludes by looking at four examples where an analysis based on ABMs complements and augments the evidence for specific causal claims provided by other methods. Manzo has done a most convincing job of showing that ABMs can be an important resource in any researcher's tool kit. Christopher Winship, Diker-Tishman Professor of Sociology, Harvard University, USA Agent-based Models and Causal Inference is a first-rate contribution to the debate on, and practice of, causal claims. With exemplary rigor, systematic precision and pedagogic clarity, this book contrasts the assumptions about causality that undergird agent-based models, experimental methods, and statistically based observational methods, discusses the challenges these methods face as far as inferences go, and, in light of this discussion, elaborates the case for combining these methods' respective strengths: a remarkable achievement. Ivan Ermakoff, Professor of Sociology, University of Wisconsin-Madison, USA Agent-based models are a uniquely powerful tool for understanding how patterns in society may arise in often surprising and counter-intuitive ways. This book offers a strong and deeply reflected argument for how ABM's can do much more: add to actual empirical explanation. The work is of great value to all social scientists interested in learning how computational modelling can help unraveling the complexity of the real social world. Andreas Flache, Professor of Sociology at the University of Groningen, Netherlands Agent-based Models and Causal Inference is an important and much-needed contribution to sociology and computational social science. The book provides a rigorous new contribution to current understandings of the foundation of causal inference and justification in the social sciences. It provides a powerful and cogent alternative to standard statistical causal-modeling approaches to causation. Especially valuable is Manzo's careful analysis of the conditions under which an agent-based simulation is relevant to causal inference. The book represents an exceptional contribution to sociology, the philosophy of social science, and the epistemology of simulations and models. Daniel Little, Professor of philosophy, University of Michigan, USA Agent-based Models and Causal Inference delivers an insightful investigation into the conditions under which different quantitative methods can legitimately hold to be able to establish causal claims. The book compares agent-based computational methods with randomized experiments, instrumental variables, and various types of causal graphs. Organized in two parts, Agent-based Models and Causal Inference connects the literature from various fields, including causality, social mechanisms, statistical and experimental methods for causal inference, and agent-based computation models to help show that causality means different things within different methods for causal analysis, and that persuasive causal claims can only be built at the intersection of these various methods. Readers will also benefit from the inclusion of: A thorough comparison between agent-based computation models to randomized experiments, instrumental variables, and several types of causal graphsA compelling argument that observational and experimental methods are not qualitatively superior to simulation-based methods in their ability to establish causal claimsPractical discussions of how statistical, experimental and computational methods can be combined to produce reliable causal inferences Perfect for academic social scientists and scholars in the fields of computational social science, philosophy, statistics, experimental design, and ecology, Agent-based Models and Causal Inference will also earn a place in the libraries of PhD students seeking a one-stop reference on the issue of causal inference in agent-based computational models.Table of ContentsList of Acronyms xi List of Tables xii Preface xiii The Book in a Nutshell xvii Introduction 1 1 The Book’s Question 3 2 The Book’s Structure 6 Part I: Conceptual and Methodological Clarifications 9 1 The Diversity of Views on Causality and Mechanisms 11 1.1 Causal Inference 11 1.2 Dependence and Production Accounts of Causality 13 1.3 Horizontal and Vertical Accounts of Mechanisms 17 1.3.1 Vertical versus Horizontal View 19 1.3.2 Horizontal versus Vertical View 21 1.4 Causality and Mechanism Accounts, and ABM’s Perception 22 2 Agent-based Models and the Vertical View on Mechanism 25 2.1 ABMs and Object-oriented Programming 26 2.2 ABMs and Heterogeneity 27 2.3 ABMs and Micro-foundations 28 2.4 ABMs and Interdependence 28 2.5 ABMs and Time 29 2.6 ABMs and Multi-level Settings 30 2.7 Variables within Statistical Methods and ABMs 31 3 The Diversity of Agent-based Models 33 3.1 Abstract versus Data-driven ABMs: An Old Opposition 34 3.2 Abstract versus Data-driven ABMs: Recent Trends 36 3.3 Theoretical, Input, and Output Realism 38 3.4 Different Paths to More Realistic ABMs 40 3.4.1 “Theoretically Blind” Data-driven ABMs 41 3.4.2 “Theoretically Informed” Data-driven ABMs 45 Part 2: Data and Arguments in Causal Inference 49 4 Agent-based Models and Causal Inference 51 4.1 ABMs as Inferential Devices 52 4.1.1 The Role of “Theoretical Realism” 52 4.1.2 The Role of “Output Realism” and Empirical Validation 54 4.1.3 The Role of “Input Realism” and Empirical Calibration 55 4.1.4 In Principle Conditions for Causally Relevant ABMs 57 4.1.5 Can Data-driven ABMs Produce Information on Their Own? 58 4.2 In Practice Limitations 59 4.2.1 ABMs’ Granularity and Data Availability 59 4.2.2 ABM’s Granularity and Data Embeddedness 61 4.3 From-Within-the-Method Reliability Tools 62 4.3.1 Sensitivity Analysis 64 4.3.2 Robustness Analysis 65 4.3.3 Dispersion Analysis 65 4.3.4 Model Analysis 66 5 Causal Inference in Experimental and Observational Methods 69 5.1 Causal Inference: Cautionary Tales 71 5.2 In Practice Untestable Assumptions 73 5.2.1 RCTs and Heterogeneity 73 5.2.2 IVs and the “Relevance” Condition 74 5.2.3 DAGs, Causal Discovery Algorithms and Graph Indistinguishability 76 5.3 In Principle Untestable Assumptions 79 5.3.1 RCTs and “Stable Unit Treatment Value Assumption” (SUTVA) 79 5.3.2 IVs and the “Exclusion” Condition 81 5.3.3 DAGs and Strategies for Causal Identification 83 5.3.3.1 DAGs and the “Backdoor” Criterion 83 5.3.3.2 DAGs and the “Front Door” Criterion 84 5.4 Are ABMs, Experimental and Observational Methods Fundamentally Similar? 85 5.4.1 Objection 1: ABM Lacks “Formal” Assumptions 86 5.4.2 Objection 2: ABM Lacks “Materiality” 89 5.4.3 Objection 3: ABMs Lack “Robustness” 91 5.5 A Common Logic: “Abduction” 94 6 Method Diversity and Causal Inference 95 6.1 Causal Pluralism, Causal Exclusivism, and Evidential Pluralism 97 6.2 A Pragmatist Account of Evidence 99 6.3 Evidential Pluralism and “Coherentism” 101 6.4 When is Diverse Evidence Most Relevant? 104 6.5 Examples of Method Synergies 106 6.5.1 Obesity: ABMs and Regression Models 106 6.5.2 Network Properties: ABMs and SIENA Models 109 6.5.3 HIV prevalence: ABMs and RCTs 111 6.5.4 HIV treatments: ABMs and DAG-based identification strategies 113 Coda 115 1 Possible Objections 116 1.1 Causation is Not Constitution 117 1.2 Lack of a Specific Research Strategy 118 1.3 A Limited Methodological Spectrum 119 2 Summary 121 References 127 Index 149

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Book SynopsisTable of ContentsIntroduction 1 Part 1: the Questions 5 Chapter 1: Basic Vocabulary 7 Chapter 2: Descriptive Statistics 11 Chapter 3: Graphing 21 Chapter 4: Random Variables and the Binomial Distribution 33 Chapter 5: The Normal Distribution 43 Chapter 6: The t-Distribution 51 Chapter 7: Sampling Distributions and the Central Limit Theorem 57 Chapter 8: Finding Room for a Margin of Error 71 Chapter 9: Confidence Intervals: Basics for Single Population Means and Proportions 75 Chapter 10: Confidence Intervals for Two Population Means and Proportions 91 Chapter 11: Claims, Tests, and Conclusions 97 Chapter 12: Hypothesis Testing Basics for a Single Population Mean: z- and t-Tests 105 Chapter 13: Hypothesis Tests for One Proportion, Two Proportions, or Two Population Means 117 Chapter 14: Surveys 127 Chapter 15: Correlation 131 Chapter 16: Simple Linear Regression 139 Chapter 17: Two-Way Tables and Independence 153 Part 2: the Answers 165 Chapter 18: Answers 167 Appendix: Tables for Reference 463 Index 475

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Book SynopsisThis book provides a comprehensive and up to date treatment of theory and practical implementation in Register-based statistics. It begins by defining the area, before explaining how to structure such systems, as well as detailing alternative approaches. It explains how to create statistical registers, how to implement quality assurance, and the use of IT systems for register-based statistics. Further to this, clear details are given about the practicalities of implementing such statistical methods, such as protection of privacy and the coordination and coherence of such an undertaking. This edition offers a full understanding of both the principles and practices of this increasingly popular area of statistics, and can be considered a first step to a more systematic way of working with register-statistical issues. This book addresses the growing global interest in the topic and employs a much broader, more international approach than the 1st edition. New chapters eTable of ContentsPreface xi Chapter 1 Register Surveys – An Introduction 1 1.1 The purpose of the book 1 1.2 The need for a new theory and new methods 3 1.3 Four ways of using administrative registers 5 1.4 Preconditions for register-based statistics 6 1.4.1 Reliable administrative systems 7 1.4.2 Legal base and public approval 8 1.5 Basic concepts and terms 10 1.5.1 What is a statistical survey? 10 1.5.2 What is a register? 11 1.5.3 What is a register survey? 13 1.5.4 The Income and Taxation Register 14 1.5.5 The Quarterly and Annual Pay Registers 16 1.6 Comparing sample surveys and register surveys 20 1.7 Conclusions 23 Chapter 2 The Nature of Administrative Data 25 2.1 Different kinds of administrative data 25 2.2 How are data recorded? 26 2.3 Administrative and statistical information systems 27 2.4 Measurement errors in statistical and administrative data 29 2.5 Why use administrative data for statistics? 30 2.6 Comparing sample survey and administrative data 32 2.6.1 A questionnaire to persons compared with register data 32 2.6.2 An enterprise questionnaire compared with register data 34 2.7 Conclusions 36 Chapter 3 Protection of Privacy and Confidentiality 37 3.1 Internal security 38 3.1.1 No text in output databases! 38 3.1.2 Existence of identity numbers 39 3.2 Disclosure risks – tables 40 3.2.1 Rules for tables with counts, totals and mean values 41 3.2.2 The threshold rule – analyse complete tables! 43 3.2.3 Frequency tables are often misunderstood 44 3.2.4 Combining tables can cause disclosure 45 3.3 Disclosure risks – micro data 45 3.4 Conclusions 46 Chapter 4 The Register System 47 4.1 A register model based on object types and relations 47 4.1.1 The register system and protection of privacy 53 4.1.2 The register system and data warehousing 53 4.2 Organising the work with the system 54 4.3 The populations in the system 56 4.3.1 How to produce consistent register-based statistics 57 4.3.2 Registers and time 58 4.3.3 Populations, variables and time 59 4.4 The variables in the system 60 4.4.1 Standardised variables in the register system 60 4.4.2 Derived variables 62 4.4.3 Variables with different origins 63 4.4.4 Variables with different functions in the system 64 4.5 Using the system for micro integration 65 4.6 Three kinds of registers with different roles 70 4.7 Register systems and register surveys within enterprises 72 4.8 Conclusions 74 Chapter 5 The Base Registers in the System 77 5.1 Characteristics of a base register 77 5.2 Requirements for base registers 78 5.2.1 Defining and deriving statistical units 78 5.2.2 Objects and identities – requirements for a base register 80 5.2.3 Coverage and spanning variables in base registers 81 5.3 The Population Register 83 5.4 The Business Register 88 5.5 The Real Estate Register 93 5.6 The Activity Register 94 5.7 Everyone should support the base registers! 98 5.8 Conclusions 101 Chapter 6 How to Create a Register – Matching and Combining Sources 103 6.1 Preconditions in different countries 103 6.2 Matching methods and problems 105 6.2.1 Deterministic record linkage 105 6.2.2 Probabilistic record linkage 106 6.2.3 Four causes of matching errors 112 6.3 Matching sources with different object types 114 6.4 Conclusions 120 Chapter 7 How to Create a Register – The Population 121 7.1 How should register surveys be structured? 121 7.2 Register survey design 125 7.2.1 Determining the research objectives 125 7.2.2 Making an inventory of different sources 128 7.2.3 Analysing the usability of administrative sources 128 7.3 Defining a register’s object set 131 7.3.1 Defining a population 131 7.3.2 Can you alter data from the National Tax Agency? 134 7.3.3 Defining a population – primary registers 135 7.3.4 Defining a population – integrated registers 136 7.3.5 Defining a calendar year population 137 7.3.6 Defining a population – frame or register population? 138 7.3.7 Base registers should be used when defining populations 141 7.4 Defining the statistical units 142 7.4.1 Units and identities when creating primary registers 143 7.4.2 Using administrative objects instead of statistical units 144 7.5 Creating longitudinal registers – the population 145 7.6 Conclusions 146 Chapter 8 How to Create a Register – The Variables 147 8.1 The variables in the register 147 8.1.1 Variable definitions 148 8.1.2 Variables in statistical science 149 8.1.3 Variables in informatics 150 8.1.4 Creating register variables – check list 151 8.2 Forming derived variables using models 151 8.2.1 Exact calculation of values using a rule 152 8.2.2 Estimating values with a rule 153 8.2.3 Estimating values with a causal model 154 8.2.4 Derived variables and imputed variable values 157 8.2.5 Creating variables by coding 158 8.3 Activity data 159 8.3.1 Activity statistics 160 8.3.2 Activity data aggregated for enterprises and organisations 161 8.3.3 Activity data aggregated for persons – multi-valued variables 161 8.4 Creating longitudinal registers – the variables 165 8.5 Conclusions 169 Chapter 9 How to Create a Register – Editing 171 9.1 Editing register data 171 9.1.1 Editing one administrative register 173 9.1.2 Consistency editing – is the population correct? 175 9.1.3 Consistency editing – are the units correct? 178 9.1.4 Consistency editing – are the variables correct? 180 9.2 Case studies – editing register data 181 9.2.1 Editing work within the Income and Taxation Register 181 9.2.2 Editing work with the Income Statement Register 183 9.2.3 What more can be learned from these examples? 184 9.3 Editing, quality assurance and survey design 185 9.3.1 Survey design in a register-based production system 185 9.3.2 Quality assessment in a register-based production system 186 9.3.3 Total survey error in a register-based production system 191 9.4 Conclusions 192 Chapter 10 Metadata 193 10.1 Primary registers – the need for metadata 193 10.1.1 Documentation of administrative sources 194 10.1.2 Documentation of sources within the system 195 10.1.3 Documentation of a new register 195 10.2 Changes over time – the need for metadata 195 10.3 Integrated registers – the need for metadata 196 10.4 Classification and definitions database 197 10.5 The need for metadata for registers 198 10.6 Conclusions 200 Chapter 11 Estimation Methods – Introduction 201 11.1 Estimation in sample surveys and register surveys 202 11.2 Estimation methods for register surveys that use weights 203 11.3 Calibration of weights in register surveys 204 11.4 Using weights for estimation 207 11.5 Conclusions 208 Chapter 12 Estimation Methods – Missing Values 209 12.1 Make no adjustments, publish ‘value unknown’ 210 12.2 Adjustment for missing values using weights 214 12.3 Adjustment for missing values by imputation 215 12.4 Missing values in a system of registers 218 12.5 Conclusions 220 Chapter 13 Estimation Methods – Coverage Problems 221 13.1 Reducing overcoverage and undercoverage 221 13.1.1 Coverage problems in the Population Register 221 13.1.2 Coverage problems in the Business Register 222 13.2 Estimation methods to correct for overcoverage 224 13.3 Undercoverage in the administrative system 226 13.4 Conclusions 228 Chapter 14 Estimation Methods – Multi-valued Variables 229 14.1 Multi-valued variables 229 14.2 Estimation methods 232 14.2.1 Occupation in the Activity and Occupation Registers 232 14.2.2 Industrial classification in the Business Register 236 14.2.3 Importing many multi-valued variables 238 14.2.4 Consistency between estimates from different registers 242 14.2.5 Multi-valued variables – what is done in practice? 245 14.2.6 Additional estimation methods 247 14.3 Application of the method 251 14.4 Linking of time series using combination objects 254 14.4.1 Linking time series 254 14.4.2 Changed industrial classification in the Business Register 256 14.5 Conclusions 258 Chapter 15 Theory and Quality of Register-based Statistics 259 15.1 Is there a theory for register surveys? 259 15.1.1 Statistical inference at a national statistical office 260 15.1.2 Theory-based methods or ad hoc methods 262 15.1.3 The survey approach and the systems approach 263 15.2 Measuring quality – why and how? 267 15.3 Analysing administrative sources – input data quality 271 15.4 Output data quality 278 15.5 The integration process – integration errors 279 15.5.1 Creating register populations – coverage errors 280 15.5.2 Creating statistical units –errors in units 282 15.5.3 Creating statistical variables – errors in variables 283 15.6 Random variation in register data 288 15.7 The register system and data warehousing 291 15.8 Conclusions 295 Chapter 16 Conclusions 297 References 301 Index 305

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Book SynopsisA reference to answer all your statistical confidentiality questions. This handbook provides technical guidance on statistical disclosure control and on how to approach the problem of balancing the need to provide users with statistical outputs and the need to protect the confidentiality of respondents.Table of ContentsPreface xi Acknowledgements xv 1 Introduction 1 1.1 Concepts and definitions 2 1.1.1 Disclosure 2 1.1.2 Statistical disclosure control 3 1.1.3 Tabular data 3 1.1.4 Microdata 3 1.1.5 Risk and utility 4 1.2 An approach to Statistical Disclosure Control 7 1.2.1 Why is confidentiality protection needed? 7 1.2.2 What are the key characteristics and uses of the data? 8 1.2.3 What disclosure risks need to be protected against? 8 1.2.4 Disclosure control methods 8 1.2.5 Implementation 9 1.3 The chapters of the handbook 9 2 Ethics, principles, guidelines and regulations – a general background 10 2.1 Introduction 10 2.2 Ethical codes and the new ISI code 11 2.2.1 ISI Declaration on Professional Ethics 11 2.2.2 New ISI Declaration on Professional Ethics 12 2.2.3 European Statistics Code of Practice 15 2.3 UNECE principles and guidelines 16 2.3.1 UNECE Principles and Guidelines on Confidentiality Aspects of Data Integration 18 2.3.2 Future activities on the UNECE principles and guidelines 19 2.4 Laws 19 2.4.1 Committee on Statistical Confidentiality 20 2.4.2 European Statistical System Committee 20 3 Microdata 23 3.1 Introduction 23 3.2 Microdata concepts 24 3.2.1 Stage 1: Assess need for confidentiality protection 24 3.2.2 Stage 2: Key characteristics and use of microdata 27 3.2.3 Stage 3: Disclosure risk 30 3.2.4 Stage 4: Disclosure control methods 32 3.2.5 Stage 5: Implementation 34 3.3 Definitions of disclosure 36 3.3.1 Definitions of disclosure scenarios 37 3.4 Definitions of disclosure risk 38 3.4.1 Disclosure risk for categorical quasi-identifiers 39 3.4.2 Notation and assumptions 40 3.4.3 Disclosure risk for continuous quasi-identifiers 41 3.5 Estimating re-identification risk 43 3.5.1 Individual risk based on the sample: Threshold rule 44 3.5.2 Estimating individual risk using sampling weights 44 3.5.3 Estimating individual risk by Poisson model 47 3.5.4 Further models that borrow information from other sources 48 3.5.5 Estimating per record risk via heuristics 49 3.5.6 Assessing risk via record linkage 50 3.6 Non-perturbative microdata masking 51 3.6.1 Sampling 51 3.6.2 Global recoding 52 3.6.3 Top and bottom coding 53 3.6.4 Local suppression 53 3.7 Perturbative microdata masking 53 3.7.1 Additive noise masking 54 3.7.2 Multiplicative noise masking 57 3.7.3 Microaggregation 60 3.7.4 Data swapping and rank swapping 72 3.7.5 Data shuffling 73 3.7.6 Rounding 73 3.7.7 Re-sampling 74 3.7.8 Pram 74 3.7.9 Massc 78 3.8 Synthetic and hybrid data 78 3.8.1 Fully synthetic data 79 3.8.2 Partially synthetic data 84 3.8.3 Hybrid data 86 3.8.4 Pros and cons of synthetic and hybrid data 98 3.9 Information loss in microdata 100 3.9.1 Information loss measures for continuous data 101 3.9.2 Information loss measures for categorical data 108 3.10 Release of multiple files from the same microdata set 110 3.11 Software 111 3.11.1 μ-argus 111 3.11.2 sdcMicro 113 3.11.3 IVEware 115 3.12 Case studies 116 3.12.1 Microdata files at Statistics Netherlands 116 3.12.2 The European Labour Force Survey microdata for research purposes 118 3.12.3 The European Structure of Earnings Survey microdata for research purposes 121 3.12.4 NHIS-linked mortality data public use file, USA 128 3.12.5 Other real case instances 130 4 Magnitude tabular data 131 4.1 Introduction 131 4.1.1 Magnitude tabular data: Basic terminology 131 4.1.2 Complex tabular data structures: Hierarchical and linked tables 132 4.1.3 Risk concepts 134 4.1.4 Protection concepts 137 4.1.5 Information loss concepts 137 4.1.6 Implementation: Software, guidelines and case study 138 4.2 Disclosure risk assessment I: Primary sensitive cells 138 4.2.1 Intruder scenarios 138 4.2.2 Sensitivity rules 140 4.3 Disclosure risk assessment II: Secondary risk assessment 152 4.3.1 Feasibility interval 152 4.3.2 Protection level 154 4.3.3 Singleton and multi cell disclosure 155 4.3.4 Risk models for hierarchical and linked tables 155 4.4 Non-perturbative protection methods 157 4.4.1 Global recoding 157 4.4.2 The concept of cell suppression 157 4.4.3 Algorithms for secondary cell suppression 158 4.4.4 Secondary cell suppression in hierarchical and linked tables 161 4.5 Perturbative protection methods 163 4.5.1 A pre-tabular method: Multiplicative noise 165 4.5.2 A post-tabular method: Controlled tabular adjustment 165 4.6 Information loss measures for tabular data 166 4.6.1 Cell costs for cell suppression 166 4.6.2 Cell costs for CTA 167 4.6.3 Information loss measures to evaluate the outcome of table protection 167 4.7 Software for tabular data protection 168 4.7.1 Empirical comparison of cell suppression algorithms 169 4.8 Guidelines: Setting up an efficient table model systematically 173 4.8.1 Defining spanning variables 174 4.8.2 Response variables and mapping rules 175 4.9 Case studies 178 4.9.1 Response variables and mapping rules of the case study 178 4.9.2 Spanning variables of the case study 179 4.9.3 Analysing the tables of the case study 179 4.9.4 Software issues of the case study 181 5 Frequency tables 183 5.1 Introduction 183 5.2 Disclosure risks 184 5.2.1 Individual attribute disclosure 185 5.2.2 Group attribute disclosure 186 5.2.3 Disclosure by differencing 187 5.2.4 Perception of disclosure risk 190 5.3 Methods 191 5.3.1 Pre-tabular 191 5.3.2 Table re-design 192 5.3.3 Post-tabular 193 5.4 Post-tabular methods 193 5.4.1 Cell suppression 193 5.4.2 ABS cell perturbation 193 5.4.3 Rounding 194 5.5 Information loss 199 5.6 Software 201 5.6.1 Introduction 201 5.6.2 Optimal, first feasible and RAPID solutions 202 5.6.3 Protection provided by controlled rounding 203 5.7 Case studies 204 5.7.1 UK Census 204 5.7.2 Australian and New Zealand Censuses 205 6 Data access issues 208 6.1 Introduction 208 6.2 Research data centres 209 6.3 Remote execution 209 6.4 Remote access 210 6.5 Licensing 211 6.6 Guidelines on output checking 211 6.6.1 Introduction 211 6.6.2 General approach 212 6.6.3 Rules for output checking 215 6.6.4 Organisational/procedural aspects of output checking 224 6.6.5 Researcher training 233 6.7 Additional issues concerning data access 236 6.7.1 Examples of disclaimers 236 6.7.2 Output description 236 6.8 Case studies 237 6.8.1 The US Census Bureau Microdata Analysis System 237 6.8.2 Remote access at Statistics Netherlands 239 Glossary 243 References 261 Author index 279 Subject index 282

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Book SynopsisStatistical Methods in Customer Relationship Management focuses on the quantitative and modeling aspects of customer management strategies that lead to future firm profitability, with emphasis on developing an understanding of Customer Relationship Management (CRM) models as the guiding concept for profitable customer management.Trade Review“Academics and practitioners involved in the area of CRM as well as instructors of applied statistics and quantitative marketing courses will benefit from this book.” (Zentralblatt MATH, 1 May 2013) Table of ContentsPreface ix 1 Customer relationship management 1 1.1 Introduction 1 1.2 What is CRM? 2 1.3 What is needed to implement CRM strategies? 3 1.3.1 Database 3 1.3.2 Technology 6 1.3.3 Metrics 7 1.4 Analytical methods 9 1.5 Conclusion 9 References 10 2 CRM in action 11 2.1 Introduction 11 2.2 The importance of customer acquisition 13 2.3 The significance of customer retention 15 2.4 The impact of customer churn 17 2.5 The benefits of customer win-back 18 2.6 Conclusion 20 References 20 3 Customer acquisition 22 3.1 Introduction 22 3.1.1 Data for empirical examples 27 3.2 Response probability 28 3.2.1 Empirical example: Response probability 32 3.2.2 How do you implement it? 34 3.3 Number of newly acquired customers and initial order quantity 35 3.3.1 Empirical example: Number of newly acquired customers 37 3.3.2 How do you implement it? 38 3.3.3 Empirical example: Initial order quantity 39 3.3.4 How do you implement it? 42 3.4 Duration/time 42 3.4.1 Empirical example: Duration/time 44 3.4.2 How do you implement it? 46 3.5 Firm’s performance (LTV, CLV, and CE) 47 3.5.1 Empirical example: Firm’s performance 49 3.5.2 How do you implement it? 52 3.6 Chapter summary 52 Customer acquisition – SAS code 53 Customer acquisition – SAS output 55 References 61 4 Customer retention 63 4.1 Introduction 63 4.1.1 Data for empirical examples 66 4.2 Repurchase or not (stay or leave) 69 4.2.1 Will a customer repurchase? 69 4.2.2 When will a customer no longer repurchase? 71 4.2.3 Empirical example: Repurchase or not (stay or leave) 73 4.2.4 How do you implement it? 78 4.3 Lifetime duration 78 4.3.1 Empirical example: Lifetime duration 83 4.3.2 How do you implement it? 85 4.4 Order quantity and order size 85 4.4.1 How much (in $) will a customer order? 85 4.4.2 How many items will a customer order? 86 4.4.3 What is the average order size? 87 4.4.4 Empirical example: Order quantity 87 4.4.5 How do you implement it? 91 4.5 Cross-buying 91 4.5.1 Empirical example: Cross-buying 92 4.5.2 How do you implement it? 97 4.6 SOW 97 4.6.1 Empirical example: SOW 98 4.6.2 How do you implement it? 101 4.7 Profitability (CLV) 102 4.7.1 Empirical example: Profitability (CLV) 103 4.7.2 How do you implement it? 105 4.8 Chapter summary 105 Customer retention – SAS code 106 Customer retention – SAS output 111 References 119 5 Balancing acquisition and retention 121 5.1 Introduction 121 5.1.1 Data for empirical examples 122 5.2 Acquisition and retention 124 5.2.1 Empirical example: Balancing acquisition and retention 128 5.3 Optimal resource allocation 137 5.3.1 How do you implement it? 140 5.4 Chapter summary 141 Balancing acquisition and retention – SAS code 142 Balancing acquisition and retention – SAS output 144 References 147 6 Customer churn 149 6.1 Introduction 149 6.1.1 Data for empirical examples 150 6.2 Customer churn 151 6.2.1 Empirical example: Customer churn 156 6.2.2 How do you implement it? 161 6.3 Chapter summary 161 Customer churn – SAS code 162 Customer churn – SAS output 163 References 164 7 Customer win-back 166 7.1 Introduction 166 7.1.1 Data for empirical examples 167 7.2 Customer win-back 168 7.2.1 Empirical example: Customer win-back 169 7.2.2 How do you implement it? 178 7.3 Chapter summary 179 Customer win-back – SAS code 180 Customer win-back – SAS output 182 References 185 8 Implementing CRM models 186 8.1 Introduction 186 8.2 CLV measurement approach 187 8.3 CRM implementation at IBM 190 8.3.1 IBM background 190 8.3.2 Implementing a CLV management framework at IBM 191 8.4 CRM implementation at a B2C firm 202 8.4.1 The focal firm background 202 8.4.2 Implementing the CLV management framework at a fashion retailer 202 8.4.3 Process to implement the CLV management framework at a fashion retailer 203 8.5 Challenges in implementing the CLV management framework 219 8.5.1 Challenges in data collection and internal collaboration 219 8.5.2 Challenges in implementing the customer-centric approach 220 References 222 9 The future of CRM 223 9.1 Introduction 223 9.2 Social media 223 9.3 Mobile marketing 226 9.4 Customized marketing campaigns 227 9.5 Conclusion 229 References 229 Appendix A: Maximum likelihood estimation 230 Appendix B: Log-linear model—an introduction 232 Appendix C: Vector autoregression modeling 235 Appendix D: Accelerated lifetime model 241 Appendix E: Type-1 Tobit model 244 Appendix F: Multinomial logit model 246 Appendix G: Survival analysis – an introduction 249 Appendix H: Discrete-time hazard 252 Appendix I: Proportional hazards model 254 Appendix J: Random intercept model 257 Appendix K: Poisson regression model 260 Appendix L: Negative binomial regression 262 Appendix M: Estimation of Tobit model with selection 265 Index 267

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Book SynopsisExperimental Design and Statistics for Psychology: A First Course is a concise, straighforward and accessible introduction to the design of psychology experiments and the statistical tests used to make sense of their results. Makes abundant use of charts, diagrams and figures. Assumes no prior knowledge of statistics. Invaluable to all psychology students needing a firm grasp of the basics, but tackling of some of the topic's more complex, controversial issues will also fire the imagination of more ambitious students. Covers different aspects of experimental design, including dependent versus independent variables, levels of treatment, experimental control, random versus systematic errors, and within versus between subjects design. Provides detailed instructions on how to perform statistical tests with SPSS. Downloadable instructor resources to supplement and support your lectures can be found at www.blackwTrade Review"This text helps to bring the research process alive and will clearly prove invaluable to all undergraduate students of psychology. The authors cleverly illustrate the progression in psychological research from hypothesis-formation to research design and finally to data analysis in a unique and informative manner." Simon Dymond PhD., undergraduate research methods instructor, University of Wales, Swansea "This will serve best as a reference book to support undergraduate teaching and as a useful companion to have on hand on introductory level methods classes. It provides first and second year psychology students with a well-grounded grasp of the basics. A well-written and long awaited text that bridges the gap between experimental design and statistical analysis." Psychology Reaching Review "Lively, friendly, amusing and lucid, this is an excellent introduction to experimental design and statistics which provides the clear yet informative explanations that most readers prefer. I would certainly recommend it to my students." Colin Gray, University of Aberdeen & co- author of 'SPSS 12 Made Simple' "This text maintains a wonderful balance of conceptual and practical focus. After each statistical test, the authors demonstrate its use in a hypothetical research study...I would recommend that anyone who teaches or takes a course in survey sampling theory and methods obtain a copy of this book" David R. Bellhouse, The American Statistician, August 2007, Vol. 61, No. 3Table of ContentsPreface. 1. Scientific Psychology and the Research Process. 2. The Nature of Psychology Experiments (I): Variables and Conditions. 3. The Nature of Psychology Experiments (II): Validity. 4. Describing Data. 5. Making Inferences from Data. 6. Selecting a Statistical Test. 7. Tests of Significance for Nominal Data. 8. Tests of Significance for Ordinal Data (and Interval/Ratio Data When Parametric Assumptions Are Not Met). 9. Tests of Significance for Interval Data. 10. Correlational Studies. Appendix 1: Statistical Tables. Glossary. A Brief List of Recommended Books. Index.

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Book SynopsisExperimental Design and Statistics for Psychology: A First Course is a concise, straighforward and accessible introduction to the design of psychology experiments and the statistical tests used to make sense of their results. * Makes abundant use of charts, diagrams and figures. * Assumes no prior knowledge of statistics.Trade Review"This text helps to bring the research process alive and will clearly prove invaluable to all undergraduate students of psychology. The authors cleverly illustrate the progression in psychological research from hypothesis-formation to research design and finally to data analysis in a unique and informative manner." Simon Dymond PhD., undergraduate research methods instructor, University of Wales, Swansea "This will serve best as a reference book to support undergraduate teaching and as a useful companion to have on hand on introductory level methods classes. It provides first and second year psychology students with a well-grounded grasp of the basics. A well-written and long awaited text that bridges the gap between experimental design and statistical analysis." Psychology Reaching Review "Lively, friendly, amusing and lucid, this is an excellent introduction to experimental design and statistics which provides the clear yet informative explanations that most readers prefer. I would certainly recommend it to my students." Colin Gray, University of Aberdeen & co- author of 'SPSS 12 Made Simple' "This text maintains a wonderful balance of conceptual and practical focus. After each statistical test, the authors demonstrate its use in a hypothetical research study...I would recommend that anyone who teaches or takes a course in survey sampling theory and methods obtain a copy of this book" David R. Bellhouse, The American Statistician, August 2007, Vol. 61, No. 3Table of ContentsPreface 1 Scientific Psychology and the Research Process 2 The Nature of Psychology Experiments (I): Variables and Conditions 3 The Nature of Psychology Experiments (II): Validity 4 Describing Data 5 Making Inferences from Data 6 Selecting a Statistical Test 7 Tests of Significance for Nominal Data 8 Tests of Significance for Ordinal Data (and Interval/Ratio Data When Parametric Assumptions Are Not Met) 9 Tests of Significance for Interval Data 10 Correlational Studies Appendix 1: Statistical Tables Glossary Recommended Books Index

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