Mathematics Books

Book SynopsisAssessing Weight-of-Evidence for DNA Profiles is an excellent introductory text to the use of statistical analysis for assessing DNA evidence. It offers practical guidance to forensic scientists with little dependence on mathematical ability as the book includes background information on statistics including likelihood ratios population genetics, and courtroom issues. The author, who is highly experienced in this field, has illustrated the book throughout with his own experiences as well as providing a theoretical underpinning to the subject. It is an ideal choice for forensic scientists and lawyers, as well as statisticians and population geneticists with an interest in forensic science and DNA.Trade Review"This book is a good example of how statistics can be explained in plain English to a nontechnical audience, a skill that every statistician needs to master for improved communication." (Technometrics, August 2008) "...this book should provide a good starting point for any reader..." (International Statistical Institute, January 2006) " … one of the most gifted writers in forensic interpretation…an excellent contribution to our field." (Science & Justice Volume 45 no. 3)Table of ContentsPreface xi 1 Introduction 1 1.1 Weight-of-evidence theory 1 1.2 About the book 3 1.3 DNA profiling technology 3 1.4 What you need to know already 4 1.5 Other resources 5 2 Crime on an island 7 2.1 Warm-up examples 7 2.1.1 Disease testing: Positive Predictive Value (PPV) 7 2.1.2 Coloured taxis 9 2.2 Rare trait identification evidence 10 2.2.1 The “island” problem 10 2.2.2 A first lesson from the island problem 11 2.3 Making the island problem more realistic 13 2.3.1 Uncertainty about p 14 2.3.2 Uncertainty about N 15 2.3.3 Possible typing errors 15 2.3.4 Searches 17 2.3.5 Other evidence 18 2.3.6 Relatives and population subdivision 19 2.4 Weight-of-evidence exercises 20 3 Assessing evidence via likelihood ratios 22 3.1 Likelihood ratios 22 3.2 The weight-of-evidence formula 24 3.2.1 Application to the island problem 25 3.2.2 The population P 25 3.3 General application of the formula 27 3.3.1 Several items of evidence 27 3.3.2 Assessing all the evidence 29 3.3.3 The role of the expert witness 30 3.4 Consequences for DNA evidence 31 3.4.1 Many possible culprits 31 3.4.2 Incorporating the non-DNA evidence 31 3.4.3 Relatives 33 3.4.4 Laboratory and handling errors 34 3.4.5 Database searches 35 3.5 Some derivations † 36 3.5.1 Bayes theorem for identification evidence 37 3.5.2 Uncertainty about p and N 38 3.5.3 Grouping the alternative possible culprits 39 3.5.4 Typing errors 40 3.6 Further weight-of-evidence exercises 40 4 Typing technologies 43 4.1 STR typing 44 4.1.1 Anomalies 46 4.1.2 Contamination 49 4.1.3 Low copy number (LCN) profiling 50 4.2 mtDNA typing 50 4.3 Y-chromosome markers 51 4.4 X-chromosome markers † 52 4.5 SNP profiles 53 4.6 Fingerprints † 54 5 Some population genetics for DNA evidence 56 5.1 A brief overview 56 5.1.1 Drift 56 5.1.2 Mutation 59 5.1.3 Migration 60 5.1.4 Selection 60 5.2 θ, or FST 62 5.3 A statistical model and sampling formula 63 5.3.1 Diallelic loci 63 5.3.2 Multi-allelic loci 68 5.4 Hardy–Weinberg equilibrium 69 5.4.1 Testing for deviations from HWE † 70 5.4.2 Interpretation of test results 74 5.5 Linkage equilibrium 75 5.6 Coancestry † 77 5.7 Likelihood-based estimation of θ † 79 5.8 Population genetics exercises 81 6 Identification 82 6.1 Choosing the hypotheses 82 6.1.1 Post-data equivalence of hypotheses 84 6.2 Calculating likelihood ratios 85 6.2.1 The match probability 85 6.2.2 One locus 87 6.2.3 Multiple loci: the “product rule” 89 6.2.4 Relatives of s 90 6.2.5 Confidence limits † 92 6.2.6 Other profiled individuals 93 6.3 Application to STR profiles 94 6.3.1 Values for the pj 95 6.3.2 The value of θ 96 6.3.3 Errors 98 6.4 Application to haploid profiles 99 6.4.1 mtDNA profiles 99 6.4.2 Y-chromosome markers 101 6.5 Mixtures 101 6.5.1 Visual interpretation of mixed profiles 101 6.5.2 Likelihood ratios under qualitative interpretation 103 6.5.3 Quantitative interpretation of mixtures 108 6.6 Identification exercises 109 7 Relatedness 111 7.1 Paternity 111 7.1.1 Weight of evidence for paternity 111 7.1.2 Prior probabilities 112 7.1.3 Calculating likelihood ratios 113 7.1.4 Multiple loci: the effect of linkage 117 7.1.5 s may be related to c but is not the father 119 7.1.6 Incest 120 7.1.7 Mother unavailable 121 7.1.8 Mutation 122 7.2 Other relatedness between two individuals 126 7.2.1 Only the two individuals profiled 126 7.2.2 Profiled individual close relative of target 127 7.2.3 Profiles of known relatives also available † 128 7.3 Software for relatedness analyses 129 7.4 Inference of ethnicity or phenotype † 131 7.5 Relatedness exercises 133 8 Other approaches to weight of evidence 135 8.1 Uniqueness 135 8.1.1 Analysis 136 8.1.2 Discussion 138 8.2 Inclusion/exclusion probabilities 138 8.2.1 Random man 138 8.2.2 Inclusion probability of a typing system 139 8.2.3 Case-specific inclusion probability 139 8.3 Hypothesis testing † 141 8.4 Other exercises 143 9 Issues for the courtroom 145 9.1 Bayesian reasoning in court 145 9.2 Some fallacies 146 9.2.1 The prosecutor’s fallacy 146 9.2.2 The defendant’s fallacy 147 9.2.3 The uniqueness fallacy 148 9.3 Some UK appeal cases 148 9.3.1 Deen (1993) 148 9.3.2 Dalby (1995) 149 9.3.3 Adams (1996) 149 9.3.4 Doheny/Adams (1996) 151 9.3.5 Watters (2000) 153 9.4 US National Research Council reports 154 9.5 Prosecutor’s fallacy exercises 155 10 Solutions to exercises 157 Bibliography 175 Index 183

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Book SynopsisPresents the fundamentals in probability and statistics along with relevant applications. This book explains the concept of probabilistic modelling and the process of model selection, verification and analysis. It also demonstrates practical problem solving with examples and exercises.Trade Review“For most practising engineers, this book would make a superb reference text, simply because there are so many worked examples, all extremely relevant to engineers.” (Significance, 1 March 2005) Table of ContentsPreface. 1. Introduction. Part A: Probability and Random Variables. 2. Basic Probability Concepts. 3. Random Variables and Probability Distributions. 4. Expectations And Moments. 5. Functions of Random Variables. 6. Some Important Discrete Distributions. 7. Some Important Continuous Distributions. Part B: Statistical Inference, Parameter Estimation, and Model Verification. 8. Observed Data and Graphical Representation. 9. Parameter Estimation. 10. Model Verification. 11. Linear Models and Linear Regression. Appendix A: Tables. Appendix B: Computer Software. Appendix C: Answers to Selected Problems. Subject Index.

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Book SynopsisPresents the fundamentals of the subject along with concepts of probabilistic modelling, and the process of model selection, verification and analysis. This book includes more than 100 examples and 200 exercises, along with a solutions manual for instructors. It presents the fundamentals in probability and statistics along with their applications.Trade Review“For most practising engineers, this book would make a superb reference text, simply because there are so many worked examples, all extremely relevant to engineers.” (Significance, 1 March 2005) "...the many engineering related examples and exercise problems are a strong feature..." (Technometrics, May 2005) "...designed for students, and as reference for lecturers, the book provides a comprehensive understanding of probability and statistics..." (New Civil Engineer, 18 March, 2004) "...written in an accessible and clear way...gives important techniques of the basic standard methods." (Zentralblatt Math, Vol.1049 2004) "...a good introduction to the ideas of probability and statistics...I would recommend it to anyone as a reference for basic theory..." (Journal of Applied Statistics, Vol 32 (6) August 2005)Table of ContentsPreface. 1. Introduction. Part A: Probability and Random Variables. 2. Basic Probability Concepts. 3. Random Variables and Probability Distributions. 4. Expectations And Moments. 5. Functions of Random Variables. 6. Some Important Discrete Distributions. 7. Some Important Continuous Distributions. Part B: Statistical Inference, Parameter Estimation, and Model Verification. 8. Observed Data and Graphical Representation. 9. Parameter Estimation. 10. Model Verification. 11. Linear Models and Linear Regression. Appendix A: Tables. Appendix B: Computer Software. Appendix C: Answers to Selected Problems. Subject Index.

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Book SynopsisPublication bias is the tendency to decide to publish a study based on the results of the study, rather than on the basis of its theoretical or methodological quality. It can arise from selective publication of favorable results, or of statistically significant results. This threatens the validity of conclusions drawn from reviews of published scientific research. Meta-analysis is now used in numerous scientific disciplines, summarizing quantitative evidence from multiple studies. If the literature being synthesised has been affected by publication bias, this in turn biases the meta-analytic results, potentially producing overstated conclusions. Publication Bias in Meta-Analysis examines the different types of publication bias, and presents the methods for estimating and reducing publication bias, or eliminating it altogether. Written by leading experts, adopting a practical and multidisciplinary approach. Provides comprehensive coverage of the topic including:Trade Review“The book adopts an inter-disciplinary approach and will make a useful reference volume for any researchers and graduate students who conduct systematic reviews or meta-analyses. University and medical libraries, as well as pharmaceutical companies and government regulatory agencies, will also find this invaluable.” (Zentralblatt MATH, 2012) "…a well-written book and will be useful for researchers or graduate students…" (Journal of the American Statistical Association, June 2007) "...the book definatly succeeds in raising the awareness of the reader to an issue that unfortunately still remains underappreciated" (Psychometrika June 2007) " … an incredibly thorough, useful book. The impressive list of contributors … is the book’s particular strength." (JRSSA, Vol. 169, No. 4, October 2006) "…a useful introduction to meta-analysis and…state-of-the-art description of the statistical problems associated…of particular value as a reference for a multi-disciplinary audience…" (Biometrics, June 2006) "This book will have a wide appeal and is a major contribution to ways of distilling evidence from scientific literature." (Journal of Tropical Pediatrics, June 2006) “I predict that this book will become the key text in the area.” (Short Book Reviews, April 2006) "…likely to become a standard reference for those who carry systematic literature reviews." (Psychometrika, June 2007) "This elegant hardcover book brings together 16 fine contributions and three appendices...It is obviously a must for medical libraries." (Journal of Applied Science, 2007) "A strong and rigorous collection of timely essays that will be useful for advanced scholars and experienced researchers in various disciplines…. It is an obvious must for medical libraries." (Journal of Applied Statistics, December 2007)Table of ContentsPreface. Acknowledgements. Notes on Contributors. Chapter 1: Publication Bias in Meta-Analysis (Hannah R. Rothstein, Alexander J. Sutton and Michael Borenstein). Part A: Publication bias in context. Chapter 2: Publication Bias: Recognizing the Problem, Understanding Its Origins and Scope, and Preventing Harm (Kay Dickersin). Chapter 3: Preventing Publication Bias: Registries and Prospective Meta-Analysis (Jesse A. Berlin and Davina Ghersi). Chapter 4: Grey Literature and Systematic Reviews (Sally Hopewell, Mike Clarke and Sue Mallett). Part B: Statistical methods for assessing publication bias. Chapter 5: The Funnel Plot (Jonathan A.C. Sterne, Betsy Jane Becker and Matthias Egger). Chapter 6: Regression Methods to Detect Publication and Other Bias in Meta-Analysis (Jonathan A.C. Sterne and Matthias Egger). Chapter 7: Failsafe N or File-Drawer Number (Betsy Jane Becker). Chapter 8: The Trim and Fill Method (Sue Duval). Chapter 9: Selection Method Approaches (Larry V. Hedges and Jack Vevea). Chapter 10: Evidence Concerning the Consequences of Publication and Related Biases (Alexander J. Sutton). Chapter 11: Software for Publication Bias (Michael Borenstein). Part C: Advanced and emerging approaches. Chapter 12: Bias in Meta-Analysis Induced by Incompletely Reported Studies (Alexander J. Sutton and Therese D. Pigott). Chapter 13: Assessing the Evolution of Effect Sizes over Time (Thomas A. Trikalinos and John P.A. Ioannidis). Chapter 14: Do Systematic Reviews Based on Individual Patient Data Offer a Means of Circumventing Biases Associated with Trial Publications? (Lesley Stewart, Jayne Tierney and Sarah Burdett). Chapter 15: Differentiating Biases from Genuine Heterogeneity: Distinguishing Artifactual from Substantive Effects (John P.A. Ioannidis). Chapter 16: Beyond Conventional Publication Bias: Other Determinants of Data Suppression (Scott D. Halpern and Jesse A. Berlin). Appendices. Appendix A: Data Sets. Appendix B: Annotated Bibliography (Hannah R. Rothstein and Ashley Busing). Glossary. Index.

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Book SynopsisSensitivity analysis should be considered a pre-requisite for statistical model building in any scientific discipline where modelling takes place. For a non-expert, choosing the method of analysis for their model is complex, and depends on a number of factors. This book guides the non-expert through their problem in order to enable them to choose and apply the most appropriate method. It offers a review of the state-of-the-art in sensitivity analysis, and is suitable for a wide range of practitioners. It is focussed on the use of SIMLAB a widely distributed freely-available sensitivity analysis software package developed by the authors for solving problems in sensitivity analysis of statistical models. Other key features: Provides an accessible overview of the current most widely used methods for sensitivity analysis. Opens with a detailed worked example to explain the motivation behind the book. Includes a range of examples to help illustrate the cTrade Review"...an interesting and informative book..." (Technometrics, May 2005) "...provides an accessible overview of the most widely used sensitivity analysis methods." (Zentralblatt Math, Vol.1049, 2004) "...well written..." (Statistical Methods in Medical Research, Vol 14 2005) Table of ContentsPREFACE. 1. A WORKED EXAMPLE. 1.1 A simple model. 1.2 Modulus version of the simple model. 1.3 Six-factor version of the simple model. 1.4 The simple model ‘by groups’. 1.5 The (less) simple correlated-input model. 1.6 Conclusions. 2. GLOBAL SENSITIVITY ANALYSIS FOR IMPORTANCE ASSESSMENT. 2.1 Examples at a glance. 2.2 What is sensitivity analysis? 2.3 Properties of an ideal sensitivity analysis method. 2.4 Defensible settings for sensitivity analysis. 2.5 Caveats. 3. TEST CASES. 3.1 The jumping man. Applying variance-based methods. 3.2 Handling the risk of a financial portfolio: the problem of hedging. Applying Monte Carlo filtering and variance-based methods. 3.3 A model of fish population dynamics. Applying the method of Morris. 3.4 The Level E model. Radionuclide migration in the geosphere. Applying variance-based methods and Monte Carlo filtering. 3.5 Two spheres. Applying variance based methods in estimation/calibration problems. 3.6 A chemical experiment. Applying variance based methods in estimation/calibration problems. 3.7 An analytical example. Applying the method of Morris. 4. THE SCREENING EXERCISE. 4.1 Introduction. 4.2 The method of Morris. 4.3 Implementing the method. 4.4 Putting the method to work: an analytical example. 4.5 Putting the method to work: sensitivity analysis of a fish population model. 4.6 Conclusions. 5. METHODS BASED ON DECOMPOSING THE VARIANCE OF THE OUTPUT. 5.1 The settings. 5.2 Factors Prioritisation Setting. 5.3 First-order effects and interactions. 5.4 Application of Si to Setting ‘Factors Prioritisation’. 5.5 More on variance decompositions. 5.6 Factors Fixing (FF) Setting. 5.7 Variance Cutting (VC) Setting. 5.8 Properties of the variance based methods. 5.9 How to compute the sensitivity indices: the case of orthogonal input. 5.9.1 A digression on the Fourier Amplitude Sensitivity Test (FAST). 5.10 How to compute the sensitivity indices: the case of non-orthogonal input. 5.11 Putting the method to work: the Level E model. 5.11.1 Case of orthogonal input factors. 5.11.2 Case of correlated input factors. 5.12 Putting the method to work: the bungee jumping model. 5.13 Caveats. 6. SENSITIVITY ANALYSIS IN DIAGNOSTIC MODELLING: MONTE CARLO FILTERING AND REGIONALISED SENSITIVITY ANALYSIS, BAYESIAN UNCERTAINTY ESTIMATION AND GLOBAL SENSITIVITY ANALYSIS. 6.1 Model calibration and Factors Mapping Setting. 6.2 Monte Carlo filtering and regionalised sensitivity analysis. 6.2.1 Caveats. 6.3 Putting MC filtering and RSA to work: the problem of hedging a financial portfolio. 6.4 Putting MC filtering and RSA to work: the Level E test case. 6.5 Bayesian uncertainty estimation and global sensitivity analysis. 6.5.1 Bayesian uncertainty estimation. 6.5.2 The GLUE case. 6.5.3 Using global sensitivity analysis in the Bayesian uncertainty estimation. 6.5.4 Implementation of the method. 6.6 Putting Bayesian analysis and global SA to work: two spheres. 6.7 Putting Bayesian analysis and global SA to work: a chemical experiment. 6.7.1 Bayesian uncertainty analysis (GLUE case). 6.7.2 Global sensitivity analysis. 6.7.3 Correlation analysis. 6.7.4 Further analysis by varying temperature in the data set: fewer interactions in the model. 6.8 Caveats. 7. HOW TO USE SIMLAB. 7.1 Introduction. 7.2 How to obtain and install SIMLAB. 7.3 SIMLAB main panel. 7.4 Sample generation. 7.4.1 FAST. 7.4.2 Fixed sampling. 7.4.3 Latin hypercube sampling (LHS). 7.4.4 The method of Morris. 7.4.5 Quasi-Random LpTau. 7.4.6 Random. 7.4.7 Replicated Latin Hypercube (r-LHS). 7.4.8 The method of Sobol’. 7.4.9 How to induce dependencies in the input factors. 7.5 How to execute models. 7.6 Sensitivity analysis. 8. FAMOUS QUOTES: SENSITIVITY ANALYSIS IN THE SCIENTIFIC DISCOURSE. REFERENCES. INDEX.

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Book SynopsisThis book covers engineering principles and state-of-the-art methods involved in the many facets of combat modeling and distributed simulation.Trade Review“Tolk and his coauthors have extensive experience in this area, making this volume a standard reference for researchers engaged in combat modeling. The complexity of the domain, the consequences of error, and the prohibitive cost of direct experimentation are as great in combat modeling as in any other problem area, making this volume a valuable source of examples and techniques for modelers in other areas that are highly complex, consequential, and inaccessible by direct experiment." (Computing Reviews, 1 October 2012) Table of ContentsPreface xi Contributors xiii Biographies xvii Acknowledgments xxvii Abbreviations xxix 1. Challenges of Combat Modeling and Distributed Simulation 1 Andreas Tolk Part I Foundations 2. Applicable Codes of Ethics 25 Andreas Tolk 3. The NATO Code of Best Practice for Command and Control Assessment 33 Andreas Tolk 4. Terms and Application Domains 55 Andreas Tolk 5. Scenario Elements 79 Andreas Tolk Part II Combat Modeling 6. Modeling the Environment 95 Andreas Tolk 7. Modeling Movement 113 Andreas Tolk 8. Modeling Sensing 127 Andreas Tolk 9. Modeling Effects 145 Andreas Tolk 10. Modeling Communications, Command, and Control 171 Andreas Tolk Part III Distributed Simulation 11. Challenges of Distributed Simulation 187 Andreas Tolk 12. Standards for Distributed Simulation 209 Andreas Tolk 13. Modeling and Simulation Development and Preparation Processes 243 Andreas Tolk 14. Verification and Validation 263 Andreas Tolk 15. Integration of M&S Solutions into the Operational Environment 295 Andreas Tolk Part IV Advanced Topics 16. History of Combat Modeling and Distributed Simulation 331 Margaret L. Loper and Charles Turnitsa 17. Serious Games, Virtual Worlds, and Interactive Digital Worlds 357 Roger D. Smith 18. Mathematical Applications for Combat Modeling 385 Patrick T. Hester and Andrew Collins 19. Combat Modeling with the High Level Architecture and Base Object Models 413 Mikel D. Petty and Paul Gustavson 20. The Test and Training Enabling Architecture (TENA) 449 Edward T. Powell and J. Russell Noseworthy 21. Combat Modeling using the DEVS Formalism 479 Tag Gon Kim and Il-Chul Moon 22. GIS Data for Combat Modeling 511 David Lashlee, Joe Bricio, Robert Holcomb, and William T. Richards 23. Modeling Tactical Data Links 537 Joe Sorroche 24. Standards-Based Combat Simulation Initialization using the Military Scenario Definition Language (MSDL) 579 Robert L. Wittman Jr 25. Multi-Resolution Combat Modeling 607 Mikel D. Petty, Robert W. Franceschini, and James Panagos 26. New Challenges: Human, Social, Cultural, and Behavioral Modeling 641 S. K. Numrich and P. M. Picucci 27. Agent Directed Simulation for Combat Modeling and Distributed Simulation 669 Gnana K. Bharathy, Levent Yilmaz, and Andreas Tolk 28. Uncertainty Representation and Reasoning for Combat Models 715 Paulo C. G. Costa, Heber Herencia-Zapana, and Kathryn Laskey 29. Model-Based Data Engineering for Distributed Simulations 747 Saikou Y. Diallo 30. Federated Simulation for System of Systems Engineering 765 Robert H. Kewley and Marc Wood 31. The Role of Architecture Frameworks in Simulation Models: The Human View Approach 811 Holly A. H. Handley 32. Multinational Computer Assisted Exercises 825 Erdal Cayirci Annex 1: M&S Organizations/Associations 841 Salim Chemlal and Tuncer Ören Annex 2: Military Simulation Systems 851 José J. Padilla Index 869

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Book SynopsisPraise for the First Edition Stahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra. CHOICE Introductory Modern Algebra: A Historical Approach, Second Edition presents the evolution of algebra and provides readers with the opportunity to view modern algebra as a consistent movement from concrete problems to abstract principles. With a few pertinent excerpts from the writings of some of the greatest mathematicians, the Second Edition uniquely facilitates the understanding of pivotal algebraic ideas. The author provides a clear, precise, and accessible introduction to modern algebra and also helps to develop a more immediate and well-grounded understanding of how equations lead to permutation groups and what those groups can inform us about such diverse items as multivariate functions and the 15-puzzle. Featuring new Trade Review“An in-depth explanation of the principles and practices of modern algebra in terms of the historical development from the Renaissance solution of the cubic equation to Dedekind's ideals.” (Expofairs.com, 12 November 2015) “This book is an excellent book for an upper-level, undergraduate, one or two semester course, in modern algebra, for a typical University student population that is not especially strong in proofs.” (MAA Reviews, 13 January 2014)Table of ContentsPreface ix 1 The Early History 1 1.1 The Breakthrough 1 2 Complex Numbers 9 2.1 Rational Functions of Complex Numbers 9 2.2 Complex Roots 17 2.3 Solvability by Radicals I 23 2.4 Ruler and Compass Constructibility 26 2.5 Orders of Roots of Unity 36 2.6 The Existence of Complex Numbers* 38 3 Solutions of Equations 45 3.1 The Cubic Formula 45 3.2 Solvability by Radicals II 49 3.3 Other Types of Solutions* 50 4 Modular Arithmetic 57 4.1 Modular Addition, Subtraction, and Multiplication 57 4.2 The Euclidean Algorithm and Modular Inverses 62 4.3 Radicals in Modular Arithmetic* 69 4.4 The Fundamental Theorem of Arithmetic* 70 5 The Binomial Theorem and Modular Powers 75 5.1 The Binomial Theorem 75 5.2 Fermat's Theorem and Modular Exponents 85 5.3 The Multinomial Theorem* 90 5.4 The Euler φ-Function* 92 6 Polynomials Over a Field 99 6.1 Fields and Their Polynomials 99 6.2 The Factorization of Polynomials 107 6.3 The Euclidean Algorithm for Polynomials 113 6.4 Elementary Symmetric Polynomials* 119 6.5 Lagrange's Solution of the Quartic Equation* 125 7 Galois Fields 131 7.1 Galois's Construction of His Fields 131 7.2 The Galois Polynomial 139 7.3 The Primitive Element Theorem 144 7.4 On the Variety of Galois Fields* 147 8 Permutations 155 8.1 Permuting the Variables of a Function I 155 8.2 Permutations 158 8.3 Permuting the Variables of a Function II 166 8.4 The Parity of a Permutation 169 9 Groups 183 9.1 Permutation Groups 183 9.2 Abstract Groups 192 9.3 Isomorphisms of Groups and Orders of Elements 199 9.4 Subgroups and Their Orders 206 9.5 Cyclic Groups and Subgroups 215 9.6 Cayley's Theorem 218 10 Quotient Groups and their Uses 225 10.1 Quotient Groups 225 10.2 Group Homomorphisms 234 10.3 The Rigorous Construction of Fields 240 10.4 Galois Groups and Resolvability of Equations 253 11 Topics in Elementary Group Theory 261 11.1 The Direct Product of Groups 261 11.2 More Classifications 265 12 Number Theory 273 12.1 Pythagorean triples 273 12.2 Sums of two squares 278 12.3 Quadratic Reciprocity 285 12.4 The Gaussian Integers 293 12.5 Eulerian integers and others 304 12.6 What is the essence of primality? 310 13 The Arithmetic of Ideals 317 13.1 Preliminaries 317 13.2 Integers of a Quadratic Field 319 13.3 Ideals 322 13.4 Cancelation of Ideals 337 13.5 Norms of Ideals 341 13.6 Prime Ideals and Unique Factorization 343 13.7 Constructing Prime Ideals 347 14 Abstract Rings 355 14.1 Rings 355 14.2 Ideals 358 14.3 Domains 361 14.4 Quotients of Rings 367 A Excerpts: Al-Khwarizmi 377 B Excerpts: Cardano 383 C Excerpts: Abel 389 D Excerpts: Galois 395 E Excerpts: Cayley 401 F Mathematical Induction 405 G Logic, Predicates, Sets and Functions 413 G.1 Truth Tables 413 G.2 Modeling Implication 415 G.3 Predicates and their Negation 418 G.4 Two Applications 419 G.5 Sets 421 G.6 Functions 422 Biographies 427 Bibliography 431 Solutions to Selected Exercises 433 Index 440 Notation 444

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Book SynopsisPraise for the Second Edition: ...a grand feast for biostatisticians. It stands ready to satisfy the appetite of any pharmaceutical scientist with a respectable statistical appetite. Journal of Clinical Research Best Practices The Third Edition of Design and Analysis of Clinical Trials provides complete, comprehensive, and expanded coverage of recent health treatments and interventions. Featuring a unified presentation, the book provides a well-balanced summary of current regulatory requirements and recently developed statistical methods as well as an overview of the various designs and analyses that are utilized at different stages of clinical research and development. Additional features of this Third Edition include: New chapters on biomarker development and target clinical trials, adaptive design, trials for evaluating diagnostic devices, statistical methods for translational medicine, and traditional Chinese medicine Trade Review�In summary, this third edition is an impressive expansion beyond a remarkable second edition. This book would be good reference for biostatisticians, clinical researchers, and pharmaceutical scientists in clinical research and development.� (Journal of Biopharmaceutical Statistics, 1 July 2014)"Design and Analysis of Clinical Trials: Concepts and Methodologies, Third Edition is a grand feast for biostatisticians. It stands ready to satisfy the appetite of any pharmaceutical scientist with a respectable statistical appetite...Essential reading for clinical research professionals." (Journal of Clinical Research Best Practice February 2014)Table of ContentsPreface xi PART I PRELIMINARIES 1 Introduction 3 1.1 What are Clinical Trials?, 3 1.2 History of Clinical Trials, 4 1.3 Regulatory Process and Requirements, 10 1.4 Investigational New Drug Application, 17 1.5 New Drug Application, 24 1.6 Clinical Development and Practice, 31 1.7 AIMS and Structure of the Book, 42 2 Basic Statistical Concepts 45 2.1 Introduction, 45 2.2 Uncertainty and Probability, 46 2.3 Bias and Variability, 49 2.4 Confounding and Interaction, 57 2.5 Descriptive and Inferential Statistics, 66 2.6 Hypotheses Testing and p-Values, 68 2.7 Clinical Significance and Clinical Equivalence, 75 2.8 Reproducibility and Generalizability, 79 3 Basic Design Considerations 85 3.1 Introduction, 85 3.2 Goals of Clinical Trials, 86 3.3 Target Population and Patient Selection, 90 3.4 Selection of Controls, 97 3.5 Statistical Considerations, 105 3.6 Other Issues, 112 3.7 Discussion, 115 4 Randomization and Blinding 117 4.1 Introduction, 117 4.2 Randomization Models, 118 4.3 Randomization Methods, 124 4.4 Implementation of Randomization, 144 4.5 Generalization of Controlled Randomized Trials, 149 4.6 Blinding, 153 4.7 Discussion, 160 PART II DESIGNS AND THEIR CLASSIFICATIONS 5 Designs for Clinical Trials 165 5.1 Introduction, 165 5.2 Parallel Group Designs, 167 5.3 Clustered Randomized Designs, 172 5.4 Crossover Designs, 177 5.5 Titration Designs, 185 5.6 Enrichment Designs, 191 5.7 Group Sequential Designs, 195 5.8 Placebo-Challenging Designs, 197 5.9 Blinded Reader Designs, 203 5.10 Discussion, 207 6 Designs for Cancer Clinical Trials 211 6.1 Introduction, 211 6.2 General Considerations for Phase I Cancer Clinical Trials, 213 6.3 Single-Stage Up-and-Down Phase I Designs, 214 6.4 Two-Stage Up-and-Down Phase I Designs, 217 6.5 Continual Reassessment Method Phase I Designs, 219 6.6 Optimal and Flexible Multiple-Stage Designs, 222 6.7 Randomized Phase II Designs, 229 6.8 Discussion, 232 7 Classification of Clinical Trials 237 7.1 Introduction, 237 7.2 Multicenter Trials, 238 7.3 Superiority Trials, 245 7.4 Active Control and Equivalence/Noninferiority Trials, 248 7.5 Dose–Response Trials, 261 7.6 Combination Trials, 266 7.7 Bridging Studies and Global Trials, 278 7.8 Vaccine Clinical Trials, 285 7.9 QT Studies, 291 7.10 Discussion, 299 PART III ANALYSIS OF CLINICAL DATA 8 Analysis of Continuous Data 305 8.1 Introduction, 305 8.2 Estimation, 306 8.3 Test Statistics, 310 8.4 Analysis of Variance, 316 8.5 Analysis of Covariance, 323 8.6 Nonparametric Methods, 325 8.7 Repeated Measures, 332 8.8 Discussion, 341 9 Analysis of Categorical Data 343 9.1 Introduction, 343 9.2 Statistical Inference for One Sample, 345 9.3 Inference of Independent Samples, 358 9.4 Ordered Categorical Data, 364 9.5 Combining Categorical Data, 368 9.6 Model-Based Methods, 374 9.7 Repeated Categorical Data, 382 9.8 Discussion, 387 10 Censored Data and Interim Analysis 389 10.1 Introduction, 389 10.2 Estimation of the Survival Function, 391 10.3 Comparison Between Survival Functions, 399 10.4 Cox’s Proportional Hazard Model, 405 10.5 Calendar Time and Information Time, 419 10.6 Group Sequential Methods, 424 10.7 Discussion, 438 11 Sample Size Determination 441 11.1 Introduction, 441 11.2 Basic Concept, 442 11.3 Two Samples, 447 11.4 Multiple Samples, 456 11.5 Censored Data, 459 11.6 Dose–Response Studies, 464 11.7 Crossover Designs, 471 11.8 Equivalence and Noninferiority Trials, 481 11.9 Multiple-Stage Design in Cancer Trials, 490 11.10 Multinational Trials, 490 11.11 Comparing Variabilities, 500 11.12 Discussion, 517 PART IV ISSUES IN EVALUATION 12 Issues in Efficacy Evaluation 521 12.1 Introduction, 521 12.2 Baseline Comparison, 523 12.3 Intention-to-Treat Principle and Efficacy Analysis, 528 12.4 Adjustment for Covariates, 536 12.5 Multicenter Trials, 541 12.6 Multiplicity, 548 12.7 Data Monitoring, 558 12.8 Use of Genetic Information for Evaluation of Efficacy, 564 12.9 Sample Size Reestimation, 570 12.10 Discussion, 572 13 Safety Assessment 573 13.1 Introduction, 573 13.2 Extent of Exposure, 574 13.3 Coding of Adverse Events, 582 13.4 Analysis of Adverse Events, 595 13.5 Analysis of Laboratory Data, 602 13.6 Analysis of QT/QTc Prolongation, 610 13.7 Discussion, 615 PART V RECENT DEVELOPMENT 14 Biomarkers and Targeted Clinical Trials 619 14.1 Introduction, 619 14.2 Concepts and Strategies, 620 14.3 Biomarker Development and Validation, 623 14.4 Designs of Targeted Clinical Trials, 630 14.5 Analyses of Targeted Clinical Trials, 640 14.6 Discussion, 647 15 Trials for Evaluating Accuracy of Diagnostic Devices 649 15.1 Introduction, 649 15.2 Study Design, 651 15.3 Measures of Diagnostic Accuracy, 656 15.4 Reporting Results, 663 15.5 Sample Size Estimation, 672 15.6 Discussion, 675 16 Statistical Methods in Translational Medicine 677 16.1 Introduction, 677 16.2 Biomarker Development, 678 16.3 Bench-to-Bedside, 682 16.4 Animal Model Versus Human Model, 689 16.5 Translation in Study Endpoints, 691 16.6 Bridging Studies, 696 16.7 Discussion, 699 16.8 Appendix, 700 17 Adaptive Clinical Trial Designs 703 17.1 Introduction, 703 17.2 What Is Adaptive Design?, 704 17.3 Well-Understood and Less Well-Understood Designs, 709 17.4 Clinical/Statistical and Regulatory Perspectives, 713 17.5 Impact of Protocol Amendments, 716 17.6 Challenges in By-Design Adaptations, 721 17.7 Obstacles of Retrospective Adaptations, 727 17.8 Discussion, 729 18 Traditional Chinese Medicine 733 18.1 Introduction, 733 18.2 Fundamental Differences, 734 18.3 Basic Considerations of TCM Clinical Trials, 741 18.4 Other Issues in TCM Research and Development, 744 18.5 Consortium for Globalization of Traditional Chinese Medicine, 751 18.6 Discussion, 752 PART VI CONDUCT OF CLINICAL TRIALS 19 Preparation and Implementation of a Clinical Protocol 755 19.1 Introduction, 755 19.2 Structure and Components of a Protocol, 756 19.3 Points to be Considered and Common Pitfalls During Development and Preparation of a Protocol, 762 19.4 Common Departures for Implementation of a Protocol, 765 19.5 Monitoring, Audit, and Inspection, 771 19.6 Quality Assessment of a Clinical Trial, 775 19.7 Discussion, 777 20 Data Management of a Clinical Trial 779 20.1 Introduction, 779 20.2 Regulatory Requirements, 781 20.3 Development of Case Report Forms, 783 20.4 Database Development, 787 20.5 Data Entry, Query, and Correction, 788 20.6 Data Validation and Quality, 791 20.7 Database Lock, Archive, and Transfer, 792 20.8 Critical Issues, 795 References 799 Appendix A 845 Index 851

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Book SynopsisThis book presents a clear, quick understanding of the basic techniques in statistical quality control that are employed by business and industrial managers alike.Table of ContentsPreface. 1 The Importance of Quality Improvement. 1.1 Introduction. 1.2 What is Statistical Process Control? 1.3 The Birth of Quality Control. 1.4 What is a Process? 1.5 Examples of Processes from Daily Life. 1.6 Implementing the Tools and Techniques. 1.7 Continuous Process Improvement. 1.8 The Goal of Statistical Process Control. 1.9 The Eight Dimensions of Quality for Manufacturing & Service. 1.10 The Cost of (Poor) Quality). 1.11 What Did We Learn? 1.12 Test Your Knowledge. 2 Graphical Display of Data. 2.1 Introduction to eZ SPC. 2.2 Qualitative and Quantitative Data. 2.3 Bar Graph. 2.4 Pie Chart. 2.5 Pareto Chart. 2.6 Radar Chart. 2.7 Histogram. 2.8 Box Plot. 2.9 Scatter Plot. 2.10 Cause and E®ect Diagram. 2.11 What Did We Learn? 2.12 Test Your Knowledge. Exercises. 3 Summarizing Data. 3.1 Central Tendency. 3.2 Variability. 3.3 Statistical Distributions. 3.4 Distributions in eZ SPC. 3.5 What Did We Learn? 3.6 Test Your Knowledge. Exercises. 4 Analyzing Data. 4.1 Confidence Intervals. 4.2 Test of Hypothesis. 4.3 The p–value. 4.4 Probability Plots. 4.5 What Did We Learn? 4.6 Test Your Knowledge. Exercises. 5 Shewhart Control Charts. 5.1 The Concepts of a Control Chart. 5.2 Managing the Process with Control Charts. 5.3 Variable Control Charts. 5.4 Attribute Control Charts. 5.5 Deciding Which Chart to Use. 5.6 What Did We Learn? 5.7 Test Your Knowledge. Exercises. 6 Advanced Control Charts. 6.1 CUSUM Control Chart. 6.2 EWMA Control Charts. 6.3 CV Control Chart. 6.4 Nonparametric Control Charts. 6.5 Process Capability. 6.6 Gage R & R. 6.7 What Did We Learn? 6.8 Test Your Knowledge. Exercises. 7 Process Improvement. 7.1 Correlation Analysis. 7.2 Regression Analysis. 7.3 Experimental Design. 7.4 Overview of Experimental Design. 7.5 Principles of Experimentation. 7.6 One-Way Analysis of Variance . 7.7 Two Way Analysis of Variance. 7.8 Two-level Factorial Design Analysis. 7.9 What Did We Learn? 7.10 Test Your Knowledge. Exercises. 8 End Material. 8.1 Final Exam. 8.2 Final Exam Solutions. 8.3 Test Your Knowledge: Answers. References. Glossary. Subject Index.

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Book SynopsisPraise for the First Edition . . . an excellent textbook . . . well organized and neatly written. Mathematical Reviews . . . amazingly interesting . . . Technometrics Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields. Beginning with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions, the book goes on to present limit theorems and simulation. The authors combine a rigorous, calculus-based development of theory with an intuitive approach that appeals to readers'' sense of reason and logic. Including more than 400 examples that help illustrate concepts and theory, the Second Edition features new material on statiTable of ContentsPreface xi Preface to the First Edition xiii 1 Basic Probability Theory 1 1.1 Introduction 1 1.2 Sample Spaces and Events 3 1.3 The Axioms of Probability 7 1.4 Finite Sample Spaces and Combinatorics 15 1.4.1 Combinatorics 17 1.5 Conditional Probability and Independence 27 1.6 The Law of Total Probability and Bayes’ Formula 41 Problems 63 2 Random Variables 76 2.1 Introduction 76 2.2 Discrete Random Variables 77 2.3 Continuous Random Variables 82 2.4 Expected Value and Variance 95 2.5 Special Discrete Distributions 111 2.6 The Exponential Distribution 123 2.7 The Normal Distribution 127 2.8 Other Distributions 131 2.9 Location Parameters 137 2.10 The Failure Rate Function 139 Problems 144 3 Joint Distributions 156 3.1 Introduction 156 3.2 The Joint Distribution Function 156 3.3 Discrete Random Vectors 158 3.4 Jointly Continuous Random Vectors 160 3.5 Conditional Distributions and Independence 164 3.5.1 Independent Random Variables 168 3.6 Functions of Random Vectors 172 3.7 Conditional Expectation 185 3.8 Covariance and Correlation 196 3.9 The Bivariate Normal Distribution 209 3.10 Multidimensional Random Vectors 216 3.11 Generating Functions 231 3.12 The Poisson Process 240 Problems 247 4 Limit Theorems 263 4.1 Introduction 263 4.2 The Law of Large Numbers 264 4.3 The Central Limit Theorem 268 4.4 Convergence in Distribution 275 Problems 278 5 Simulation 281 5.1 Introduction 281 5.2 Random Number Generation 282 5.3 Simulation of Discrete Distributions 283 5.4 Simulation of Continuous Distributions 285 5.5 Miscellaneous 290 Problems 292 6 Statistical Inference 294 6.1 Introduction 294 6.2 Point Estimators 294 6.3 Confidence Intervals 304 6.4 Estimation Methods 312 6.5 Hypothesis Testing 327 6.6 Further Topics in Hypothesis Testing 334 6.7 Goodness of Fit 339 6.8 Bayesian Statistics 351 6.9 Nonparametric Methods 363 Problems 378 7 Linear Models 391 7.1 Introduction 391 7.2 Sampling Distributions 392 7.3 Single Sample Inference 395 7.4 Comparing Two Samples 402 7.5 Analysis of Variance 409 7.6 Linear Regression 415 7.7 The General Linear Model 431 Problems 436 8 Stochastic Processes 444 8.1 Introduction 444 8.2 Discrete -Time Markov Chains 445 8.3 Random Walks and Branching Processes 464 8.4 Continuous -Time Markov Chains 475 8.5 Martingales 494 8.6 Renewal Processes 502 8.7 Brownian Motion 509 Problems 517 Appendix A Tables 527 Appendix B Answers to Selected Problems 535 Further Reading 551 Index 553

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Book SynopsisAn original account of willful ignorance and how this principle relates to modern probability and statistical methods Through a series of colorful stories about great thinkers and the problems they chose to solve, the author traces the historical evolution of probability and explains how statistical methods have helped to propel scientific research. However, the past success of statistics has depended on vast, deliberate simplifications amounting to willful ignorance, and this very success now threatens future advances in medicine, the social sciences, and other fields. Limitations of existing methods result in frequent reversals of scientific findings and recommendations, to the consternation of both scientists and the lay public. Willful Ignorance: The Mismeasure of Uncertainty exposes the fallacy of regarding probability as the full measure of our uncertainty. The book explains how statistical methodology, though enormously productive andTrade Review“This volume is an outstanding example of the need to keep our scientific methods in context and the value of careful historical research to provide this context. It should be a required part of the statistical training of every scientist.” (Computing Reviews, 24 March 2015) Table of ContentsPREFACE xi ACKNOWLEDGMENTS xv 1 THE OPPOSITE OF CERTAINTY 1 Two Dead Ends 2 Analytical Engines 4 What is Probability? 6 Uncertainty 9 Willful Ignorance 12 Toward a New Science 15 2 A QUIET REVOLUTION 19 Thinking the Unthinkable 21 Inventing Probability 24 Statistics 27 The Taming of Chance 31 The Ignorance Fallacy 34 The Dilemma of Science 35 3 A MATTER OF CHANCE 41 Origins 43 Probability 44 The Famous Correspondence 56 What Did Not Happen Next 60 AgainstThe Odds 64 4 HARDLY TOUCHED UPON 71 The Mathematics of Chance 73 Empirical Frequencies 82 A Quantum of Certainty 100 5 A MATHEMATICIAN OF BASEL 114 Publication at Last 116 The Art of Conjecturing 117 A Tragic Ending 142 6 A DEFECT OF CHARACTER 147 Man Without a Country 150 A Fraction of Chances 165 7 CLASSICAL PROBABILITY 171 Revolutionary Reverends 173 From Chances to Probability 194 8 BABEL 213 The Great Unraveling 216 Probability as a Relative Frequency 219 Probability as a Logical Relationship 228 Probability as a Subjective Assessment 239 Probability as a Propensity 247 9 PROBABILITY AND REALITY 253 The Razor’s Edge 255 What Fisher Knew 257 What Reference Class? 262 A Postulate of Ignorance 270 Laplace’s Error 279 10 THE DECISION FACTORY 283 Beyond Moral Certainty 284 Decisions, Decisions 298 Machine-Made Knowledge 309 11 THE LOTTERY IN SCIENCE 312 Scientific Progress 313 Fooled by Causality 319 Statistics for Humans: Bias or Ambiguity? 331 Regression toward the Mean 339 12 TRUST, BUT VERIFY 346 A New Problem 347 Trust,… 354 …But Verify 357 The Future 363 Mindful Ignorance 368 APPENDIX: THE PASCAL–FERMAT CORRESPONDENCE OF 1654 373 NOTES 387 BIBLIOGRAPHY 415 INDEX 429

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Book SynopsisA complete set of statistical tools for beginning financial analysts from a leading authority Written by one of the leading experts on the topic, An Introduction to Analysis of Financial Data with R explores basic concepts of visualization of financial data. Through a fundamental balance between theory and applications, the book supplies readers with an accessible approach to financial econometric models and their applications to real-world empirical research. The author supplies a hands-on introduction to the analysis of financial data using the freely available R software package and case studies to illustrate actual implementations of the discussed methods. The book begins with the basics of financial data, discussing their summary statistics and related visualization methods. Subsequent chapters explore basic time series analysis and simple econometric models for business, finance, and economics as well as related topics including: LinearTrade Review“I found this book highly informative and interesting to read. The proper mix of theory and hands-on programming examples makes it recommended reading for both R programmers interested in finance and financial analysts with a basic programming background. Well written and following a clear and defined logical layout, the author has written a current reference text on using a powerful open-source programming language for typical financial analysis.” (Computing Reviews, 25 March 2014) “All in all, this book is a good and useful introduction to financial time series with many real-world examples. It is suitable for use both as a textbook and for self-study, with exercises provided at the end of each chapter.” (International Statistical Review, 14 June 2013) Table of ContentsPreface xiii 1 FINANCIAL DATA AND THEIR PROPERTIES 1 1.1 Asset Returns 2 1.2 Bond Yields and Prices 7 1.3 Implied Volatility 10 1.4 R Packages and Demonstrations 12 1.4.1 Installation of R Packages 12 1.4.2 The Quantmod Package 12 1.4.3 Some Basic R Commands 16 1.5 Examples of Financial Data 17 1.6 Distributional Properties of Returns 20 1.6.1 Review of Statistical Distributions and Their Moments 20 1.7 Visualization of Financial Data 27 1.8 Some Statistical Distributions 32 1.8.1 Normal Distribution 32 1.8.2 Lognormal Distribution 32 1.8.3 Stable Distribution 33 1.8.4 Scale Mixture of Normal Distributions 33 1.8.5 Multivariate Returns 34 Exercises 36 References 37 2 LINEAR MODELS FOR FINANCIAL TIME SERIES 39 2.1 Stationarity 40 2.2 Correlation and Autocorrelation Function 43 2.3 White Noise and Linear Time Series 50 2.4 Simple Autoregressive Models 51 2.4.1 Properties of AR Models 52 2.4.2 Identifying AR Models in Practice 60 2.4.3 Goodness of Fit 67 2.4.4 Forecasting 67 2.5 Simple Moving Average Models 69 2.5.1 Properties of MA Models 72 2.5.2 Identifying MA Order 73 2.5.3 Estimation 74 2.5.4 Forecasting Using MA Models 75 2.6 Simple ARMA Models 78 2.6.1 Properties of ARMA(1,1) Models 79 2.6.2 General ARMA Models 80 2.6.3 Identifying ARMA Models 81 2.6.4 Forecasting Using an ARMA Model 84 2.6.5 Three Model Representations for an ARMA Model 84 2.7 Unit-Root Nonstationarity 86 2.7.1 Random Walk 86 2.7.2 Random Walk with Drift 88 2.7.3 Trend-Stationary Time Series 90 2.7.4 General Unit-Root Nonstationary Models 91 2.7.5 Unit-Root Test 91 2.8 Exponential Smoothing 96 2.9 Seasonal Models 98 2.9.1 Seasonal Differencing 99 2.9.2 Multiplicative Seasonal Models 101 2.9.3 Seasonal Dummy Variable 107 2.10 Regression Models with Time Series Errors 110 2.11 Long-Memory Models 117 2.12 Model Comparison and Averaging 120 2.12.1 In-sample Comparison 120 2.12.2 Out-of-sample Comparison 121 2.12.3 Model Averaging 125 Exercises 125 References 127 3 CASE STUDIES OF LINEAR TIME SERIES 128 3.1 Weekly Regular Gasoline Price 129 3.1.1 Pure Time Series Model 130 3.1.2 Use of Crude Oil Prices 133 3.1.3 Use of Lagged Crude Oil Prices 134 3.1.4 Out-of-Sample Predictions 135 3.2 Global Temperature Anomalies 140 3.2.1 Unit-Root Stationarity 141 3.2.2 Trend-Nonstationarity 145 3.2.3 Model Comparison 148 3.2.4 Long-Term Prediction 150 3.2.5 Discussion 153 3.3 US Monthly Unemployment Rates 157 3.3.1 Univariate Time Series Models 157 3.3.2 An Alternative Model 161 3.3.3 Model Comparison 165 3.3.4 Use of Initial Jobless Claims 165 3.3.5 Comparison 173 Exercises 174 References 175 4 ASSET VOLATILITY AND VOLATILITY MODELS 176 4.1 Characteristics of Volatility 177 4.2 Structure of a Model 178 4.3 Model Building 181 4.4 Testing for ARCH Effect 182 4.5 The ARCH Model 185 4.5.1 Properties of ARCH Models 186 4.5.2 Advantages and Weaknesses of ARCH Models 187 4.5.3 Building an ARCH Model 188 4.5.4 Some Examples 193 4.6 The GARCH Model 199 4.6.1 An Illustrative Example 201 4.6.2 Forecasting Evaluation 210 4.6.3 A Two-Pass Estimation Method 210 4.7 The Integrated GARCH Model 211 4.8 The GARCH-M Model 213 4.9 The Exponential Garch Model 215 4.9.1 An Illustrative Example 217 4.9.2 An Alternative Model Form 218 4.9.3 Second Example 218 4.9.4 Forecasting Using an EGARCH Model 220 4.10 The Threshold Garch Model 222 4.11 Asymmetric Power ARCH Models 224 4.12 Nonsymmetric GARCH Model 226 4.13 The Stochastic Volatility Model 228 4.14 Long-Memory Stochastic Volatility Models 230 4.15 Alternative Approaches 232 4.15.1 Use of High Frequency Data 232 4.15.2 Use of Daily Open, High, Low, and Close Prices 235 Exercises 239 References 241 5 APPLICATIONS OF VOLATILITY MODELS 243 5.1 Garch Volatility Term Structure 244 5.1.1 Term Structure 246 5.2 Option Pricing and Hedging 248 5.3 Time-Varying Correlations and Betas 251 5.3.1 Time-Varying Betas 256 5.4 Minimum Variance Portfolios 259 5.5 Prediction 263 Exercises 271 References 272 6 HIGH FREQUENCY FINANCIAL DATA 274 6.1 Nonsynchronous Trading 275 6.2 Bid–Ask Spread of Trading Prices 279 6.3 Empirical Characteristics of Trading Data 282 6.4 Models for Price Changes 285 6.4.1 Ordered Probit Model 288 6.4.2 A Decomposition Model 293 6.5 Duration Models 298 6.5.1 Diurnal Component 299 6.5.2 The ACD Model 301 6.5.3 Estimation 303 6.6 Realized Volatility 308 6.6.1 Handling Microstructure Noises 313 6.6.2 Discussion 317 Appendix A: Some Probability Distributions 320 Appendix B: Hazard Function 323 Exercises 324 References 325 7 VALUE AT RISK 327 7.1 Risk Measure and Coherence 328 7.1.1 Value at Risk (VaR) 329 7.1.2 Expected Shortfall 334 7.2 Remarks on Calculating Risk Measures 336 7.3 Riskmetrics 337 7.3.1 Discussion 342 7.3.2 Multiple Positions 343 7.4 An Econometric Approach 345 7.4.1 Multiple Periods 348 7.5 Quantile Estimation 352 7.5.1 Quantile and Order Statistics 353 7.5.2 Quantile Regression 354 7.6 Extreme Value Theory 358 7.6.1 Review of Extreme Value Theory 358 7.6.2 Empirical Estimation 361 7.6.3 Application to Stock Returns 363 7.7 An Extreme Value Approach to Var 368 7.7.1 Discussion 370 7.7.2 Multiperiod VaR 371 7.7.3 Return Level 371 7.8 Peaks Over Thresholds 372 7.8.1 Statistical Theory 373 7.8.2 Mean Excess Function 374 7.8.3 Estimation 376 7.8.4 An Alternative Parameterization 378 7.9 The Stationary Loss Processes 381 Exercises 383 References 384 Index 387

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Book SynopsisDigital systems design requires a rigorous modeling and simulation analysis that eliminates design risks and potential harm to users. Introduction to Digital Systems Modeling and Simulation allows readers to model and simulate digital principles using Very High Speed Integrated Circuit Hardware Description Language (VHDL) programming.Trade Review“Extensively classroom- and laboratory-tested, the text provides scholars, practitioners and students with learning objectives at the beginning of each chapter as well as with practical applications of modeling and synthesis to the design of digital system to establish a basis for effective design.” (Zentralblatt MATH, 2012) "The level is suitable for graduate or upper-level students in electronics, computer science, and similar fields." (Book News, 1 August 2011)Table of ContentsPreface. 1 Digital System Modeling and Simulation. 1.1 Objectives. 1.2 Modeling, Synthesis, and Simulation Design. 1.3 History of Digital Systems. 1.4 Standard Logic Devices. 1.5 Custom-Designed Logic Devices. 1.6 Programmable Logic Devices. 1.7 Simple Programmable Logic Devices. 1.8 Complex Programmable Logic Devices. 1.9 Field-Programmable Gate Arrays. 1.10 Future of Digital Systems. Problems. 2 Number Systems. 2.1 Objectives. 2.2 Bases and Number Systems. 2.3 Number Conversions. 2.4 Data Organization. 2.5 Signed and Unsigned Numbers. 2.6 Binary Arithmetic. 2.7 Addition of Signed Numbers. 2.8 Binary-Coded Decimal Representation. 2.9 BCD Addition. Problems. 3 Boolean Algebra and Logic. 3.1 Objectives. 3.2 Boolean Theory. 3.3 Logic Variables and Logic Functions. 3.4 Boolean Axioms and Theorems. 3.5 Basic Logic Gates and Truth Tables. 3.6 Logic Representations and Circuit Design. 3.7 Truth Table. 3.8 Timing Diagram. 3.9 Logic Design Concepts. 3.10 Sum-of-Products Design. 3.11 Product-of-Sums Design. 3.12 Design Examples. 3.13 NAND and NOR Equivalent Circuit Design. 3.14 Standard Logic Integrated Circuits. Problems. 4 VHDL Design Concepts. 4.1 Objectives. 4.2 CAD Tool–Based Logic Design. 4.3 Hardware Description Languages. 4.4 VHDL Language. 4.5 VHDL Programming Structure. 4.6 Assignment Statements. 4.7 VHDL Data Types. 4.8 VHDL Operators. 4.9 VHDL Signal and Generate Statements. 4.10 Sequential Statements. 4.11 Loops and Decision-Making Statements. 4.12 Subcircuit Design. 4.13 Packages and Components. Problems. 5 Integrated Logic. 5.1 Objectives. 5.2 Logic Signals. 5.3 Logic Switches. 5.4 NMOS and PMOS Logic Gates. 5.5 CMOS Logic Gates. 5.6 CMOS Logic Networks. 5.7 Practical Aspects of Logic Gates. 5.8 Transmission Gates. Problems. 6 Logic Function Optimization. 6.1 Objectives. 6.2 Logic Function Optimization Process. 6.3 Karnaugh Maps. 6.4 Two-Variable Karnaugh Map. 6.5 Three-Variable Karnaugh Map. 6.6 Four-Variable Karnaugh Map. 6.7 Five-Variable Karnaugh Map. 6.8 XOR and NXOR Karnaugh Maps. 6.9 Incomplete Logic Functions. 6.10 Quine–McCluskey Minimization. Problems. 7 Combinational Logic. 7.1 Objectives. 7.2 Combinational Logic Circuits. 7.3 Multiplexers. 7.4 Logic Design with Multiplexers. 7.5 Demultiplexers. 7.6 Decoders. 7.7 Encoders. 7.8 Code Converters. 7.9 Arithmetic Circuits. Problems. 8 Sequential Logic. 8.1 Objectives. 8.2 Sequential Logic Circuits. 8.3 Latches. 8.4 Flip-Flops. 8.5 Registers. 8.6 Counters. Problems. 9 Synchronous Sequential Logic. 9.1 Objectives. 9.2 Synchronous Sequential Circuits. 9.3 Finite-State Machine Design Concepts. 9.4 Finite-State Machine Synthesis. 9.5 State Assignment. 9.6 One-Hot Encoding Method. 9.7 Finite-State Machine Analysis. 9.8 Sequential Serial Adder. 9.9 Sequential Circuit Counters. 9.10 State Optimization. 9.11 Asynchronous Sequential Circuits. Problems. Index.

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Book SynopsisPraise for the First Edition . . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations. SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-dependent problems. The book treats differential equations and difference methods with a parallel development, thus achieving a more useful analysis of numerical methods. The Second Edition presents hyperbolic equations in great detail as well as new coverage on second-order systems of wave equations including acoustic waves, elastic waves, and Einstein equations. Compared to fiTable of ContentsPreface ix Preface to the First Edition xi PART I PROBLEMS WITH PERIODIC SOLUTIONS 1 1. Model Equations 3 1.1. Periodic Gridfunctions and Difference Operators 3 1.2. First-Order Wave Equation Convergence and Stability 10 1.3. Leap-Frog Scheme 20 1.4. Implicit Methods 24 1.5. Truncation Error 27 1.6. Heat Equation 30 1.7. Convection–Diffusion Equation 36 1.8. Higher Order Equations 39 1.9. Second-Order Wave Equation 41 1.10. Generalization to Several Space Dimensions 43 2. Higher Order Accuracy 47 2.1. Efficiency of Higher Order Accurate Difference Approximations 47 2.2. Time Discretization 57 3. Well-Posed Problems 65 3.1. Introduction 65 3.2. Scalar Differential Equations with Constant Coefficients in One Space Dimension 70 3.3. First-Order Systems with Constant Coefficients in One Space Dimension 72 3.4. Parabolic Systems with Constant Coefficients in One Space Dimension 77 3.5. General Systems with Constant Coefficients 80 3.6. General Systems with Variable Coefficients 81 3.7. Semibounded Operators with Variable Coefficients 83 3.8. Stability and Well-Posedness 90 3.9. The Solution Operator and Duhamel’s Principle 93 3.10. Generalized Solutions 97 3.11. Well-Posedness of Nonlinear Problems 99 3.12. The Principle of A Priori Estimates 102 3.13. The Principle of Linearization 107 4. Stability and Convergence for Difference Methods 109 4.1. The Method of Lines 109 4.2. General Fully Discrete Methods 119 4.3. Splitting Methods 147 5. Hyperbolic Equations and Numerical Methods 153 5.1. Systems with Constant Coefficients in One Space Dimension 153 5.2. Systems with Variable Coefficients in One Space Dimension 156 5.3. Systems with Constant Coefficients in Several Space Dimensions 158 5.4. Systems with Variable Coefficients in Several Space Dimensions 160 5.5. Approximations with Constant Coefficients 162 5.6. Approximations with Variable Coefficients 165 5.7. The Method of Lines 167 5.8. Staggered Grids 172 6. Parabolic Equations and Numerical Methods 177 6.1. General Parabolic Systems 177 6.2. Stability for Difference Methods 181 7. Problems with Discontinuous Solutions 189 7.1. Difference Methods for Linear Hyperbolic Problems 189 7.2. Method of Characteristics 193 7.3. Method of Characteristics in Several Space Dimensions 199 7.4. Method of Characteristics on a Regular Grid 200 7.5. Regularization Using Viscosity 208 7.6. The Inviscid Burgers’ Equation 210 7.7. The Viscous Burgers’ Equation and Traveling Waves 214 7.8. Numerical Methods for Scalar Equations Based on Regularization 221 7.9. Regularization for Systems of Equations 227 7.10. High Resolution Methods 235 PART II INITIAL–BOUNDARY VALUE PROBLEMS 247 8. The Energy Method for Initial–Boundary Value Problems 249 8.1. Characteristics and Boundary Conditions for Hyperbolic Systems in One Space Dimension 249 8.2. Energy Estimates for Hyperbolic Systems in One Space Dimension 258 8.3. Energy Estimates for Parabolic Differential Equations in One Space Dimension 266 8.4. Stability and Well-Posedness for General Differential Equations 271 8.5. Semibounded Operators 274 8.6. Quarter-Space Problems in More than One Space Dimension 279 9. The Laplace Transform Method for First-Order Hyperbolic Systems 287 9.1. A Necessary Condition for Well-Posedness 287 9.2. Generalized Eigenvalues 291 9.3. The Kreiss Condition 292 9.4. Stability in the Generalized Sense 295 9.5. Derivative Boundary Conditions for First-Order Hyperbolic Systems 303 10. Second-Order Wave Equations 307 10.1. The Scalar Wave Equation 307 10.2. General Systems of Wave Equations 324 10.3. A Modified Wave Equation 327 10.4. The Elastic Wave Equations 331 10.5. Einstein’s Equations and General Relativity 335 11. The Energy Method for Difference Approximations 339 11.1. Hyperbolic Problems 339 11.2. Parabolic Problems 350 11.3. Stability Consistency and Order of Accuracy 357 11.4. SBP Difference Operators 362 12. The Laplace Transform Method for Difference Approximations 377 12.1. Necessary Conditions for Stability 377 12.2. Sufficient Conditions for Stability 387 12.3. Stability in the Generalized Sense for Hyperbolic Systems 405 12.4. An Example that Does Not Satisfy the Kreiss Condition But is Stable in the Generalized Sense 416 12.5. The Convergence Rate 423 13. The Laplace Transform Method for Fully Discrete Approximations 431 13.1. General Theory for Approximations of Hyperbolic Systems 431 13.2. The Method of Lines and Stability in the Generalized Sense 451 Appendix A Fourier Series and Trigonometric Interpolation 465 A.1. Some Results from the Theory of Fourier Series 465 A.2. Trigonometric Interpolation 469 A.3. Higher Dimensions 473 Appendix B Fourier and Laplace Transform 477 B.1. Fourier Transform 477 B.2. Laplace Transform 480 Appendix C Some Results from Linear Algebra 485 Appendix D SBP Operators 489 References 499 Index 507

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Book SynopsisGame-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk's Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito's stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical contextTable of ContentsPreface xi Acknowledgments xv Part I Examples in Discrete Time 1 1 Borel’s Law of Large Numbers 5 1.1 A Protocol for Testing Forecasts 6 1.2 A Game-Theoretic Generalization of Borel’s Theorem 8 1.3 Binary Outcomes 16 1.4 Slackenings and Supermartingales 18 1.5 Calibration 19 1.6 The Computation of Strategies 21 1.7 Exercises 21 1.8 Context 24 2 Bernoulli’s and De Moivre’s Theorems 31 2.1 Game-Theoretic Expected Value and Probability 33 2.2 Bernoulli’s Theorem for Bounded Forecasting 37 2.3 A Central Limit Theorem 39 2.4 Global Upper Expected Values for Bounded Forecasting 45 2.5 Exercises 46 2.6 Context 49 3 Some Basic Supermartingales 55 3.1 Kolmogorov’s Martingale 56 3.2 Doléans’s Supermartingale 56 3.3 Hoeffding’s Supermartingale 58 3.4 Bernstein’s Supermartingale 63 3.5 Exercises 66 3.6 Context 67 4 Kolmogorov’s Law of Large Numbers 69 4.1 Stating Kolmogorov’s Law 70 4.2 Supermartingale Convergence Theorem 73 4.3 How Skeptic Forces Convergence 80 4.4 How Reality Forces Divergence 81 4.5 Forcing Games 82 4.6 Exercises 86 4.7 Context 89 5 The Law of the Iterated Logarithm 93 5.1 Validity of the Iterated-Logarithm Bound 94 5.2 Sharpness of the Iterated-Logarithm Bound 99 5.3 Additional Recent Game-Theoretic Results 100 5.4 Connections with Large Deviation Inequalities 104 5.5 Exercises 104 5.6 Context 106 Part II Abstract Theory in Discrete Time 109 6 Betting on a Single Outcome 111 6.1 Upper and Lower Expectations 113 6.2 Upper and Lower Probabilities 115 6.3 Upper Expectations with Smaller Domains 118 6.4 Offers 121 6.5 Dropping the Continuity Axiom 125 6.6 Exercises 127 6.7 Context 131 7 Abstract Testing Protocols 135 7.1 Terminology and Notation 136 7.2 Supermartingales 136 7.3 Global Upper Expected Values 142 7.4 Lindeberg’s Central Limit Theorem for Martingales 145 7.5 General Abstract Testing Protocols 146 7.6 Making the Results of Part I Abstract 151 7.7 Exercises 153 7.8 Context 155 8 Zero-One Laws 157 8.1 Lévy’s Zero-One Law 158 8.2 Global Upper Expectation 160 8.3 Global Upper and Lower Probabilities 162 8.4 Global Expected Values and Probabilities 163 8.5 Other Zero-One Laws 165 8.6 Exercises 169 8.7 Context 170 9 Relation to Measure-Theoretic Probability 175 9.1 Ville’s Theorem 176 9.2 Measure-Theoretic Representation of Upper Expectations 180 9.3 Embedding Game-Theoretic Martingales in Probability Spaces 189 9.4 Exercises 191 9.5 Context 192 Part III Applications in Discrete Time 195 10 Using Testing Protocols in Science and Technology 197 10.1 Signals in Open Protocols 198 10.2 Cournot’s Principle 201 10.3 Daltonism 202 10.4 Least Squares 207 10.5 Parametric Statistics with Signals 212 10.6 Quantum Mechanics 215 10.7 Jeffreys’s Law 217 10.8 Exercises 225 10.9 Context 226 11 Calibrating Lookbacks and p-Values 229 11.1 Lookback Calibrators 230 11.2 Lookback Protocols 235 11.3 Lookback Compromises 241 11.4 Lookbacks in Financial Markets 242 11.5 Calibrating p-Values 245 11.6 Exercises 248 11.7 Context 250 12 Defensive Forecasting 253 12.1 Defeating Strategies for Skeptic 255 12.2 Calibrated Forecasts 259 12.3 Proving the Calibration Theorems 264 12.4 Using Calibrated Forecasts for Decision Making 270 12.5 Proving the Decision Theorems 274 12.6 From Theory to Algorithm 286 12.7 Discontinuous Strategies for Skeptic 291 12.8 Exercises 295 12.9 Context 299 Part IV Game-Theoretic Finance 305 13 Emergence of Randomness in Idealized Financial Markets 309 13.1 Capital Processes and Instant Enforcement 310 13.2 Emergence of Brownian Randomness 312 13.3 Emergence of Brownian Expectation 320 13.4 Applications of Dubins–Schwarz 325 13.5 Getting Rich Quick with the Axiom of Choice 331 13.6 Exercises 333 13.7 Context 334 14 A Game-Theoretic Itô Calculus 339 14.1 Martingale Spaces 340 14.2 Conservatism of Continuous Martingales 348 14.3 Itô Integration 350 14.4 Covariation and Quadratic Variation 355 14.5 Itô’s Formula 357 14.6 Doléans Exponential and Logarithm 358 14.7 Game-Theoretic Expectation and Probability 360 14.8 Game-Theoretic Dubins–Schwarz Theorem 361 14.9 Coherence 362 14.10 Exercises 363 14.11 Context 365 15 Numeraires in Market Spaces 371 15.1 Market Spaces 372 15.2 Martingale Theory in Market Spaces 375 15.3 Girsanov’s Theorem 376 15.4 Exercises 382 15.5 Context 382 16 Equity Premium and CAPM 385 16.1 Three Fundamental Continuous I-Martingales 387 16.2 Equity Premium 389 16.3 Capital Asset Pricing Model 391 16.4 Theoretical Performance Deficit 395 16.5 Sharpe Ratio 396 16.6 Exercises 397 16.7 Context 398 17 Game-Theoretic Portfolio Theory 403 17.1 Stroock–Varadhan Martingales 405 17.2 Boosting Stroock–Varadhan Martingales 407 17.3 Outperforming the Market with Dubins–Schwarz 413 17.4 Jeffreys’s Law in Finance 414 17.5 Exercises 415 17.6 Context 416 Terminology and Notation 419 List of Symbols 425 References 429 Index 455

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Book Synopsis* Montgomery, Runger, and Hubele provide modern coverage of engineering statistics, focusing on how statistical tools are integrated into the engineering problem-solving process.

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Book SynopsisPraise for the First Edition This book is refreshing to read since it takes an important topic... and presents it in a clear and concise manner by using examples that include visual presentations of the problem, solution methods, and results along with an explanation of the mathematical and procedural steps required to model the problem and work through to a solution. Journal of Classification Thoroughly updated and revised, Network and Discrete Location: Models, Algorithms, and Applications, Second Edition remains the go-to guide on facility location modeling. The book offers a unique introduction to methodological tools for solving location models and provides insight into when each approach is useful and what information can be obtained. The Second Edition focuses on real-world extensions of the basic models used in locating facilities, including production and diTable of ContentsPreface to the First and Second Editions xi Acknowledgments xvii 1. Introduction to Location Theory and Models 1 1.1 Introduction 1 1.2 Key Questions Addressed by Location Models 3 1.3 Example Problem Descriptions 4 1.3.1 Ambulance Location 4 1.3.2 Siting Landfills for Hazardous Wastes 10 1.3.3 Summary 10 1.4 Key Dimensions of Location Problems and Models 11 1.4.1 Planar Versus Network Versus Discrete Location Models 11 1.4.2 Tree Problems Versus General Graph Problems 12 1.4.3 Distance Metrics 13 1.4.4 Number of Facilities to Locate 14 1.4.5 Static Versus Dynamic Location Problems 15 1.4.6 Deterministic Versus Probabilistic Models 16 1.4.7 Single- Versus Multiple-Product Models 16 1.4.8 Private Versus Public Sector Problems 17 1.4.9 Single- Versus Multiple-Objective Problems and Models 17 1.4.10 Elastic Versus Inelastic Demand 18 1.4.11 Capacitated Versus Uncapacitated Facilities 18 1.4.12 Nearest Facility Versus General Demand Allocation Models 18 1.4.13 Hierarchical Versus Single-Level Models 19 1.4.14 Desirable Versus Undesirable Facilities 19 1.5 A Taxonomy of Location Models 20 1.5.1 Typology of Location Models 20 1.5.2 A Simple Analytic Model 22 1.6 Summary 26 Exercises 27 2. Review of Linear Programming 29 2.1 Introduction 29 2.2 The Canonical Form of a Linear Programming Problem 31 2.3 Constructing the Dual of an LP Problem 34 2.4 Complementary Slackness and the Relationships Between the Primal and the Dual Linear Programming Problems 36 2.5 Solving a Linear Programming Problem in Excel 43 2.6 The Transportation Problem 47 2.7 The Shortest Path Problem 64 2.7.1 The Shortest Path Problem in Excel 78 2.7.2 The Shortest Path Problem in AMPL 80 2.8 The Out-of-Kilter Flow Algorithm 80 2.9 Integer Programming Problems 92 2.10 Summary 96 Exercises 97 3. An Overview of Complexity Analysis 111 3.1 Introduction 111 3.2 Basic Concepts and Notation 112 3.3 Example Computation of an Algorithm’s Complexity 115 3.4 The Classes P and NP (and NP-Hard and NP-Complete) 117 3.5 Summary 122 Exercises 123 4. Covering Problems 124 4.1 Introduction and the Notion of Coverage 124 4.2 The Set Covering Model 125 4.3 Applications of the Set Covering Model 137 4.4 Variants of the Set Covering Location Model 140 4.5 The Maximum Covering Location Model 143 4.5.1 The Greedy Adding Algorithm: A Heuristic Algorithm for Solving the Maximum Covering Location Model 146 4.5.2 Lagrangian Relaxation: An Optimization-Based Heuristic Algorithm for Solving the Maximum Covering Location Model 154 4.5.3 Other Solution Approaches and Example Results 163 4.6 An Interesting Model Property or It Ain’t Necessarily So 164 4.7 The Maximum Expected Covering Location Model 168 4.8 Summary 174 Exercises 175 5. Center Problems 193 5.1 Introduction 193 5.2 Vertex P-Center Formulation 198 5.3 The Absolute 1- and 2-Center Problems on a Tree 201 5.3.1 Absolute 1-Center on an Unweighted Tree 201 5.3.2 Absolute 2-Centers on an Unweighted Tree 205 5.3.3 Absolute 1-Center on a Weighted Tree 206 5.4 The Unweighted Vertex P-Center Problem on a General Graph 211 5.5 The Unweighted Absolute P-Center Problem on a General Graph 215 5.5.1 Characteristics of the Solution to the Absolute P-Center Problem 215 5.5.2 An Algorithm for the Unweighted Absolute P-Center on a General Graph 219 5.6 Summary 229 Exercises 230 6. Median Problems 235 6.1 Introduction 235 6.2 Formulation and Properties 237 6.3 1-Median Problem on a Tree 241 6.4 Heuristic Algorithms for the P-Median Problem 246 6.5 An Optimization-Based Lagrangian Algorithm for the P-Median Problem 260 6.5.1 Methodological Development 260 6.5.2 Numerical Example 265 6.5.3 Extensions and Enhancements to the Lagrangian Procedures 271 6.6 Computational Results Using the Heuristic Algorithms and the Lagrangian Relaxation Algorithm 271 6.7 Another Interesting Property or It Still Ain’t Necessarily So 277 6.8 Summary 283 Exercises 285 7. Fixed Charge Facility Location Problems 294 7.1 Introduction 294 7.2 Uncapacitated Fixed Charge Facility Location Problems 297 7.2.1 Heuristic Construction Algorithms 298 7.2.2 Heuristic Improvement Algorithms 305 7.2.3 A Lagrangian Relaxation Approach 311 7.2.4 A Dual-Based Approach 314 7.3 Capacitated Fixed Charge Facility Location Problems 325 7.3.1 Lagrangian Relaxation Approaches 328 7.3.2 Bender’s Decomposition 345 7.4 Summary 355 Exercises 356 8. Extensions of Location Models 362 8.1 Introduction 362 8.2 Multiobjective Problems 362 8.3 Hierarchical Facility Location Models 375 8.3.1 Basic Notions of Hierarchical Facilities 375 8.3.2 Basic Median-Based Hierarchical Location Formulations 379 8.3.3 Coverage-Based Hierarchical Location Formulations 383 8.3.4 Extensions of Hierarchical Location Formulations 385 8.4 Models of Interacting Facilities 387 8.4.1 Flows Between Facilities 387 8.4.2 Facilities with Proximity Constraints 390 8.5 Multiproduct Flows and Production/Distribution Systems 393 8.6 Location/Routing Problems 399 8.7 Hub Location Problems 410 8.8 Dispersion Models and Models for the Location of Undesirable Facilities 425 8.8.1 Dispersion Models 426 8.8.2 A Maxisum Model for the Location of Undesirable Facilities 429 8.9 An Integrated Location-Inventory Model 435 8.9.1 A Multiobjective Location-Inventory/Covering Model 448 8.9.2 A Look at Aggregation Effects 452 8.10 Reliability and Facility Location Modeling 455 8.10.1 The Expected Failure Case 458 8.10.2 Modeling a Malevolent Attacker 461 8.11 Summary 466 Exercises 468 9. Location Modeling in Perspective 480 9.1 Introduction 480 9.2 The Planning Process for Facility Location 481 9.2.1 Problem Definition 481 9.2.2 Analysis 483 9.2.3 Communication and Decision 489 9.2.4 Implementation 495 9.2.5 Caveats on the Planning Process 496 9.3 Summary 496 Exercises 497 References 499 Index 509

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Book SynopsisRather than teach mathematics and the structure of proofssimultaneously, this book first introduces logic as the foundationof proofs and then demonstrates how logic applies to mathematicaltopics. This method ensures that readers gain a firmunderstanding of how logic interacts with mathematics and empowersthem to solve more complex problems.Table of ContentsPreface xiii Acknowledgments xv List of Symbols xvii 1 Propositional Logic 1 1.1 Symbolic Logic 1 Propositions 2 Propositional Forms 5 Interpreting Propositional Forms 7 Valuations and Truth Tables 10 1.2 Inference 19 Semantics 21 Syntactics 23 1.3 Replacement 31 Semantics 31 Syntactics 34 1.4 Proof Methods 40 Deduction Theorem 40 Direct Proof 44 Indirect Proof 47 1.5 The Three Properties 51 Consistency 51 Soundness 55 Completeness 58 2 First-Order Logic 63 2.1 Languages 63 Predicates 63 Alphabets 67 Terms 70 Formulas 71 2.2 Substitution 75 Terms 75 Free Variables 76 Formulas 78 2.3 Syntactics 85 Quantifier Negation 85 Proofs with Universal Formulas 87 Proofs with Existential Formulas 90 2.4 Proof Methods 96 Universal Proofs 97 Existential Proofs 99 Multiple Quantifiers 100 Counterexamples 102 Direct Proof 103 Existence and Uniqueness 104 Indirect Proof 105 Biconditional Proof 107 Proof of Disunctions 111 Proof by Cases 112 3 Set Theory 117 3.1 Sets and Elements 117 Rosters 118 Famous Sets 119 Abstraction 121 3.2 Set Operations 126 Union and Intersection 126 Set Difference 127 Cartesian Products 130 Order of Operations 132 3.3 Sets within Sets 135 Subsets 135 Equality 137 3.4 Families of Sets 148 Power Set 151 Union and Intersection 151 Disjoint and Pairwise Disjoint 155 4 Relations and Functions 161 4.1 Relations 161 Composition 163 Inverses 165 4.2 Equivalence Relations 168 Equivalence Classes 171 Partitions 172 4.3 Partial Orders 177 Bounds 180 Comparable and Compatible Elements 181 Well-Ordered Sets 183 4.4 Functions 189 Equality 194 Composition 195 Restrictions and Extensions 196 Binary Operations 197 4.5 Injections and Surjections 203 Injections 205 Surjections 208 Bijections 211 Order Isomorphims 212 4.6 Images and Inverse Images 216 5 Axiomatic Set Theory 225 5.1 Axioms 225 Equality Axioms 226 Existence and Uniqueness Axioms 227 Construction Axioms 228 Replacement Axioms 229 Axiom of Choice 230 Axiom of Regularity 234 5.2 Natural Numbers 237 Order 239 Recursion 242 Arithmetic 243 5.3 Integers and Rational Numbers 249 Integers 250 Rational Numbers 253 Actual Numbers 256 5.4 Mathematical Induction 257 Combinatorics 260 Euclid’s Lemma 264 5.5 Strong Induction 268 Fibonacci Sequence 268 Unique Factorization 271 5.6 Real Numbers 274 Dedekind Cuts 275 Arithmetic 278 Complex Numbers 280 6 Ordinals and Cardinals 283 6.1 Ordinal Numbers 283 Ordinals 286 Classification 290 BuraliForti and Hartogs 292 Transfinite Recursion 293 6.2 Equinumerosity 298 Order 300 Diagonalization 303 6.3 Cardinal Numbers 307 Finite Sets 308 Countable Sets 310 Alephs 313 6.4 Arithmetic 316 Ordinals 316 Cardinals 322 6.5 Large Cardinals 327 Regular and Singular Cardinals 328 Inaccessible Cardinals 331 7 Models 333 7.1 First-Order Semantics 333 Satisfaction 335 Groups 340 Consequence 346 Coincidence 348 Rings 353 7.2 Substructures 361 Subgroups 363 Subrings 366 Ideals 368 7.3 Homomorphisms 374 Isomorphisms 380 Elementary Equivalence 384 Elementary Substructures 388 7.4 The Three Properties Revisited 394 Consistency 394 Soundness 397 Completeness 399 7.5 Models of Different Cardinalities 409 Peano Arithmetic 410 Compactness Theorem 414 Löwenheim–Skolem Theorems 415 The von Neumann Hierarchy 417 Appendix: Alphabets 427 References 429 Index 435

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Book SynopsisProvides the tools needed to successfully perform adaptive tests across a broad range of datasets Adaptive Tests of Significance Using Permutations of Residuals with R and SAS illustrates the power of adaptive tests and showcases their ability to adjust the testing method to suit a particular set of data.Trade Review“Each chapter provides detailed information on R and SAS code, respectively. Moreover, each chapter closes with illustrating exercises (without solutions). This is ideal for researchers who wish to implement anadaptive test of significance for their specific problem.” (Biometrical Journal, 1 May 2013) Table of ContentsPreface xv 1 Introduction 1 1.1 Why Use Adaptive Tests? 1 1.2 A Brief History of Adaptive Tests 2 1.3 The Adaptive Test of Hogg, Fisher, and Randies 5 1.4 Limitations of Rank-Based Tests 8 1.5 The Adaptive Weighted Least Squares Approach 9 1.6 Development of the Adaptive WLS Test 12 2 Smoothing Methods and Normalizing Transformations 15 2.1 Traditional Estimators of the Median and the Interquartile Range 15 2.2 Percentile Estimators that Use the Smooth Cumulative Distribution Function 16 2.3 Estimating the Bandwidth 21 2.4 Normalizing Transformations 23 2.5 The Weighting Algorithm 27 2.6 Computing the Bandwidth 30 2.7 Examples of Transformed Data 37 3 A Two-Sample Adaptive Test 43 3.1 A Two-Sample Model 44 3.2 Computing the Adaptive Weights 45 3.3 The Test Statistics for Adaptive Tests 47 3.4 Permutation Methods for Two-Sample Tests 50 3.5 An Example of a Two-Sample Test 54 3.6 R Code for the Two-Sample Test 56 3.7 Level of Significance of the Adaptive Test 61 3.8 Power of the Adaptive Test 63 3.9 Sample Size Estimation 65 3.10 A SAS Macro for the Adaptive Test 68 3.11 Modifications for One-Tailed Tests 70 3.12 Justification of the Weighting Method 70 3.13 Comments on the Adaptive Two-sample Test 71 4 Permutation Tests with Linear Models 75 4.1 Introduction 75 4.2 Notation 76 4.3 Permutations with Blocking 77 4.4 Linear Models in Matrix Form 77 4.5 Permutation Methods 78 4.6 Permutation Test Statistics 81 4.7 An Important Rule of Test Construction 82 4.8 A Permutation Algorithm 82 4.9 A Performance Comparison of the Permutation Methods 83 4.10 Discussion 84 5 An Adaptive Test for a Subset of Coefficients 87 5.1 The General Adaptive Testing Method 87 5.2 Simple Linear Regression 91 5.3 An Example of a Simple Linear Regression 93 5.4 Multiple Linear Regression 96 5.5 An Example of a Test in Multiple Regression 100 5.6 Conclusions 105 6 More Applications of Adaptive Tests 111 6.1 The Completely Randomized Design 111 6.2 Tests for Randomized Complete Block Designs 120 6.3 Adaptive Tests for Two-way Designs 127 6.4 Dealing with Unequal Variances 134 6.5 Extensions to More Complex Designs 140 7 The Adaptive Analysis of Paired Data 149 7.1 Introduction 149 7.2 The Adaptive Test of Miao and Gastwirth 151 7.3 An Adaptive Weighted Least Squares Test 153 7.4 An Example Using Paired Data 160 7.5 Simulation Study 161 7.6 Sample Size Estimation 163 7.7 Discussion of Tests for Paired Data 165 8 Multicenter and Cross-Over Trials 169 8.1 Tests in Multicenter Clinical Trials 170 8.2 Adaptive Analysis of Cross-over Trials 176 9 Adaptive Multivariate Tests 191 9.1 The Traditional Likelihood Ratio Test 191 9.2 An Adaptive Multivariate Test 192 9.3 An Example with Two Dependent Variables 196 9.4 Performance of the Adaptive Test 199 9.5 Conclusions for Multivariate Tests 203 10 Analysis of Repeated Measures Data 207 10.1 Introduction 207 10.2 The Multivariate LR Test 209 10.3 The Adaptive Test 209 10.4 The Mixed Model Test 210 10.5 Two-Sample Tests 211 10.6 Two-Sample Tests for Parallelism 212 10.7 Two-Sample Tests for Group Effect 219 10.8 An Example of Repeated Measures Data 223 10.9 Dealing with Missing Data 227 10.10 Conclusions and Recommendations 229 11 Rank-Based Tests of Significance 235 11.1 The Quest for Power 235 11.2 Two-Sample Rank Tests 236 11.3 The HFR Test 242 11.4 Significance Level of Adaptive Tests 243 11.5 Biining's Adaptive Test for Location 244 11.6 An Adaptive Test for Location and Scale 245 11.7 Other Adaptive Rank Tests 247 11.8 Maximum Test 248 11.9 Discussion 249 12 Adaptive Confidence Intervals and Estimates 253 12.1 The Relationship Between Tests and Confidence Intervals 253 12.2 The Iterative Procedure of Garthwaite 254 12.3 Confidence Interval for a Difference 259 12.4 A 95% Confidence Interval for Slope 263 12.5 A General Formula for Confidence Limits 264 12.6 Computing a Confidence Interval Using R 266 12.7 Computing a 95% Confidence Interval Using SAS 268 12.8 Adaptive Estimation 268 12.9 Adaptive Estimation of the Difference Between Two Population Means 271 12.10 Adaptive Estimation of a Slope in a Multiple Regression Model 272 12.11 Computing an Adaptive Estimate Using R 274 12.12 Computing an Adaptive Estimate Using SAS 278 12.13 Discussion 278 Exercises 279 Appendix A: R Code for Univariate Adaptive Tests 283 Appendix B: SAS Macro for Adaptive Tests 287 Appendix C: SAS Macro for Multiple Comparisons Procedures 299 Appendix D: R Code for Adaptive Tests with Blocking Factors 303 Appendix E: R Code for Adaptive Test with Paired Data 305 Appendix F: SAS Macro for Adaptive Test with Paired Data 309 Appendix G: R Code for Multivariate Adaptive Tests 313 Appendix H: R Code for Confidence Intervals and Estimates 317 Appendix I: SAS Macro for Confidence Intervals 321 Appendix J: SAS Macro for Estimates 329 References 333 Index 341

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Book SynopsisThis book grew out of an online interactive offered through statcourse. com, and it soon became apparent to the author that the course was too limited in terms of time and length in light of the broad backgrounds of the enrolled students.Table of ContentsPreface. 1. Very Large Arrays. 2. Permutation Tests. 3. Applying the Permutation Test. 4. Gathering and Preparing Data for Analysis. 5. Multiple Tests. 6. Bootstrap. 7. Classification Methods. 8. Applying Decision Trees. Glossary: Biological Terms. Glossary: Statistical Terms. Appendix: An R Primer. Bibliography. Author Index Subject Index.

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Book SynopsisA clear and lucid bottom-up approach to the basic principles of evolutionary algorithms Evolutionary algorithms (EAs) are a type of artificial intelligence. EAs are motivated by optimization processes that we observe in nature, such as natural selection, species migration, bird swarms, human culture, and ant colonies. This book discusses the theory, history, mathematics, and programming of evolutionary optimization algorithms. Featured algorithms include genetic algorithms, genetic programming, ant colony optimization, particle swarm optimization, differential evolution, biogeography-based optimization, and many others. Evolutionary Optimization Algorithms: Provides a straightforward, bottom-up approach that assists the reader in obtaining a clear?but theoretically rigorous?understanding of evolutionary algorithms, with an emphasis on implementation Gives a careful treatment of recently developed EAs?including opposition-based learning, artiTable of ContentsAcknowledgments xxi Acronyms xxiii List of Algorithms xxvii Part I: Introduction to Evolutionary Optimization 1 Introduction 1 2 Optimization 11 Part II: Classic Evolutionary Algorithms 3 Generic Algorithms 35 4 Mathematical Models of Genetic Algorithms 63 5 Evolutionary Programming 95 6 Evolution Strategies 117 7 Genetic Programming 141 8 Evolutionary Algorithms Variations 179 Part III: More Recent Evolutionary Algorithms 9 Simulated Annealing 223 10 Ant Colony Optimization 241 11 Particle Swarm Optimization 265 12 Differential Evolution 293 13 Estimation of Distribution Algorithms 313 14 Biogeography-Based Optimization 351 15 Cultural Algorithms 377 16 Opposition-Based Learning 397 17 Other Evolutionary Algorithms 421 Part IV: Special Type of Optimization Problems 18 Combinatorial Optimization 449 19 Constrained Optimization 481 20 Multi-Objective Optimization 517 21 Expensive, Noisy and Dynamic Fitness Functions 563 Appendices A Some Practical Advice 607 B The No Free Lunch Theorem and Performance Testing 613 C Benchmark Optimization Functions 641 References 685 Topic Index 727

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Book SynopsisProvides an easy to understand mathematical tool set for professionals an students in electromagnetic study Non-axiomatic, non-challenging, less formal tutorial approach on the subject Includes appendices with reference material that includes a helpful glossary of terms .Trade Review"This book will benefit scientists and engineers who use electromagnetic theory in the course of their work.” (Zentralblatt MATH, 1 May 2013)Table of ContentsPreface xi Reading Guide xv 1. Introduction 1 2. A Quick Tour of Geometric Algebra 7 2.1 The Basic Rules of a Geometric Algebra 16 2.2 3D Geometric Algebra 17 2.3 Developing the Rules 19 2.3.1 General Rules 20 2.3.2 3D 21 2.3.3 The Geometric Interpretation of Inner and Outer Products 22 2.4 Comparison with Traditional 3D Tools 24 2.5 New Possibilities 24 2.6 Exercises 26 3. Applying the Abstraction 27 3.1 Space and Time 27 3.2 Electromagnetics 28 3.2.1 The Electromagnetic Field 28 3.2.2 Electric and Magnetic Dipoles 30 3.3 The Vector Derivative 32 3.4 The Integral Equations 34 3.5 The Role of the Dual 36 3.6 Exercises 37 4. Generalization 39 4.1 Homogeneous and Inhomogeneous Multivectors 40 4.2 Blades 40 4.3 Reversal 42 4.4 Maximum Grade 43 4.5 Inner and Outer Products Involving a Multivector 44 4.6 Inner and Outer Products between Higher Grades 48 4.7 Summary So Far 50 4.8 Exercises 51 5. (3+1)D Electromagnetics 55 5.1 The Lorentz Force 55 5.2 Maxwell’s Equations in Free Space 56 5.3 Simplifi ed Equations 59 5.4 The Connection between the Electric and Magnetic Fields 60 5.5 Plane Electromagnetic Waves 64 5.6 Charge Conservation 68 5.7 Multivector Potential 69 5.7.1 The Potential of a Moving Charge 70 5.8 Energy and Momentum 76 5.9 Maxwell’s Equations in Polarizable Media 78 5.9.1 Boundary Conditions at an Interface 84 5.10 Exercises 88 6. Review of (3+1)D 91 7. Introducing Spacetime 97 7.1 Background and Key Concepts 98 7.2 Time as a Vector 102 7.3 The Spacetime Basis Elements 104 7.3.1 Spatial and Temporal Vectors 106 7.4 Basic Operations 109 7.5 Velocity 111 7.6 Different Basis Vectors and Frames 112 7.7 Events and Histories 115 7.7.1 Events 115 7.7.2 Histories 115 7.7.3 Straight-Line Histories and Their Time Vectors 116 7.7.4 Arbitrary Histories 119 7.8 The Spacetime Form of ∇ 121 7.9 Working with Vector Differentiation 123 7.10 Working without Basis Vectors 124 7.11 Classifi cation of Spacetime Vectors and Bivectors 126 7.12 Exercises 127 8. Relating Spacetime to (3+1)D 129 8.1 The Correspondence between the Elements 129 8.1.1 The Even Elements of Spacetime 130 8.1.2 The Odd Elements of Spacetime 131 8.1.3 From (3+1)D to Spacetime 132 8.2 Translations in General 133 8.2.1 Vectors 133 8.2.2 Bivectors 135 8.2.3 Trivectors 136 8.3 Introduction to Spacetime Splits 137 8.4 Some Important Spacetime Splits 140 8.4.1 Time 140 8.4.2 Velocity 141 8.4.3 Vector Derivatives 142 8.4.4 Vector Derivatives of General Multivectors 144 8.5 What Next? 144 8.6 Exercises 145 9. Change of Basis Vectors 147 9.1 Linear Transformations 147 9.2 Relationship to Geometric Algebras 149 9.3 Implementing Spatial Rotations and the Lorentz Transformation 150 9.4 Lorentz Transformation of the Basis Vectors 153 9.5 Lorentz Transformation of the Basis Bivectors 155 9.6 Transformation of the Unit Scalar and Pseudoscalar 156 9.7 Reverse Lorentz Transformation 156 9.8 The Lorentz Transformation with Vectors in Component Form 158 9.8.1 Transformation of a Vector versus a Transformation of Basis 158 9.8.2 Transformation of Basis for Any Given Vector 162 9.9 Dilations 165 9.10 Exercises 166 10. Further Spacetime Concepts 169 10.1 Review of Frames and Time Vectors 169 10.2 Frames in General 171 10.3 Maps and Grids 173 10.4 Proper Time 175 10.5 Proper Velocity 176 10.6 Relative Vectors and Paravectors 178 10.6.1 Geometric Interpretation of the Spacetime Split 179 10.6.2 Relative Basis Vectors 183 10.6.3 Evaluating Relative Vectors 185 10.6.4 Relative Vectors Involving Parameters 188 10.6.5 Transforming Relative Vectors and Paravectors to a Different Frame 190 10.7 Frame-Dependent versus Frame-Independent Scalars 192 10.8 Change of Basis for Any Object in Component Form 194 10.9 Velocity as Seen in Different Frames 196 10.10 Frame-Free Form of the Lorentz Transformation 200 10.11 Exercises 202 11. Application of the Spacetime Geometric Algebra to Basic Electromagnetics 203 11.1 The Vector Potential and Some Spacetime Splits 204 11.2 Maxwell’s Equations in Spacetime Form 208 11.2.1 Maxwell’s Free Space or Microscopic Equation 208 11.2.2 Maxwell’s Equations in Polarizable Media 210 11.3 Charge Conservation and the Wave Equation 212 11.4 Plane Electromagnetic Waves 213 11.5 Transformation of the Electromagnetic Field 217 11.5.1 A General Spacetime Split for F 217 11.5.2 Maxwell’s Equation in a Different Frame 219 11.5.3 Transformation of F by Replacement of Basis Elements 221 11.5.4 The Electromagnetic Field of a Plane Wave Under a Change of Frame 223 11.6 Lorentz Force 224 11.7 The Spacetime Approach to Electrodynamics 227 11.8 The Electromagnetic Field of a Moving Point Charge 232 11.8.1 General Spacetime Form of a Charge’s Electromagnetic Potential 232 11.8.2 Electromagnetic Potential of a Point Charge in Uniform Motion 234 11.8.3 Electromagnetic Field of a Point Charge in Uniform Motion 237 11.9 Exercises 240 12. The Electromagnetic Field of a Point Charge Undergoing Acceleration 243 12.1 Working with Null Vectors 243 12.2 Finding F for a Moving Point Charge 248 12.3 Frad in the Charge’s Rest Frame 252 12.4 Frad in the Observer’s Rest Frame 254 12.5 Exercises 258 13. Conclusion 259 14. Appendices 265 14.1 Glossary 265 14.2 Axial versus True Vectors 273 14.3 Complex Numbers and the 2D Geometric Algebra 274 14.4 The Structure of Vector Spaces and Geometric Algebras 275 14.4.1 A Vector Space 275 14.4.2 A Geometric Algebra 275 14.5 Quaternions Compared 281 14.6 Evaluation of an Integral in Equation (5.14) 283 14.7 Formal Derivation of the Spacetime Vector Derivative 284 References 287 Further Reading 291 Index 293 The IEEE Press Series on Electromagnetic Wave Theory

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Book SynopsisAn insightful, hands-on focus on the statistical methods used by compensation and human resources professionals in their everyday work Across various industries, compensation professionals work to organize and analyze aspects of employment that deal with elements of pay, such as deciding base salary, bonus, and commission provided by an employer to its employees for work performed. Acknowledging the numerous quantitative analyses of data that are a part of this everyday work, Statistics for Compensation provides a comprehensive guide to the key statistical tools and techniques needed to perform those analyses and to help organizations make fully informed compensation decisions. This self-contained book is the first of its kind to explore the use of various quantitative methodsfrom basic notions about percents to multiple linear regressionthat are used in the management, design, and implementation of powerful compensation strategies. Drawing upon his exteTrade Review“As an experienced compensation manager for a publicly traded Fortune 500 company, I have found this book to be an all-inclusive, highly useful and infor­mative desk reference. It certainly has been extremely valuable in helping me to contribute to successful strategic decisions at my company.” (Workspan, 1 January 2013) "The book can serve as a text for students specializing in compensation or human resources, or as a reference for practitioners. He provides worked examples throughout." (Booknews, 1 June 2011) Table of ContentsPreface xiii Chapter 1 Introduction 1 1.1 Why do Statistical Analysis? 2 Example Analysis 3 1.2 Statistics 5 1.3 Numbers Raise Issues 6 1.4 Behind Every Data Point, There Is a Story 8 1.5 Aggressive Inquisitiveness 9 1.6 Model Building Framework 9 Example Model 10 1.7 Data Sets 10 1.8 Prerequisites 11 Chapter 2 Basic Notions 13 2.1 Percent 14 Graphical Displays of Percents 16 2.2 Percent Difference 21 2.3 Compound Interest 23 Future Value 24 Present Value 26 Translating 27 Practice Problems 28 Chapter 3 Frequency Distributions and Histograms 31 3.1 Definitions and Construction 41 Rules for Categories 43 3.2 Comparing Distributions 48 Absolute Comparison and Relative Comparison 48 Comparing More Than Two Distributions 50 3.3 Information Loss and Comprehension Gain 51 3.4 Category Selection 51 3.5 Distribution Shapes 54 Uniform Distribution 55 Bell-Shaped Distribution 55 Normal Distribution 56 Skewed Distribution 59 Bimodal Distribution 60 Practice Problems 62 Chapter 4 Measures of Location 67 4.1 Mode 67 4.2 Median 68 4.3 Mean 70 4.4 Trimmed Mean 73 4.5 Overall Example and Comparison 73 Comparison 75 4.6 Weighted and Unweighted Average 76 Which Measure to Use? 78 Application of Weighted Averages to Salary Increase Guidelines 80 4.7 Simpson’s Paradox 82 4.8 Percentile 85 Reverse Percentile 88 4.9 Percentile Bars 90 Practice Problems 92 Chapter 5 Measures of Variability 95 5.1 Importance of Knowing Variability 95 5.2 Population and Sample 96 Examples of Populations 96 Examples of Samples and Populations 96 5.3 Types of Samples 97 5.4 Standard Deviation 98 Interpretations and Applications of Standard Deviation 100 5.5 Coefficient of Variation 107 Interpretations and Applications of Coefficient of Variation 108 5.6 Range 109 Interpretations and Applications of Range 109 5.7 P90/P10 110 Interpretations and Applications of P90/P10 111 5.8 Comparison and Summary 112 Practice Problems 115 Chapter 6 Model Building 119 6.1 Prelude to Models 119 6.2 Introduction 120 6.3 Scientific Method 122 6.4 Models 123 6.5 Model Building Process 126 Plotting Points 128 Functional Forms 132 Method of Least Squares 136 Practice Problems 138 Chapter 7 Linear Model 141 7.1 Examples 141 7.2 Straight Line Basics 143 Interpretations of Intercept and Slope 144 Using the Equation 145 7.3 Fitting the Line to the Data 147 What We Are Predicting 148 Interpretations of Intercept and Slope 149 7.4 Model Evaluation 149 Appearance 150 Coefficient of Determination 150 Correlation 152 Standard Error of Estimate 154 Common Sense 154 7.5 Summary of Interpretations and Evaluation 155 7.6 Cautions 155 7.7 Digging Deeper 158 7.8 Keep the Horse before the Cart 160 Practice Problems 164 Chapter 8 Exponential Model 167 8.1 Examples 167 8.2 Logarithms 168 Antilogs 170 Scales 170 Why Logarithms? 171 8.3 Exponential Model 172 8.4 Model Evaluation 176 Appearance 176 Coefficient of Determination 177 Correlation 177 Standard Error of Estimate 177 Common Sense 178 Summary of Evaluation 178 Practice Problems 178 Chapter 9 Maturity Curve Model 181 9.1 Maturity Curves 181 9.2 Building the Model 184 Cubic Model 184 Cubic Model Evaluation 186 Spline Model 187 Spline Model Evaluation 188 9.3 Comparison of Models 190 Practice Problems 190 Chapter 10 Power Model 193 10.1 Building the Model 193 10.2 Model Evaluation 197 Appearance 197 Coefficient of Determination 198 Correlation 198 Standard Error of Estimate 198 Common Sense 199 Summary of Evaluation 199 Practice Problems 200 Chapter 11 Market Models and Salary Survey Analysis 201 11.1 Introduction 201 11.2 Commonalities of Approaches 203 11.3 Final Market-Based Salary Increase Budget 205 Initial Market-Based Salary Increase Budget and Market Position 205 Final Market-Based Salary Increase Budget 206 Raises Given Throughout the Year 206 Raises Given on a Common Date 208 11.4 Other Factors Influencing the Final Salary Increase Budget Recommendation 210 Assumptions 211 11.5 Salary Structure 211 Practice Problems 213 Chapter 12 Integrated Market Model: Linear 215 12.1 Gather Market Data 215 12.2 Age Data to a Common Date 217 12.3 Create an Integrated Market Model 217 Interpretations 219 12.4 Compare Employee Pay with Market Model 222 Practice Problems 228 Chapter 13 Integrated Market Model: Exponential 233 Practice Problems 246 Chapter 14 Integrated Market Model: Maturity Curve 251 Practice Problems 261 Chapter 15 Job Pricing Market Model: Group of Jobs 265 Practice Problems 272 Chapter 16 Job Pricing Market Model: Power Model 277 Practice Problems 280 Chapter 17 Multiple Linear Regression 283 17.1 What It Is 283 17.2 Similarities and Differenceswith Simple Linear Regression 284 17.3 Building the Model 285 First x-Variable 292 Second x-Variable 295 Standardized Coefficient 298 Third x-Variable 300 Multicollinearity 301 17.4 Model Evaluation 305 Regression Coefficients 305 Standardized Coefficients 306 Coefficient of Determination 306 Standard Error of Estimate 306 Multicollinearity 306 Simplicity 307 Common Sense 307 Acceptability 307 Reality 307 Decision 307 17.5 Mixed Messages in Evaluating A Model 308 r2 Versus Common Sense 308 r2 Versus Simplicity 308 Simplicity Versus Acceptability 308 17.6 Summary of Regressions 308 17.7 Digging Deeper 310 Summary 315 Practice Problems 317 Appendix 319 A.1 Value Exchange Theory 319 Achieving Organization Goals 319 Value Exchange 319 A Fair Value Exchange Is a Good Deal 320 A.2 Factors Determining a Person’s Pay 321 System Factors 322 Individual Factors 323 A.3 Types of Numbers 324 Definitions and Properties 324 Histograms with All Four Types of Measurements 327 A.4 Significant Figures 330 A.5 Scientific Notation 331 A.6 Accuracy and Precision 332 Which Is More Important? 333 A.7 Compound Interest–Additional 333 Other Formulas 333 A.8 Rule of 72 334 Derivation of the Rule of 72 335 A.9 Normal Distribution 336 Central Limit Theorem 337 Distribution of Salary Survey Data 338 A.10 Linear Regression Technical Note 338 A.11 Formulas for Regression Terms 340 A.12 Logarithmic Conversion 340 A.13 Range Spread Relationships 340 Overlap 343 A.14 Statistical Inference in Regression 344 t-Statistic and Its Probability 347 F-Statistic and Its Probability 348 Mixed Messages in Evaluating a Model 349 A.15 Additional Multiple Linear Regression Topics 349 Adjusted r2 349 Coding of Indicator Variables 350 Interaction Terms 351 GLOSSARY 357 REFERENCES 369 ANSWERS TO PRACTICE PROBLEMS 371 INDEX 433

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Book SynopsisStatistics in Psychology covers all statistical methods needed in education and research in psychology. This book looks at research questions when planning data sampling, that is to design the intended study and to calculate the sample sizes in advance.Table of ContentsIntroduction. 1 Concept of the Book. 2 Measuring in Psychology. 2.1 Types of psychological measurements. 2.2 Measurement techniques in psychological assessment. 2.3 Quality criteria in psychometrics. 2.4 Additional psychological measurement techniques. 2.5 Statistical models of measurement with psychological roots. 3 Psychology: An Empirical Science. 3.1 Gain of insight in psychology. 3.2 Steps of empirical research. 4 Definition: Character, Chance, Experiment, and Survey. 4.1 Nominal scale. 4.2 Ordinal scale. 4.3 Interval scale. 4.4 Ratio scale. 4.5 Characters and factors. II Descriptive Statistics. 5 Numerical and graphical Data Analysis. 5.1 Introduction to data analysis. 5.2 Frequencies and empirical distributions. 5.3 Statistics. 5.4 Frequency distribution for several characters. III Inferential Statistics for one Character. 6 Probability and distribution. 6.1 Relative frequencies and probabilities. 6.2 Random variable and theoretical distributions. 6.3 Quantiles of theoretical distribution functions. 6.4 Mean and variance of theoretical distributions. 6.5 Estimation of unknown parameters. 7 Assumptions: Random Sampling and Randomization. 7.1 Simple random sampling in surveys. 7.2 Principles of random sampling and randomization. 8 One Sample from one Population. 8.1 Introduction. 8.2 The Parameter mof acharacter modeled by a normally distributed random variable. 8.3 Planning a study for hypothesis testing with respect to m. 8.4 Sequential tests for the unknown parameter m. 8.5 Estimation, hypothesis testing, planning the study, and sequential testing concerning other parameters. 9 Two Samples from two Populations. 9.1 Hypothesis testing, study planning and sequential testing regarding the unknown parameters m1 and m2. 9.2 Hypothesis testing, study planning and sequential testing for other parameters. 9.3 Equivalence testing. 10 Samples from more than two Populations. 10.1 The various problem situations. 10.2. Selection procedures. 10.3 Multiple comparisons of means. 10.4 Analysis of variance. IV Descriptive and Inferential Statistics for two Characters. 11 Regression and Correlation. 11.1 Introduction. 11.2 Regression model. 11.3 Correlation coefficients and measures of association. 11.4 Hypothesis testing and planning the study concerning correlation coefficients. 11.5 Correlation analysis in two samples. V Inferential Statistics for more than two Characters. 12 One Sample from one Population. 12.1 Association between three or more characters. 12.2 Hypothesis testing concerning a vector of means m. 12.3 Comparisons of means and "homological" methods for matched observations. 13 Samples from more than one Population. 13.1 General linear model. 13.2 Analysis of covariance. 13.3. Multivariate analysis of variance. 13.4 Discriminant analysis. VI Model Generation and Theory-Generating Procedures. 14 Model Generation. 14.1 Theoretical basics of model generation. 14.2 Methods for determining the quality and excellence of a model. 14.2.1 Goodness of fit tests. 14.2.2 Coefficients of the goodness of fit. 14.2.3 Cross-validation. 14.4 Simulation: Non-analytical solutions to statistical problems. 15 Theory-Generating Procedures. 15.1 Descriptive statistics' methods. 15.2 Methods of inferential statistics.

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Book SynopsisModern Analysis of Customer Surveys: with applications using R Customer survey studies deal with customer, consumer and user satisfaction from a product or service. In practice, many of the customer surveys conducted by business and industry are analyzed in a very simple way, without using models or statistical methods. Typical reports include descriptive statistics and basic graphical displays. This book demonstrates how integrating such basic analysis with more advanced tools, provides insights into non-obvious patterns and important relationships between the survey variables. This knowledge can significantly affect the conclusions derived from a survey. Key features: Provides an integrated case studies-based approach to analysing customer survey data. Presents a general introduction to customer surveys, within an organization's business cycle. Contains classical techniques with modern and non standard tools.Table of ContentsForeword xvii Preface xix Contributors xxiii Part I Basic Aspects of Customer Satisfaction Survey Data Analysis 1 Standards and Classical Techniques in Data Analysis of Customer Satisfaction Surveys 3 Silvia Salini and Ron S. Kenett 1.1 Literature on customer satisfaction surveys 4 1.2 Customer satisfaction surveys and the business cycle 4 1.3 Standards used in the analysis of survey data 7 1.4 Measures and models of customer satisfaction 12 1.4.1 The conceptual construct 12 1.4.2 The measurement process 13 1.5 Organization of the book 15 1.6 Summary 17 References 17 2 The ABC Annual Customer Satisfaction Survey 19 Ron S. Kenett and Silvia Salini 2.1 The ABC company 19 2.2 ABC 2010 ACSS: Demographics of respondents 20 2.3 ABC 2010 ACSS: Overall satisfaction 22 2.4 ABC 2010 ACSS: Analysis of topics 24 2.5 ABC 2010 ACSS: Strengths and weaknesses and decision drivers 27 2.6 Summary 28 References 28 Appendix 29 3 Census and Sample Surveys 37 Giovanna Nicolini and Luciana Dalla Valle 3.1 Introduction 37 3.2 Types of surveys 39 3.2.1 Census and sample surveys 39 3.2.2 Sampling design 40 3.2.3 Managing a survey 40 3.2.4 Frequency of surveys 41 3.3 Non-sampling errors 41 3.3.1 Measurement error 42 3.3.2 Coverage error 42 3.3.3 Unit non-response and non-self-selection errors 43 3.3.4 Item non-response and non-self-selection error 44 3.4 Data collection methods 44 3.5 Methods to correct non-sampling errors 46 3.5.1 Methods to correct unit non-response errors 46 3.5.2 Methods to correct item non-response 49 3.6 Summary 51 References 52 4 Measurement Scales 55 Andrea Bonanomi and Gabriele Cantaluppi 4.1 Scale construction 55 4.1.1 Nominal scale 56 4.1.2 Ordinal scale 57 4.1.3 Interval scale 58 4.1.4 Ratio scale 59 4.2 Scale transformations 60 4.2.1 Scale transformations referred to single items 61 4.2.2 Scale transformations to obtain scores on a unique interval scale 66 Acknowledgements 69 References 69 5 Integrated Analysis 71 Silvia Biffignandi 5.1 Introduction 71 5.2 Information sources and related problems 73 5.2.1 Types of data sources 73 5.2.2 Advantages of using secondary source data 73 5.2.3 Problems with secondary source data 74 5.2.4 Internal sources of secondary information 75 5.3 Root cause analysis 78 5.3.1 General concepts 78 5.3.2 Methods and tools in RCA 81 5.3.3 Root cause analysis and customer satisfaction 85 5.4 Summary 87 Acknowledgement 87 References 87 6 Web Surveys 89 Roberto Furlan and Diego Martone 6.1 Introduction 89 6.2 Main types of web surveys 90 6.3 Economic benefits of web survey research 91 6.3.1 Fixed and variable costs 92 6.4 Non-economic benefits of web survey research 94 6.5 Main drawbacks of web survey research 96 6.6 Web surveys for customer and employee satisfaction projects 100 6.7 Summary 102 References 102 7 The Concept and Assessment of Customer Satisfaction 107 Irena Ograjenšek and Iddo Gal 7.1 Introduction 107 7.2 The quality–satisfaction–loyalty chain 108 7.2.1 Rationale 108 7.2.2 Definitions of customer satisfaction 108 7.2.3 From general conceptions to a measurement model of customer satisfaction 110 7.2.4 Going beyond SERVQUAL: Other dimensions of relevance to the B2B context 112 7.2.5 From customer satisfaction to customer loyalty 113 7.3 Customer satisfaction assessment: Some methodological considerations 115 7.3.1 Rationale 115 7.3.2 Think big: An assessment programme 115 7.3.3 Back to basics: Questionnaire design 116 7.3.4 Impact of questionnaire design on interpretation 118 7.3.5 Additional concerns in the B2B setting 119 7.4 The ABC ACSS questionnaire: An evaluation 119 7.4.1 Rationale 119 7.4.2 Conceptual issues 119 7.4.3 Methodological issues 120 7.4.4 Overall ABC ACSS questionnaire asssessment 121 7.5 Summary 121 References 122 Appendix 126 8 Missing Data and Imputation Methods 129 Alessandra Mattei, Fabrizia Mealli and Donald B. Rubin 8.1 Introduction 129 8.2 Missing-data patterns and missing-data mechanisms 131 8.2.1 Missing-data patterns 131 8.2.2 Missing-data mechanisms and ignorability 132 8.3 Simple approaches to the missing-data problem 134 8.3.1 Complete-case analysis 134 8.3.2 Available-case analysis 135 8.3.3 Weighting adjustment for unit nonresponse 135 8.4 Single imputation 136 8.5 Multiple imputation 138 8.5.1 Multiple-imputation inference for a scalar estimand 138 8.5.2 Proper multiple imputation 139 8.5.3 Appropriately drawing imputations with monotone missing-data patterns 140 8.5.4 Appropriately drawing imputations with nonmonotone missing-data patterns 141 8.5.5 Multiple imputation in practice 142 8.5.6 Software for multiple imputation 143 8.6 Model-based approaches to the analysis of missing data 144 8.7 Addressing missing data in the ABC annual customer satisfaction survey: An example 145 8.8 Summary 149 Acknowledgements 150 References 150 9 Outliers and Robustness for Ordinal Data 155 Marco Riani, Francesca Torti and Sergio Zani 9.1 An overview of outlier detection methods 155 9.2 An example of masking 157 9.3 Detection of outliers in ordinal variables 159 9.4 Detection of bivariate ordinal outliers 160 9.5 Detection of multivariate outliers in ordinal regression 161 9.5.1 Theory 161 9.5.2 Results from the application 163 9.6 Summary 168 References 168 Part II Modern Techniques in Customer Satisfaction Survey Data Analysis 10 Statistical Inference for Causal Effects 173 Fabrizia Mealli, Barbara Pacini and Donald B. Rubin 10.1 Introduction to the potential outcome approach to causal inference 173 10.1.1 Causal inference primitives: Units, treatments, and potential outcomes 175 10.1.2 Learning about causal effects: Multiple units and the stable unit treatment value assumption 176 10.1.3 Defining causal estimands 177 10.2 Assignment mechanisms 179 10.2.1 The criticality of the assignment mechanism 179 10.2.2 Unconfounded and strongly ignorable assignment mechanisms 180 10.2.3 Confounded and ignorable assignment mechanisms 181 10.2.4 Randomized and observational studies 181 10.3 Inference in classical randomized experiments 182 10.3.1 Fisher’s approach and extensions 183 10.3.2 Neyman’s approach to randomization-based inference 183 10.3.3 Covariates, regression models, and Bayesian model-based inference 184 10.4 Inference in observational studies 185 10.4.1 Inference in regular designs 186 10.4.2 Designing observational studies: The role of the propensity score 186 10.4.3 Estimation methods 188 10.4.4 Inference in irregular designs 188 10.4.5 Sensitivity and bounds 189 10.4.6 Broken randomized experiments as templates for the analysis of some irregular designs 189 References 190 11 Bayesian Networks Applied to Customer Surveys 193 Ron S. Kenett, Giovanni Perruca and Silvia Salini 11.1 Introduction to Bayesian networks 193 11.2 The Bayesian network model in practice 197 11.2.1 Bayesian network analysis of the ABC 2010 ACSS 197 11.2.2 Transport data analysis 201 11.2.3 R packages and other software programs used for studying BNs 210 11.3 Prediction and explanation 211 11.4 Summary 213 References 213 12 Log-linear Model Methods 217 Stephen E. Fienberg and Daniel Manrique-Vallier 12.1 Introduction 217 12.2 Overview of log-linear models and methods 218 12.2.1 Two-way tables 218 12.2.2 Hierarchical log-linear models 220 12.2.3 Model search and selection 222 12.2.4 Sparseness in contingency tables and its implications 223 12.2.5 Computer programs for log-linear model analysis 223 12.3 Application to ABC survey data 224 12.4 Summary 227 References 228 13 CUB Models: Statistical Methods and Empirical Evidence 231 Maria Iannario and Domenico Piccolo 13.1 Introduction 231 13.2 Logical foundations and psychological motivations 233 13.3 A class of models for ordinal data 233 13.4 Main inferential issues 236 13.5 Specification of CUB models with subjects’ covariates 238 13.6 Interpreting the role of covariates 240 13.7 A more general sampling framework 241 13.7.1 Objects’ covariates 241 13.7.2 Contextual covariates 243 13.8 Applications of CUB models 244 13.8.1 Models for the ABC annual customer satisfaction survey 245 13.8.2 Students’ satisfaction with a university orientation service 246 13.9 Further generalizations 248 13.10 Concluding remarks 251 Acknowledgements 251 References 251 Appendix 255 A program in R for CUB models 255 A.1 Main structure of the program 255 A.2 Inference on CUB models 255 A.3 Output of CUB models estimation program 256 A.4 Visualization of several CUB models in the parameter space 257 A.5 Inference on CUB models in a multi-object framework 257 A.6 Advanced software support for CUB models 258 14 The Rasch Model 259 Francesca De Battisti, Giovanna Nicolini and Silvia Salini 14.1 An overview of the Rasch model 259 14.1.1 The origins and the properties of the model 259 14.1.2 Rasch model for hierarchical and longitudinal data 263 14.1.3 Rasch model applications in customer satisfaction surveys 265 14.2 The Rasch model in practice 267 14.2.1 Single model 267 14.2.2 Overall model 268 14.2.3 Dimension model 272 14.3 Rasch model software 277 14.4 Summary 278 References 279 15 Tree-based Methods and Decision Trees 283 Giuliano Galimberti and Gabriele Soffritti 15.1 An overview of tree-based methods and decision trees 283 15.1.1 The origins of tree-based methods 283 15.1.2 Tree graphs, tree-based methods and decision trees 284 15.1.3 CART 287 15.1.4 CHAID 293 15.1.5 PARTY 295 15.1.6 A comparison of CART, CHAID and PARTY 297 15.1.7 Missing values 297 15.1.8 Tree-based methods for applications in customer satisfaction surveys 298 15.2 Tree-based methods and decision trees in practice 300 15.2.1 ABC ACSS data analysis with tree-based methods 300 15.2.2 Packages and software implementing tree-based methods 303 15.3 Further developments 304 References 304 16 PLS Models 309 Giuseppe Boari and Gabriele Cantaluppi 16.1 Introduction 309 16.2 The general formulation of a structural equation model 310 16.2.1 The inner model 310 16.2.2 The outer model 312 16.3 The PLS algorithm 313 16.4 Statistical interpretation of PLS 319 16.5 Geometrical interpretation of PLS 320 16.6 Comparison of the properties of PLS and LISREL procedures 321 16.7 Available software for PLS estimation 323 16.8 Application to real data: Customer satisfaction analysis 323 References 329 17 Nonlinear Principal Component Analysis 333 Pier Alda Ferrari and Alessandro Barbiero 17.1 Introduction 333 17.2 Homogeneity analysis and nonlinear principal component analysis 334 17.2.1 Homogeneity analysis 334 17.2.2 Nonlinear principal component analysis 336 17.3 Analysis of customer satisfaction 338 17.3.1 The setting up of indicator 338 17.3.2 Additional analysis 340 17.4 Dealing with missing data 340 17.5 Nonlinear principal component analysis versus two competitors 343 17.6 Application to the ABC ACSS data 344 17.6.1 Data preparation 344 17.6.2 The homals package 345 17.6.3 Analysis on the ‘complete subset’ 346 17.6.4 Comparison of NLPCA with PCA and Rasch analysis 350 17.6.5 Analysis of ‘entire data set’ for the comparison of missing data treatments 352 17.7 Summary 355 References 355 18 Multidimensional Scaling 357 Nadia Solaro 18.1 An overview of multidimensional scaling techniques 357 18.1.1 The origins of MDS models 358 18.1.2 MDS input data 359 18.1.3 MDS models 362 18.1.4 Assessing the goodness of MDS solutions 369 18.1.5 Comparing two MDS solutions: Procrustes analysis 371 18.1.6 Robustness issues in the MDS framework 371 18.1.7 Handling missing values in MDS framework 373 18.1.8 MDS applications in customer satisfaction surveys 373 18.2 Multidimensional scaling in practice 374 18.2.1 Data sets analysed 375 18.2.2 MDS analyses of overall satisfaction with a set of ABC features: The complete data set 375 18.2.3 Weighting objects or items 381 18.2.4 Robustness analysis with the forward search 382 18.2.5 MDS analyses of overall satisfaction with a set of ABC features: The incomplete data set 383 18.2.6 Package and software for MDS methods 384 18.3 Multidimensional scaling in a future perspective 386 18.4 Summary 386 References 387 19 Multilevel Models for Ordinal Data 391 Leonardo Grilli and Carla Rampichini 19.1 Ordinal variables 391 19.2 Standard models for ordinal data 393 19.2.1 Cumulative models 394 19.2.2 Other models 395 19.3 Multilevel models for ordinal data 395 19.3.1 Representation as an underlying linear model with thresholds 396 19.3.2 Marginal versus conditional effects 397 19.3.3 Summarizing the cluster-level unobserved heterogeneity 397 19.3.4 Consequences of adding a covariate 398 19.3.5 Predicted probabilities 399 19.3.6 Cluster-level covariates and contextual effects 399 19.3.7 Estimation of model parameters 400 19.3.8 Inference on model parameters 401 19.3.9 Prediction of random effects 402 19.3.10 Software 403 19.4 Multilevel models for ordinal data in practice: An application to student ratings 404 References 408 20 Quality Standards and Control Charts Applied to Customer Surveys 413 Ron S. Kenett, Laura Deldossi and Diego Zappa 20.1 Quality standards and customer satisfaction 413 20.2 ISO 10004 guidelines for monitoring and measuring customer satisfaction 414 20.3 Control Charts and ISO 7870 417 20.4 Control charts and customer surveys: Standard assumptions 420 20.4.1 Introduction 420 20.4.2 Standard control charts 420 20.5 Control charts and customer surveys: Non-standard methods 426 20.5.1 Weights on counts: Another application of the c chart 426 20.5.2 The χ2 chart 427 20.5.3 Sequential probability ratio tests 428 20.5.4 Control chart over items: A non-standard application of SPC methods 429 20.5.5 Bayesian control chart for attributes: A modern application of SPC methods 432 20.5.6 Control chart for correlated Poisson counts: When things become fairly complicated 433 20.6 The M-test for assessing sample representation 433 20.7 Summary 435 References 436 21 Fuzzy Methods and Satisfaction Indices 439 Sergio Zani, Maria Adele Milioli and Isabella Morlini 21.1 Introduction 439 21.2 Basic definitions and operations 440 21.3 Fuzzy numbers 441 21.4 A criterion for fuzzy transformation of variables 443 21.5 Aggregation and weighting of variables 445 21.6 Application to the ABC customer satisfaction survey data 446 21.6.1 The input matrices 446 21.6.2 Main results 448 21.7 Summary 453 References 455 Appendix an Introduction to R 457 Stefano Maria Iacus A.1 Introduction 457 A.2 How to obtain R 457 A.3 Type rather than ‘point and click’ 458 A.3.1 The workspace 458 A.3.2 Graphics 458 A.3.3 Getting help 459 A.3.4 Installing packages 459 A.4 Objects 460 A.4.1 Assignments 460 A.4.2 Basic object types 462 A.4.3 Accessing objects and subsetting 466 A.4.4 Coercion between data types 469 A.5 S4 objects 470 A.6 Functions 472 A.7 Vectorization 473 A.8 Importing data from different sources 475 A.9 Interacting with databases 476 A.10 Simple graphics manipulation 477 A.11 Basic analysis of the ABC data 481 A.12 About this document 496 A.13 Bibliographical notes 496 References 496 Index 499

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Book SynopsisLatent Variable Models and Factor Analysis provides a comprehensive and unified approach to factor analysis and latent variable modeling from a statistical perspective. This book presents a general framework to enable the derivation of the commonly used models, along with updated numerical examples.Trade Review“Latent Variable Models and Factor Analysis provides a comprehensive and unified approach to factor analysis and latent variable modeling from a statistical perspective.” (Mathematical Reviews, 2012) "Statistical techniques to study the nature and interpretation of a latent variable should be highly useful for researchers and practitioners across several fields. The third edition of this book is comprehensive and provides a solid foundation for understanding these techniques, and is strongly recommended." (Book Pleasures, 2012)Table of ContentsPreface xi Acknowledgements xv 1 Basic Ideas and Examples 1 1.1 The statistical problem 1 1.2 The basic idea 3 1.3 Two Examples 4 1.4 A broader theoretical view 6 1.5 Illustration of an alternative approach 8 1.6 An overview of special cases 10 1.7 Principal components 11 1.8 The historical context 12 1.9 Closely related fields in Statistics 17 2 The General Linear Latent Variable Model 19 2.1 Introduction 19 2.2 The model 19 2.3 Some properties of the model 20 2.4 A special case 21 2.5 The sufficiency principle 22 2.6 Principal special cases 24 2.7 Latent variable models with non-linear terms 25 2.8 Fitting the models 27 2.9 Fitting by maximum likelihood 29 2.10 Fitting by Bayesian methods 30 2.11 Rotation 33 2.12 Interpretation 35 2.13 Sampling error of parameter estimates 38 2.14 The prior distribution 39 2.15 Posterior analysis 41 2.16 A further note on the prior 43 2.17 Psychometric Inference 44 3 The Normal Linear Factor Model 47 3.1 The model 47 3.2 Some distributional properties 48 3.3 Constraints on the model 50 3.4 Maximum likelihood estimation 50 3.5 Maximum likelihood estimation by the E-M algorithm 53 3.6 Sampling variation of estimators 55 3.7 Goodness of fit and choice of q 58 3.8 Fitting without normality assumptions: Least squares methods 59 3.9 Other methods of fitting 61 3.10 Approximate methods for estimating 62 3.11 Goodness-of-fit and choice of q for least squares methods 63 3.12 Further estimation issues 64 3.13 Rotation and related matters 69 3.14 Posterior analysis: The normal case 67 3.15 Posterior analysis: least squares 72 3.16 Posterior analysis: a reliability approach 74 3.17 Examples 74 4 Binary Data: Latent Trait Models 83 4.1 Preliminaries 83 4.2 The logit/normal model 84 4.3 The probit/normal model 86 4.4 The equivalence of the response function and underlying variable approaches 88 4.5 Fitting the logit/normal model: the E-M algorithm 90 4.6 Sampling properties of the maximum likelihood estimators 94 4.7 Approximate maximum likelihood estimators 95 4.8 Generalised least squares methods 96 4.9 Goodness of fit 97 4.10 Posterior analysis 100 4.11 Fitting the logit/normal and probit/normal models: Markov Chain Monte Carlo 102 4.12 Divergence of the estimation algorithm 109 4.13 Examples 109 5 Polytomous Data: Latent Trait Models 119 5.1 Introduction 119 5.2 A response function model based on the sufficiency principle 120 5.3 Parameter interpretation 124 5.4 Rotation 124 5.5 Maximum likelihood estimation of the polytomous logit model 125 5.6 An approximation to the likelihood 126 5.7 Binary data as a special case 134 5.8 Ordering of categories 136 5.9 An alternative underlying variable model 144 5.10 Posterior analysis 147 5.11 Further observations 148 5.12 Examples of the analysis of polytomous data using the logit model 149 6 Latent Class Models 157 6.1 Introduction 157 6.2 The latent class model with binary manifest variables 158 6.3 The latent class model for binary data as a latent trait model 159 6.4 Latent Classes within the GLLVM 161 6.5 Maximum likelihood estimation 162 6.6 Standard errors 164 6.7 Posterior analysis of the latent class model with binary manifest variables 166 6.8 Goodness of Fit 167 6.9 Examples for binary Data 167 6.10 Latent class models with unordered polytomous manifest variables 170 6.11 Latent class models with ordered polytomous manifest variables 171 6.12 Maximum likelihood estimation 172 6.13 Examples for unordered polytomous data 174 6.14 Identifiability 178 6.15 Starting values 180 6.16 Latent class models with metrical manifest variables 180 6.17 Models with ordered latent classes 181 6.18 Hybrid models 182 7 Models and Methods for Manifest Variables of Mixed Type 191 7.1 Introduction 191 7.2 Principal results 192 7.3 Other members of the exponential family 193 7.4 Maximum likelihood estimation 195 7.5 Sampling properties and Goodness of Fit 201 7.6 Mixed latent class models 202 7.7 Posterior analysis 203 7.8 Examples 204 7.9 Ordered categorical variables and other generalisations 208 8 Relationships Between Latent Variables 213 8.1 Scope 213 8.2 Correlated latent variables 213 8.3 Procrustes methods 215 8.4 Sources of prior knowledge 215 8.5 Linear structural relations models 216 8.6 The LISREL model 218 8.7 Adequacy of a structural equation model 221 8.8 Structural relationships in a general setting 222 8.9 Generalisations of the LISREL model 223 8.10 Examples of models which are indistinguishable 224 8.11 Implications for analysis 227 9 Related Techniques for Investigating Dependency 229 9.1 Introduction 229 9.2 Principal Components Analysis, (PCA) 229 9.3 An alternative to the normal factor model 236 9.4 Replacing latent variables by linear functions of the manifest variables 238 9.5 Estimation of correlations and regressions between latent variables 240 9.6 Q-Methodology 242 9.7 Concluding reflections of the role of latent variables in statistical modelling 244 References 247 Software appendix 247 References 249 Author Index 265 Subject Index 271

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Book SynopsisEssential Maths for Geoscientists An Introduction Essential Maths for Geoscientists: An Introduction is an accessible, student-friendly introduction to the mathematics required by those students taking degree courses within the geosciences. Clearly structured throughout, this book carefully guides students step by step through the first mathematics they will encounter and provides numerous applied examples throughout to enhance students' understanding and to place each technique in context. Opening with a chapter explaining the need for studying mathematics within geosciences, this book then moves on to cover algebra, solving equations, logarithms and exponentials, uncertainties, errors and statistics, trigonometry, vectors and basic calculus. The final chapter helps to bring the subject all together and provides detailed applied questions to test students' knowledge. Worked applied examples are included in each chapter along with applied problemTable of ContentsPreface xi 1 How Do You Know that Global Warming is Not a Hoax? 1 2 Preamble 7 2.1 The scientific method: pushing back the frontiers of ignorance 7 2.2 Subscript and superscripts 9 2.3 Scientific number format 10 2.4 Significant figures and rounding numbers 12 2.5 Units and dimensions 13 2.6 Symbols and numbers 14 2.7 Mean, median and variance: commonly encountered statistics 15 2.8 Guesstimation 19 2.9 Exercises 21 3 Algebra 37 3.1 Introduction 37 3.2 Evaluating algebraic equations 37 3.2.1 Preamble: symbols and numbers 37 3.2.2 Powers, roots and bases 38 3.3 Simplifying algebraic equations 39 3.4 Factorization 44 3.4.1 Factorizing quadratic equations 46 3.5 Transposing formulae 46 3.6 Word problems 49 3.7 Exercises 50 4 Solving Equations 53 4.1 Solving linear equations 53 4.1.1 Graphically 54 4.1.2 Analytically 58 4.2 Solving simultaneous equations 58 4.3 Solving quadratic equations 59 4.3.1 Square roots 60 4.3.2 Completing the square 60 4.4 Exercises 62 5 Logarithms and Exponentials 67 5.1 Exponentials 67 5.2 Logarithms 67 5.2.1 Logarithm laws 68 5.2.2 Solving exponential equations 69 5.2.3 Power laws and scaling exponents 69 5.3 Log-normal and log–log plots: when and how to use them 72 5.4 Exercises 74 6 Uncertainties, Errors, and Statistics 77 6.1 Errors 77 6.1.1 Important definitions 78 6.1.2 Measures of error 80 6.2 Combining errors 83 6.2.1 Equations with one variable 83 6.2.2 Equations with two or more variables 84 6.2.3 Linear equations 84 6.2.4 Products 85 6.2.5 Combining results of different experiments 86 6.3 Statistics 87 6.3.1 Graphs 87 6.3.2 Descriptive statistics 89 6.4 Correlations 91 6.5 Exercises 93 7 Trigonometry 95 7.1 Some geoscience applications of trigonometry 95 7.2 Anatomy of a triangle 96 7.3 Angles: degrees and radians 99 7.4 Calculating angles given a trigonometric ratio 100 7.5 Cosine and sine rules for non-right-angled triangles 101 7.6 Exercises 101 8 Vectors 105 8.1 What is a vector? 105 8.2 Resolving a vector 105 8.3 Vector algebra 107 8.3.1 Adding and subtracting vectors 107 8.3.2 Multiplying a vector by a scalar 107 8.3.3 The resultant of two perpendicular vectors 107 8.4 Resolving non-perpendicular vectors 108 8.5 Exercises 110 9 Calculus 1: Differentiation 113 9.1 A graphical interpretation of differentiation 114 9.2 A general formula for differentiation 116 9.3 The derivative of some common functions 118 9.4 Differentiation of the sum and difference of functions 118 9.5 Higher derivatives 120 9.6 Maxima and minima 120 9.7 Exercises 122 10 Calculus 2: Integration 125 10.1 Introduction 125 10.2 Definite integrals 127 10.3 Numerical integration 129 10.4 Exercises 130 11 Bringing It All Together 133 A Answers to Problems 143 A.1 Chapter 2: Preamble 143 A.2 Chapter 3: Algebra 148 A.3 Chapter 4: Solving Equations 152 A.4 Chapter 5: Logarithms and Exponentials 158 A.5 Chapter 6: Uncertainties, Errors, and Statistics 162 A.6 Chapter 7: Trigonometry 166 A.7 Chapter 8: Vectors 171 A.8 Chapter 9: Differentiation 174 A.9 Chapter 10: Integration 179 A.10 Chapter 11: Bringing it all together 182 B A Brief Note on Excel 197 C Further Reading 199 Index 201

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Book SynopsisA practical guide for determining the evidential value of physicochemical data Microtraces of various materials (e.g. glass, paint, fibres, and petroleum products) are routinely subjected to physicochemical examination by forensic experts, whose role is to evaluate such physicochemical data in the context of the prosecution and defence propositions. Such examinations return various kinds of information, including quantitative data. From the forensic point of view, the most suitable way to evaluate evidence is the likelihood ratio. This book provides a collection of recent approaches to the determination of likelihood ratios and describes suitable software, with documentation and examples of their use in practice. The statistical computing and graphics software environment R, pre-computed Bayesian networks using Hugin Researcher and a new package, calcuLatoR, for the computation of likelihood ratios are all explored. Statistical Analysis in ForeTable of ContentsPreface xiii 1 Physicochemical data obtained in forensic science laboratories 1 1.1 Introduction 1 1.2 Glass 2 1.3 Flammable liquids: ATD-GC/MS technique 8 1.4 Car paints: Py-GC/MS technique 10 1.5 Fibres and inks: MSP-DAD technique 13 References 15 2 Evaluation of evidence in the form of physicochemical data 19 2.1 Introduction 19 2.2 Comparison problem 21 2.3 Classification problem 27 2.4 Likelihood ratio and Bayes’ theorem 31 References 32 3 Continuous data 35 3.1 Introduction 35 3.2 Data transformations 37 3.3 Descriptive statistics 39 3.4 Hypothesis testing 59 3.5 Analysis of variance 78 3.6 Cluster analysis 85 3.7 Dimensionality reduction 92 References 105 4 Likelihood ratio models for comparison problems 107 4.1 Introduction 107 4.2 Normal between-object distribution 108 4.3 Between-object distribution modelled by kernel density estimation 110 4.4 Examples 112 4.5 R Software 140 References 149 5 Likelihood ratio models for classification problems 151 5.1 Introduction 151 5.2 Normal between-object distribution 152 5.3 Between-object distribution modelled by kernel density estimation 155 5.4 Examples 157 5.5 R software 172 References 179 6 Performance of likelihood ratio methods 181 6.1 Introduction 181 6.2 Empirical measurement of the performance of likelihood ratios 182 6.3 Histograms and Tippett plots 183 6.4 Measuring discriminating power 186 6.5 Accuracy equals discriminating power plus calibration: Empirical cross-entropy plots 192 6.6 Comparison of the performance of different methods for LR computation 200 6.7 Conclusions: What to measure, and how 214 6.8 Software 215 References 216 Appendix A Probability 218 A.1 Laws of probability 218 A.2 Bayes’ theorem and the likelihood ratio 222 A.3 Probability distributions for discrete data 225 A.4 Probability distributions for continuous data 227 References 227 Appendix B Matrices: An introduction to matrix algebra 228 B.1 Multiplication by a constant 228 B.2 Adding matrices 229 B.3 Multiplying matrices 230 B.4 Matrix transposition 232 B.5 Determinant of a matrix 232 B.6 Matrix inversion 233 B.7 Matrix equations 235 B.8 Eigenvectors and eigenvalues 237 Reference 239 Appendix C Pool adjacent violators algorithm 240 References 243 Appendix D Introduction to R software 244 D.1 Becoming familiar with R 244 D.2 Basic mathematical operations in R 246 D.3 Data input 252 D.4 Functions in R 254 D.5 Dereferencing 255 D.6 Basic statistical functions 257 D.7 Graphics with R 258 D.8 Saving data 266 D.9 R codes used in Chapters 4 and 5 266 D.10 Evaluating the performance of LR models 289 Reference 293 Appendix E Bayesian network models 294 E.1 Introduction to Bayesian networks 294 E.2 Introduction to Hugin ResearcherTM software 296 References 308 Appendix F Introduction to calcuLatoR software 309 F.1 Introduction 309 F.2 Manual 309 Reference 314 Index 315

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Book SynopsisIndustrial Statistics with MINITAB demonstrates the use of MINITAB as a tool for performing statistical analysis in an industrial context. This book covers introductory industrial statistics, exploring the most commonly used techniques alongside those that serve to give an overview of more complex issues.Table of ContentsPreface xiii Part One Introduction and Graphical Techniques 1 1 A First Look 3 1.1 Initial Screen 3 1.2 Entering Data 4 1.3 Saving Data: Worksheets and Projects 5 1.4 Data Operations: An Introduction 5 1.5 Deleting and Inserting Columns and Rows 7 1.6 First Statistical Analyses 8 1.7 Getting Help 10 1.8 Personal Configuration 12 1.9 Assistant 13 1.10 Any Difficulties? 14 2 Graphics for Univariate Data 15 2.1 File ‘PULSE’ 15 2.2 Histograms 16 2.3 Changing the Appearance of Histograms 17 2.4 Histograms for Various Data Sets 21 2.5 Dotplots 23 2.6 Boxplots 24 2.7 Bar Diagrams 25 2.8 Pie Charts 27 2.9 Updating Graphs Automatically 28 2.10 Adding Text or Figures to a Graph 29 3 Pareto Charts and Cause–Effect Diagrams 31 3.1 File ‘DETERGENT’ 31 3.2 Pareto Charts 32 3.4 Cause-and-Effect Diagrams 35 4 Scatterplots 37 4.1 File ‘pulse’ 37 4.2 Stratification 38 4.3 Identifying Points on a Graph 39 4.4 Using the ‘Crosshairs’ Option 45 4.5 Scatterplots with Panels 46 4.6 Scatterplots with Marginal Graphs 48 4.7 Creating an Array of Scatterplots 50 5 Three Dimensional Plots 52 5.1 3D Scatterplots 52 5.2 3D Surface Plots 55 5.3 Contour Plots 58 6 Part One: Case Studies – Introduction and Graphical Techniques 62 6.1 Cork 62 6.2 Copper 68 6.3 Bread 73 6.4 Humidity 76 Part Two Hypothesis Testing. Comparison of Treatments 79 7 Random Numbers and Numbers Following a Pattern 81 7.1 Introducing Values Following a Pattern 81 7.2 Sampling Random Data from a Column 83 7.3 Random Number Generation 83 7.4 Example: Solving a Problem Using Random Numbers 85 8 Computing Probabilities 87 8.1 Probability Distributions 87 8.2 Option ‘Probability Density’ or ‘Probability’ 88 8.3 Option ‘Cumulative Probability’ 89 8.4 Option ‘Inverse Cumulative Probability’ 89 8.5 Viewing the Shape of the Distributions 92 8.6 Equivalence between Sigmas of the Process and Defects per Million Parts Using ‘Cumulative Probability’ 92 9 Hypothesis Testing for Means and Proportions. Normality Test 95 9.1 Hypothesis Testing for One Mean 95 9.2 Hypothesis Testing and Confidence Interval for a Proportion 99 9.3 Normality Test 100 10 Comparison of Two Means, Two Variances or Two Proportions 103 10.1 Comparison of Two Means 103 10.2 Comparison of Two Variances 107 10.3 Comparison of Two Proportions 109 11 Comparison of More than Two Means: Analysis of Variance 110 11.1 ANOVA (Analysis of Variance) 110 11.2 ANOVA with a Single Factor 110 11.3 ANOVA with Two Factors 114 11.4 Test for Homogeneity of Variances 119 12 Part Two: Case Studies – Hypothesis Testing. Comparison of Treatments 120 12.1 Welding 120 12.2 Rivets 124 12.3 Almonds 126 12.4 Arrow 127 12.5 U Piece 131 12.6 Pores 133 Part Three Measurement Systems Studies and Capability Studies 137 13 Measurement System Study 139 13.1 Crossed Designs and Nested Designs 139 13.2 File ‘RR_CROSSED’ 140 13.3 Graphical Analysis 140 13.4 R&R Study for the Data in File ‘RR_CROSSED’ 141 13.5 File ‘RR_NESTED’ 147 13.6 Gage R&R Study for the Data in File ‘RR_NESTED’ 147 13.7 File ‘GAGELIN’ 148 13.8 Calibration and Linearity Study of the Measurement System 148 14 Capability Studies 151 14.1 Capability Analysis: Available Options 151 14.2 File ‘VITA_C’ 152 14.3 Capability Analysis (Normal Distribution) 152 14.4 Interpreting the Obtained Information 152 14.5 Customizing the Study 154 14.6 ‘Within’ Variability and ‘Overall’ Variability 155 14.7 Capability Study when the Sample Size is Equal to One 158 14.8 A More Detailed Data Analysis (Capability Sixpack) 161 15 Capability Studies for Attributes 163 15.1 File ‘BANK’ 163 15.2 Capability Study for Variables that Follow a Binomial Distribution 163 15.3 File ‘OVEN_PAINTED’ 166 15.4 Capability Study for Variables that Follow a Poisson Distribution 166 16 Part Three: Case Studies – R&R Studies and Capability Studies 168 16.1 Diameter_measure 168 16.2 Diameter_capability_1 173 16.3 Diameter_capability_2 174 16.4 Web_visits 176 Part Four Multi-Vari Charts and Statistical Process Control 181 17 Multi-Vari Charts 183 17.1 File ‘MUFFIN’ 183 17.2 Multi-Vari Chart with Three Sources of Variation 184 17.3 Multi-Vari Chart with Four Sources of Variation 186 18 Control Charts I: Individual Observations 188 18.1 File ‘CHLORINE’ 188 18.2 Graph of Individual Observations 188 18.3 Customizing the Graph 191 18.4 I Chart Options 192 18.5 Graphs of Moving Ranges 196 18.6 Graph of Individual Observations – Moving Ranges 197 19 Control Charts II: Means and Ranges 198 19.1 File ‘VITA_C’ 198 19.2 Means Chart 199 19.3 Graphs of Ranges and Standard Deviations 200 19.4 Graphs of Means-Ranges 201 19.5 Some Ideas on How to Use Minitab as a Simulator of Processes for Didactic Reasons 201 20 Control Charts for Attributes 204 20.1 File ‘MOTORS’ 204 20.2 Plotting the Proportion of Defective Units (P) 204 20.3 File ‘CATHETER’ 205 20.4 Plotting the Number of Defective Units (NP) 206 20.5 Plotting the Number of Defects per Constant Unit of Measurement (C) 208 20.6 File ‘FABRIC’ 210 20.7 Plotting the Number of Defects per Variable Unit of Measurement (U) 210 21 Part Four: Case Studies – Multi-Vari Charts and Statistical Process Control 212 21.1 Bottles 212 21.2 Mattresses (1st Part) 217 21.3 Mattresses (2nd Part) 221 21.4 Plastic (1st Part) 223 21.5 Plastic (2nd Part) 224 Part Five Regression and Multivariate Analysis 231 22 Correlation and Simple Regression 235 22.1 Correlation Coefficient 235 22.2 Simple Regression 238 22.3 Simple Regression with ‘Fitted Line Plot’ 239 22.4 Simple Regression with ‘Regression’ 244 23 Multiple Regression 247 23.1 File ‘CARS2’ 247 23.2 Exploratory Analysis 247 23.3 Multiple Regression 249 23.4 Option Buttons 250 23.5 Selection of the Best Equation: Best Subsets 252 23.6 Selection of the Best Equation: Stepwise 254 24 Multivariate Analysis 256 24.1 File ‘LATIN_AMERICA’ 256 24.2 Principal Components 257 24.3 Cluster Analysis for Observations 263 24.4 Cluster Analysis for Variables 266 24.5 Discriminant Analysis 267 25 Part Five: Case Studies – Regression and Multivariate Analysis 272 25.1 Tree 272 25.2 Power Plant 278 25.3 Wear 285 25.4 TV Failure 290 Part Six Experimental Design and Reliability 293 26 Factorial Designs: Creation 295 26.1 Creation of the Design Matrix 295 26.2 Design Matrix with Data Already in the Worksheet 301 27 Factorial Designs: Analysis 303 27.1 Calculating the Effects and Determining the Significant Ones 303 27.2 Interpretation of Results 308 27.3 A Recap with a Fractional Factorial Design 310 28 Response Surface Methodology 313 28.1 Matrix Design Creation and Data Collection 313 28.2 Analysis of the Results 317 28.3 Contour Plots and Response Surface Plots 322 29 Reliability 325 29.1 File 325 29.2 Nonparametric Analysis 326 29.3 Identification of the Best Model for the Data 329 29.4 Parametric Analysis 330 29.5 General Graphical Display of Reliability Data 333 30 Part Six: Case Studies – Design of Experiments and Reliability 335 30.1 Cardigan 335 30.2 Steering wheel – 1 340 30.3 Steering Wheel – 2 343 30.4 Paper Helicopters 345 30.5 Microorganisms 349 30.6 Jam 359 30.7 Photocopies 365 Appendices 371 A1 Appendix 1: Answers to Questions that Arise at the Beginning 373 A2 Appendix 2: Managing Data 377 A2.1 Copy Columns with Restrictions (File: ‘PULSE’) 377 A2.2 Selection of Data when Plotting a Graph 381 A2.3 Stacking and Unstacking of Columns (File ‘BREAD’) 382 A2.4 Coding and Sorting Data 386 A3 Appendix 3: Customization of Minitab 390 A3.1 Configuration Options 390 A3.2 Use of Toolbars 392 A3.3 Add Elements to an Existing Toolbar 392 A3.4 Create Custom Toolbars 393 Index 397

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Book Synopsis* The first book to chart the development and applications of this growing subject. * Provides a comprehensive introduction to imprecise probabilities, including theory and applications reflecting the current state of the art. * Each chapter is written by leading experts in their field.Table of ContentsIntroduction xiii A brief outline of this book xv Guide to the reader xvii Contributors xxi Acknowledgements xxvii 1 Desirability 1 Erik Quaeghebeur 1.1 Introduction 1 1.2 Reasoning about and with sets of desirable gambles 2 1.2.1 Rationality criteria 2 1.2.2 Assessments avoiding partial or sure loss 3 1.2.3 Coherent sets of desirable gambles 4 1.2.4 Natural extension 5 1.2.5 Desirability relative to subspaces with arbitrary vector orderings 5 1.3 Deriving and combining sets of desirable gambles 6 1.3.1 Gamble space transformations 6 1.3.2 Derived coherent sets of desirable gambles 7 1.3.3 Conditional sets of desirable gambles 8 1.3.4 Marginal sets of desirable gambles 8 1.3.5 Combining sets of desirable gambles 9 1.4 Partial preference orders 11 1.4.1 Strict preference 12 1.4.2 Nonstrict preference 12 1.4.3 Nonstrict preferences implied by strict ones 14 1.4.4 Strict preferences implied by nonstrict ones 15 1.5 Maximally committal sets of strictly desirable gambles 16 1.6 Relationships with other, nonequivalent models 18 1.6.1 Linear previsions 18 1.6.2 Credal sets 19 1.6.3 To lower and upper previsions 21 1.6.4 Simplified variants of desirability 22 1.6.5 From lower previsions 23 1.6.6 Conditional lower previsions 25 1.7 Further reading 26 Acknowledgements 27 2 Lower previsions 28 Enrique Miranda and Gert de Cooman 2.1 Introduction 28 2.2 Coherent lower previsions 29 2.2.1 Avoiding sure loss and coherence 31 2.2.2 Linear previsions 35 2.2.3 Sets of desirable gambles 39 2.2.4 Natural extension 40 2.3 Conditional lower previsions 42 2.3.1 Coherence of a finite number of conditional lower previsions 45 2.3.2 Natural extension of conditional lower previsions 47 2.3.3 Coherence of an unconditional and a conditional lower prevision 49 2.3.4 Updating with the regular extension 52 2.4 Further reading 53 2.4.1 The work of Williams 53 2.4.2 The work of Kuznetsov 54 2.4.3 The work of Weichselberger 54 Acknowledgements 55 3 Structural judgements 56 Enrique Miranda and Gert de Cooman 3.1 Introduction 56 3.2 Irrelevance and independence 57 3.2.1 Epistemic irrelevance 59 3.2.2 Epistemic independence 61 3.2.3 Envelopes of independent precise models 63 3.2.4 Strong independence 65 3.2.5 The formalist approach to independence 66 3.3 Invariance 67 3.3.1 Weak invariance 68 3.3.2 Strong invariance 69 3.4 Exchangeability 71 3.4.1 Representation theorem for finite sequences 72 3.4.2 Exchangeable natural extension 74 3.4.3 Exchangeable sequences 75 3.5 Further reading 77 3.5.1 Independence 77 3.5.2 Invariance 77 3.5.3 Exchangeability 77 Acknowledgements 78 4 Special cases 79 Sébastien Destercke and Didier Dubois 4.1 Introduction 79 4.2 Capacities and n-monotonicity 80 4.3 2-monotone capacities 81 4.4 Probability intervals on singletons 82 4.5 ∞-monotone capacities 82 4.5.1 Constructing ∞-monotone capacities 83 4.5.2 Simple support functions 83 4.5.3 Further elements 84 4.6 Possibility distributions, p-boxes, clouds and related models 84 4.6.1 Possibility distributions 84 4.6.2 Fuzzy intervals 86 4.6.3 Clouds 87 4.6.4 p-boxes 88 4.7 Neighbourhood models 89 4.7.1 Pari-mutuel 89 4.7.2 Odds-ratio 90 4.7.3 Linear-vacuous 90 4.7.4 Relations between neighbourhood models 91 4.8 Summary 91 5 Other uncertainty theories based on capacities 93 Sébastien Destercke and Didier Dubois 5.1 Imprecise probability = modal logic + probability 95 5.1.1 Boolean possibility theory and modal logic 95 5.1.2 A unifying framework for capacity based uncertainty theories 97 5.2 From imprecise probabilities to belief functions and possibility theory 97 5.2.1 Random disjunctive sets 98 5.2.2 Numerical possibility theory 100 5.2.3 Overall picture 102 5.3 Discrepancies between uncertainty theories 102 5.3.1 Objectivist vs. Subjectivist standpoints 103 5.3.2 Discrepancies in conditioning 104 5.3.3 Discrepancies in notions of independence 107 5.3.4 Discrepancies in fusion operations 109 5.4 Further reading 112 6 Game-theoretic probability 114 Vladimir Vovk and Glenn Shafer 6.1 Introduction 114 6.2 A law of large numbers 115 6.3 A general forecasting protocol 118 6.4 The axiom of continuity 122 6.5 Doob’s argument 124 6.6 Limit theorems of probability 127 6.7 Lévy’s zero-one law 128 6.8 The axiom of continuity revisited 129 6.9 Further reading 132 Acknowledgements 134 7 Statistical inference 135 Thomas Augustin, Gero Walter, and Frank P. A. Coolen 7.1 Background and introduction 136 7.1.1 What is statistical inference? 136 7.1.2 (Parametric) statistical models and i.i.d. samples 137 7.1.3 Basic tasks and procedures of statistical inference 139 7.1.4 Some methodological distinctions 140 7.1.5 Examples: Multinomial and normal distribution 141 7.2 Imprecision in statistics, some general sources and motives 143 7.2.1 Model and data imprecision; sensitivity analysis and ontological views on imprecision 143 7.2.2 The robustness shock, sensitivity analysis 144 7.2.3 Imprecision as a modelling tool to express the quality of partial knowledge 145 7.2.4 The law of decreasing credibility 145 7.2.5 Imprecise sampling models: Typical models and motives 146 7.3 Some basic concepts of statistical models relying on imprecise probabilities 147 7.3.1 Most common classes of models and notation 147 7.3.2 Imprecise parametric statistical models and corresponding i.i.d. samples 148 7.4 Generalized Bayesian inference 149 7.4.1 Some selected results from traditional Bayesian statistics 150 7.4.2 Sets of precise prior distributions, robust Bayesian inference and the generalized Bayes rule 154 7.4.3 A closer exemplary look at a popular class of models: The IDM and other models based on sets of conjugate priors in exponential families 155 7.4.4 Some further comments and a brief look at other models for generalized Bayesian inference 164 7.5 Frequentist statistics with imprecise probabilities 165 7.5.1 The nonrobustness of classical frequentist methods 166 7.5.2 (Frequentist) hypothesis testing under imprecise probability: Huber-Strassen theory and extensions 169 7.5.3 Towards a frequentist estimation theory under imprecise probabilities – some basic criteria and first results 171 7.5.4 A brief outlook on frequentist methods 174 7.6 Nonparametric predictive inference 175 7.6.1 Overview 175 7.6.2 Applications and challenges 177 7.7 A brief sketch of some further approaches and aspects 178 7.8 Data imprecision, partial identification 179 7.8.1 Data imprecision 180 7.8.2 Cautious data completion 181 7.8.3 Partial identification and observationally equivalent models 183 7.8.4 A brief outlook on some further aspects 186 7.9 Some general further reading 187 7.10 Some general challenges 188 Acknowledgements 189 8 Decision making 190 Nathan Huntley, Robert Hable, and Matthias C. M. Troffaes 8.1 Non-sequential decision problems 190 8.1.1 Choosing from a set of gambles 191 8.1.2 Choice functions for coherent lower previsions 192 8.2 Sequential decision problems 197 8.2.1 Static sequential solutions: Normal form 198 8.2.2 Dynamic sequential solutions: Extensive form 199 8.3 Examples and applications 202 8.3.1 Ellsberg’s paradox 202 8.3.2 Robust Bayesian statistics 205 9 Probabilistic graphical models 207 Alessandro Antonucci, Cassio P. de Campos, and Marco Zaffalon 9.1 Introduction 207 9.2 Credal sets 208 9.2.1 Definition and relation with lower previsions 208 9.2.2 Marginalization and conditioning 210 9.2.3 Composition 212 9.3 Independence 213 9.4 Credal networks 215 9.4.1 Nonseparately specified credal networks 217 9.5 Computing with credal networks 220 9.5.1 Credal networks updating 220 9.5.2 Modelling and updating with missing data 221 9.5.3 Algorithms for credal networks updating 223 9.5.4 Inference on credal networks as a multilinear programming task 224 9.6 Further reading 226 Acknowledgements 229 10 Classification 230 Giorgio Corani, Joaquín Abellán, Andrés Masegosa, Serafin Moral, and Marco Zaffalon 10.1 Introduction 230 10.2 Naive Bayes 231 10.2.1 Derivation of naive Bayes 232 10.3 Naive credal classifier (NCC) 233 10.3.1 Checking Credal-dominance 233 10.3.2 Particular behaviours of NCC 235 10.3.3 NCC2: Conservative treatment of missing data 236 10.4 Extensions and developments of the naive credal classifier 237 10.4.1 Lazy naive credal classifier 237 10.4.2 Credal model averaging 238 10.4.3 Profile-likelihood classifiers 239 10.4.4 Tree-augmented networks (TAN) 240 10.5 Tree-based credal classifiers 242 10.5.1 Uncertainty measures on credal sets: The maximum entropy function 242 10.5.2 Obtaining conditional probability intervals with the imprecise Dirichlet model 245 10.5.3 Classification procedure 246 10.6 Metrics, experiments and software 249 10.7 Scoring the conditional probability of the class 251 10.7.1 Software 251 10.7.2 Experiments 251 10.7.3 Experiments comparing conditional probabilities of the class 253 Acknowledgements 257 11 Stochastic processes 258 Filip Hermans and Damjan Škulj 11.1 The classical characterization of stochastic processes 258 11.1.1 Basic definitions 258 11.1.2 Precise Markov chains 259 11.2 Event-driven random processes 261 11.3 Imprecise Markov chains 263 11.3.1 From precise to imprecise Markov chains 264 11.3.2 Imprecise Markov models under epistemic irrelevance 265 11.3.3 Imprecise Markov models under strong independence 268 11.3.4 When does the interpretation of independence (not) matter? 270 11.4 Limit behaviour of imprecise Markov chains 272 11.4.1 Metric properties of imprecise probability models 272 11.4.2 The Perron-Frobenius theorem 273 11.4.3 Invariant distributions 274 11.4.4 Coefficients of ergodicity 275 11.4.5 Coefficients of ergodicity for imprecise Markov chains 275 11.5 Further reading 277 12 Financial risk measurement 279 Paolo Vicig 12.1 Introduction 279 12.2 Imprecise previsions and betting 280 12.3 Imprecise previsions and risk measurement 282 12.3.1 Risk measures as imprecise previsions 283 12.3.2 Coherent risk measures 284 12.3.3 Convex risk measures (and previsions) 285 12.4 Further reading 289 13 Engineering 291 Michael Oberguggenberger 13.1 Introduction 291 13.2 Probabilistic dimensioning in a simple example 295 13.3 Random set modelling of the output variability 298 13.4 Sensitivity analysis 300 13.5 Hybrid models 301 13.6 Reliability analysis and decision making in engineering 302 13.7 Further reading 303 14 Reliability and risk 305 Frank P. A. Coolen and Lev V. Utkin 14.1 Introduction 305 14.2 Stress-strength reliability 306 14.3 Statistical inference in reliability and risk 310 14.4 Nonparametric predictive inference in reliability and risk 312 14.5 Discussion and research challenges 317 15 Elicitation 318 Michael Smithson 15.1 Methods and issues 318 15.2 Evaluating imprecise probability judgements 322 15.3 Factors affecting elicitation 324 15.4 Matching methods with purposes 327 15.5 Further reading 328 16 Computation 329 Matthias C. M. Troffaes and Robert Hable 16.1 Introduction 329 16.2 Natural extension 329 16.2.1 Conditional lower previsions with arbitrary domains 330 16.2.2 The Walley–Pelessoni–Vicig algorithm 331 16.2.3 Choquet integration 332 16.2.4 Möbius inverse 334 16.2.5 Linear-vacuous mixture 334 16.3 Decision making 335 16.3.1 Γ-maximin, Γ-maximax and Hurwicz 335 16.3.2 Maximality 335 16.3.3 E-admissibility 336 16.3.4 Interval dominance 337 References 338 Author index 375 Subject index 385

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Book SynopsisThis is an introductory statistics textbook for business and management students which uses the innovative approach of a statistical thinkinga .Table of ContentsIntroduction. Data Display and Summary. The Normal Model for Chance Variation. Process Monitoring, Control Charts and Statistical. Principles of Statistical Inference. Simple Linear Regression. Frequency Data Analysis. Multiple Linear Regression. Tme Series. Simple Statistical Models in Finance. Data production: Surveys, Experiments, Archives. Statistical Analysis in Context: Management Perspective.

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Book SynopsisExpanded and revised to include new computing exercises using actual data along with tips, solutions and a set of updated questions. Computer use is encouraged to facilitate analysis of data sets too large to be done by hand; to assist in the drawing of diagrams, histograms and scatter plots; to simulate probability models in order to illustrate probability and statistical theory. Explains how to tackle computing exercises using the statistical package MINITAB.Table of ContentsIntroduction List of projects Notation 1. Populations and variates 2. Measures of the centre of a set of observations 3. Samples and populations 4. The measurement of variability 5. Looking at data 6. Probability 7. Probabilities of compound events 8. Discrete random variables 9. Expectation of random variables 10. Joint distributions 11. Estimation 12. Collecting data 13. Significance testing 14. Continuous random variables 15. The normal distribution 16. Sampling distributions of means and related quantities 17. Significance tests using the normal distribution 18. Estimation of intervals and parameters 19. Hypothesis tests using the y2 distribution 20. The Poisson distribution 21. Correlation 22. The analysis of variance 23. Simple linear regression 24. Multiple regression Appendix I. The binomial series expansion Appendix II. The exponential function Appendix III. Derivatives and integrals of the exponential function Appendix IV. Integrals related to the normal distribution Appendix V. The limit of (1 + x/n)n as n OC OC Appendix VI. A derivation of the Poisson distribution Appendix VII. Partial differentiation Bibliography Answers Hints on computing exercises Tables Index

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Book SynopsisStatistics Analysis of Geographical Data: An Introduction provides a comprehensive and accessible introduction to the theory and practice of statistical analysis in geography.Table of ContentsPreface xi 1 Dealing with data 1 1.1 The role of statistics in geography 1 1.2 About this book 3 1.3 Data and measurement error 3 2 Collecting and summarizing data 13 2.1 Sampling methods 13 2.2 Graphicalsummaries 17 2.3 Summarizing data numerically 24 3 Probability and sampling distributions 37 3.1 Probability 37 3.2 Probability and the normal distribution: z]scores 39 3.3 Sampling distributions and the central limit theorem 43 4 Estimating parameters with confidence intervals 49 4.1 Confidence intervals on the mean of a normal distribution: the basics 49 4.2 Confidence intervals in practice: the t]distribution 50 4.3 Sample size 53 4.4 Confidence intervals for a proportion 53 5 Comparing datasets 55 5.1 Hypothesis testing with one sample: general principles 55 5.2 Comparing means from small samples: one]sample t]test 61 5.3 Comparing proportions for one sample 63 5.4 Comparing two samples 64 5.5 Non]parametric hypothesis testing 75 6 Comparing distributions: the Chi]squared test 81 6.1 Chi]squared test with one sample 81 6.2 Chi]squared test for two samples 84 7 Analysis of variance 89 7.1 Oneway analysis of variance 90 7.2 Assumptions and diagnostics 99 7.3 Multiple comparison tests after analysis of variance 101 7.4 Non]parametric methods in the analysis of variance 105 7.5 Summary and further applications 106 8 Correlation 109 8.1 Correlation analysis 109 8.2 Pearson’s product]moment correlation coefficient 110 8.3 Significance tests of correlation coefficient 112 8.4 Spearman’s rank correlation coefficient 114 8.5 Correlation and causality 116 9 Linear regression 121 9.1 Least]squares linear regression 121 9.2 Scatter plots 122 9.3 Choosing the line of best fit: the ‘least]squares’procedure 124 9.4 Analysis of residuals 128 9.5 Assumptions and caveats with regression 130 9.6 Is the regression significant? 131 9.7 Coefficient of determination 135 9.8 Confidence intervals and hypothesis tests concerning regression parameters 137 9.9 Reduced major axis regression 140 10 Spatial statistics 145 10.1 Spatial data 145 10.2 Summarizing spatial data 157 10.3 Identifying clusters 159 10.4 Interpolation and plotting contour maps 162 10.5 Spatial relationships 163 11 Time series analysis 173 11.1 Time series in geographical research 173 11.2 Analysing time series 174 Appendix A: Introduction to the R package 193 Appendix B: Statistical tables 205 References 241 Index 243

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Book SynopsisStatistics Analysis of Geographical Data: An Introduction provides a comprehensive and accessible introduction to the theory and practice of statistical analysis in geography.Table of ContentsPreface xi 1 Dealing with data 1 1.1 The role of statistics in geography 1 1.1.1 Why do geographers need to use statistics? 1 1.2 About this book 3 1.3 Data and measurement error 3 1.3.1 Types of geographical data: nominal, ordinal, interval, and ratio 3 1.3.2 Spatial data types 5 1.3.3 Measurement error, accuracy and precision 6 1.3.4 Reporting data and uncertainties 7 1.3.5 Significant figures 9 1.3.6 Scientific notation (standard form) 10 1.3.7 Calculations in scientific notation 11 Exercises 12 2 Collecting and summarizing data 13 2.1 Sampling methods 13 2.1.1 Research design 13 2.1.2 Random sampling 15 2.1.3 Systematic sampling 16 2.1.4 Stratified sampling 17 2.2 Graphical summaries 17 2.2.1 Frequency distributions and histograms 17 2.2.2 Time series plots 21 2.2.3 Scatter plots 22 2.3 Summarizing data numerically 24 2.3.1 Measures of central tendency: mean, median and mode 24 2.3.2 Mean 24 2.3.3 Median 25 2.3.4 Mode 25 2.3.5 Measures of dispersion 28 2.3.6 Variance 29 2.3.7 Standard deviation 30 2.3.8 Coefficient of variation 30 2.3.9 Skewness and kurtosis 33 Exercises 33 3 Probability and sampling distributions 37 3.1 Probability 37 3.1.1 Probability, statistics and random variables 37 3.1.2 The properties of the normal distribution 38 3.2 Probability and the normal distribution: z‐scores 39 3.3 Sampling distributions and the central limit theorem 43 Exercises 47 4 Estimating parameters with confidence intervals 49 4.1 Confidence intervals on the mean of a normal distribution: the basics 49 4.2 Confidence intervals in practice: the t‐distribution 50 4.3 Sample size 53 4.4 Confidence intervals for a proportion 53 Exercises 54 5 Comparing datasets 55 5.1 Hypothesis testing with one sample: general principles 55 5.1.1 Comparing means: one‐sample z‐test 56 5.1.2 p‐values 60 5.1.3 General procedure for hypothesis testing 61 5.2 Comparing means from small samples: one‐sample t‐test 61 5.3 Comparing proportions for one sample 63 5.4 Comparing two samples 64 5.4.1 Independent samples 64 5.4.2 Comparing means: t‐test with unknown population variances assumed equal 64 5.4.3 Comparing means: t‐test with unknown population variances assumed unequal 68 5.4.4 t‐test for use with paired samples (paired t‐test) 71 5.4.5 Comparing variances: F‐test 74 5.5 Non‐parametric hypothesis testing 75 5.5.1 Parametric and non‐parametric tests 75 5.5.2 Mann–whitney U‐test 75 Exercises 79 6 Comparing distributions: the Chi‐squared test 81 6.1 Chi‐squared test with one sample 81 6.2 Chi‐squared test for two samples 84 Exercises 87 7 Analysis of variance 89 7.1 One‐way analysis of variance 90 7.2 Assumptions and diagnostics 99 7.3 Multiple comparison tests after analysis of variance 101 7.4 Non‐parametric methods in the analysis of variance 105 7.5 Summary and further applications 106 Exercises 107 8 Correlation 109 8.1 Correlation analysis 109 8.2 Pearson’s product‐moment correlation coefficient 110 8.3 Significance tests of correlation coefficient 112 8.4 Spearman’s rank correlation coefficient 114 8.5 Correlation and causality 116 Exercises 117 9 Linear regression 121 9.1 Least‐squares linear regression 121 9.2 Scatter plots 122 9.3 Choosing the line of best fit: the ‘least‐squares’ procedure 124 9.4 Analysis of residuals 128 9.5 Assumptions and caveats with regression 130 9.6 Is the regression significant? 131 9.7 Coefficient of determination 135 9.8 Confidence intervals and hypothesis tests concerning regression parameters 137 9.8.1 Standard error of the regression parameters 137 9.8.2 Tests on the regression parameters 138 9.8.3 Confidence intervals on the regression parameters 139 9.8.4 Confidence interval about the regression line 140 9.9 Reduced major axis regression 140 9.10 Summary 142 Exercises 142 10 Spatial statistics 145 10.1 Spatial data 145 10.1.1 Types of spatial data 145 10.1.2 Spatial data structures 146 10.1.3 Map projections 149 10.2 Summarizing spatial data 157 10.2.1 Mean centre 157 10.2.2 Weighted mean centre 157 10.2.3 Density estimation 158 10.3 Identifying clusters 159 10.3.1 Quadrat test 159 10.3.2 Nearest neighbour statistics 162 10.4 Interpolation and plotting contour maps 162 10.5 Spatial relationships 163 10.5.1 Spatial autocorrelation 163 10.5.2 Join counts 164 Exercises 171 11 Time series analysis 173 11.1 Time series in geographical research 173 11.2 Analysing time series 174 11.2.1 Describing time series: definitions 174 11.2.2 Plotting time series 175 11.2.3 Decomposing time series: trends, seasonality and irregular fluctuations 179 11.2.4 Analysing trends 180 11.2.5 Removing trends (‘detrending’ data) 186 11.2.6 Quantifying seasonal variation 187 11.2.7 Autocorrelation 189 11.3 Summary 190 Exercises 190 Appendix A: Introduction to the R package 193 Appendix B: Statistical tables 205 References 241 Index 243

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Book SynopsisSurvival analysis concerns sequential occurrences of events governed by probabilistic laws. Recent decades have witnessed many applications of survival analysis in various disciplines. This book introduces both classic survival models and theories along with newly developed techniques. Readers will learn how to perform analysis of survival data by following numerous empirical illustrations in SAS. Survival Analysis: Models and Applications: Presents basic techniques before leading onto some of the most advanced topics in survival analysis. Assumes only a minimal knowledge of SAS whilst enabling more experienced users to learn new techniques of data input and manipulation. Provides numerous examples of SAS code to illustrate each of the methods, along with step-by-step instructions to perform each technique. Highlights the strengths and limitations of each technique covered. Covering a wide scope of survival techniqTable of ContentsPreface xi 1 Introduction 1 1.1 What is survival analysis and how is it applied? 1 1.2 The history of survival analysis and its progress 2 1.3 General features of survival data structure 3 1.4 Censoring 4 1.4.1 Mechanisms of right censoring 5 1.4.2 Left censoring, interval censoring, and left truncation 6 1.5 Time scale and the origin of time 7 1.5.1 Observational studies 8 1.5.2 Biomedical studies 9 1.5.3 Health care utilization 9 1.6 Basic lifetime functions 10 1.6.1 Continuous lifetime functions 10 1.6.2 Discrete lifetime functions 12 1.6.3 Basic likelihood functions for right, left, and interval censoring 14 1.7 Organization of the book and data used for illustrations 16 1.8 Criteria for performing survival analysis 17 2 Descriptive approaches of survival analysis 20 2.1 The Kaplan–Meier (product-limit) and Nelson–Aalen estimators 21 2.1.1 Kaplan–Meier estimating procedures with or without censoring 21 2.1.2 Formulation of the Kaplan–Meier and Nelson–Aalen estimators 24 2.1.3 Variance and standard error of the survival function 27 2.1.4 Confi dence intervals and confi dence bands of the survival function 29 2.2 Life table methods 36 2.2.1 Life table indicators 37 2.2.2 Multistate life tables 40 2.2.3 Illustration: Life table estimates for older Americans 44 2.3 Group comparison of survival functions 46 2.3.1 Logrank test for survival curves of two groups 48 2.3.2 The Wilcoxon rank sum test on survival curves of two groups 51 2.3.3 Comparison of survival functions for more than two groups 55 2.3.4 Illustration: Comparison of survival curves between married and unmarried persons 58 2.4 Summary 61 3 Some popular survival distribution functions 63 3.1 Exponential survival distribution 63 3.2 The Weibull distribution and extreme value theory 68 3.2.1 Basic specifi cations of the Weibull distribution 68 3.2.2 The extreme value distribution 72 3.3 Gamma distribution 73 3.4 Lognormal distribution 77 3.5 Log-logistic distribution 80 3.6 Gompertz distribution and Gompertz-type hazard models 83 3.7 Hypergeometric distribution 89 3.8 Other distributions 91 3.9 Summary 92 4 Parametric regression models of survival analysis 93 4.1 General specifi cations and inferences of parametric regression models 94 4.1.1 Specifi cations of parametric regression models on the hazard function 94 4.1.2 Specifi cations of accelerated failure time regression models 96 4.1.3 Inferences of parametric regression models and likelihood functions 99 4.1.4 Procedures of maximization and hypothesis testing on ML estimates 101 4.2 Exponential regression models 103 4.2.1 Exponential regression model on the hazard function 103 4.2.2 Exponential accelerated failure time regression model 106 4.2.3 Illustration: Exponential regression model on marital status and survival among older Americans 108 4.3 Weibull regression models 113 4.3.1 Weibull hazard regression model 114 4.3.2 Weibull accelerated failure time regression model 115 4.3.3 Conversion of Weibull proportional hazard and AFT parameters 117 4.3.4 Illustration: A Weibull regression model on marital status and survival among older Americans 121 4.4 Log-logistic regression models 127 4.4.1 Specifi cations of the log-logistic AFT regression model 127 4.4.2 Retransformation of AFT parameters to untransformed log-logistic parameters 129 4.4.3 Illustration: The log-logistic regression model on marital status and survival among the oldest old Americans 131 4.5 Other parametric regression models 135 4.5.1 The lognormal regression model 136 4.5.2 Gamma distributed regression models 137 4.6 Parametric regression models with interval censoring 138 4.6.1 Inference of parametric regression models with interval censoring 138 4.6.2 Illustration: A parametric survival model with independent interval censoring 139 4.7 Summary 142 5 The Cox proportional hazard regression model and advances 144 5.1 The Cox semi-parametric hazard model 145 5.1.1 Basic specifi cations of the Cox proportional hazard model 145 5.1.2 Partial likelihood 147 5.1.3 Procedures of maximization and hypothesis testing on partial likelihood 150 5.2 Estimation of the Cox hazard model with tied survival times 154 5.2.1 The discrete-time logistic regression model 154 5.2.2 Approximate methods handling ties in the proportional hazard model 155 5.2.3 Illustration on tied survival data: Smoking cigarettes and the mortality of older Americans 157 5.3 Estimation of survival functions from the Cox proportional hazard model 161 5.3.1 The Kalbfl eisch–Prentice method 162 5.3.2 The Breslow method 164 5.3.3 Illustration: Comparing survival curves for smokers and nonsmokers among older Americans 165 5.4 The hazard rate model with time-dependent covariates 169 5.4.1 Categorization of time-dependent covariates 169 5.4.2 The hazard rate model with time-dependent covariates 171 5.4.3 Illustration: A hazard model on time-dependent marital status and the mortality of older Americans 173 5.5 Stratified proportional hazard rate model 176 5.5.1 Specifications of the stratifi ed hazard rate model 177 5.5.2 Illustration: Smoking cigarettes and the mortality of older Americans with stratifi cation on three age groups 178 5.6 Left truncation, left censoring, and interval censoring 183 5.6.1 The Cox model with left truncation, left censoring, and interval censoring 184 5.6.2 Illustration: Analyzing left truncated survival data on smoking cigarettes and the mortality of unmarried older Americans 185 5.7 Qualitative factors and local tests 191 5.7.1 Qualitative factors and scaling approaches 191 5.7.2 Local tests 193 5.7.3 Illustration of local tests: Educational attainment and the mortality of older Americans 195 5.8 Summary 199 6 Counting processes and diagnostics of the Cox model 201 6.1 Counting processes and the martingale theory 202 6.1.1 Counting processes 202 6.1.2 The martingale theory 204 6.1.3 Stochastic integrated processes as martingale transforms 207 6.1.4 Martingale central limit theorems 208 6.1.5 Counting process formulation for the Cox model 211 6.2 Residuals of the Cox proportional hazard model 213 6.2.1 Cox–Snell residuals 213 6.2.2 Schoenfeld residuals 214 6.2.3 Martingale residuals 216 6.2.4 Score residuals 218 6.2.5 Deviance residuals 219 6.2.6 Illustration: Residual analysis on the Cox model of smoking cigarettes and the mortality of older Americans 220 6.3 Assessment of proportional hazards assumption 222 6.3.1 Checking proportionality by adding a time-dependent variable 225 6.3.2 The Andersen plots for checking proportionality 227 6.3.3 Checking proportionality with scaled Schoenfeld residuals 228 6.3.4 The Arjas plots 229 6.3.5 Checking proportionality with cumulative sums of martingale-based residuals 230 6.3.6 Illustration: Checking the proportionality assumption in the Cox model for the effect of age on the mortality of older Americans 232 6.4 Checking the functional form of a covariate 236 6.4.1 Checking model fit statistics for different link functions 236 6.4.2 Checking the functional form with cumulative sums of martingale-based residuals 237 6.4.3 Illustration: Checking the functional form of age in the Cox model on the mortality of older Americans 239 6.5 Identifi cation of infl uential observations in the Cox model 243 6.5.1 The likelihood displacement statistic approximation 244 6.5.2 LMAX statistic for identifi cation of infl uential observations 247 6.5.3 Illustration: Checking influential observations in the Cox model on the mortality of older Americans 248 6.6 Summary 253 7 Competing risks models and repeated events 255 7.1 Competing risks hazard rate models 256 7.1.1 Latent failure times of competing risks and model specifications 256 7.1.2 Competing risks models and the likelihood function without covariates 259 7.1.3 Inference for competing risks models with covariates 261 7.1.4 Competing risks model using the multinomial logit regression 263 7.1.5 Competing risks model with dependent failure types 266 7.1.6 Illustration of competing risks models: Smoking cigarettes and the mortality of older Americans from three causes of death 268 7.2 Repeated events 282 7.2.1 Andersen and Gill model (AG) 283 7.2.2 PWP total time and gap time models (PWP-CP and PWP-GT) 286 7.2.3 The WLW model and extensions 288 7.2.4 Proportional rate and mean functions of repeated events 291 7.2.5 Illustration: The effects of a medical treatment on repeated patient visits 294 7.3 Summary 308 8 Structural hazard rate regression models 310 8.1 Some thoughts about the structural hazard regression models 310 8.2 Structural hazard rate model with retransformation of random errors 313 8.2.1 Model specification 314 8.2.2 The estimation of the full model 317 8.2.3 The estimation of reduced-form equations 318 8.2.4 Decomposition of causal effects on hazard rates and survival functions 323 8.2.5 Illustration: The effects of veteran status on the mortality of older Americans and its pathways 327 8.3 Summary 344 9 Special topics 347 9.1 Informative censoring 347 9.1.1 Selection model 348 9.1.2 Sensitivity analysis models 351 9.1.3 Comments on current models handling informative censoring 352 9.2 Bivariate and multivariate survival functions 352 9.2.1 Inference of the bivariate survival model 353 9.2.2 Estimation of bivariate and multivariate survival models 355 9.2.3 Illustration of marginal models handling multivariate survival data 359 9.3 Frailty models 359 9.3.1 Hazard models with individual frailty 360 9.3.2 The correlated frailty model 364 9.3.3 Illustration of frailty models: The effect of veteran status on the mortality of older Americans revisited 366 9.4 Mortality crossovers and the maximum life span 376 9.4.1 Basic specifications 378 9.4.2 Relative acceleration of the hazard rate and timing of mortality crossing 381 9.4.3 Mathematical conditions for maximum life span and mortality crossover 383 9.5 Survival convergence and the preceding mortality crossover 384 9.5.1 Mathematical proofs for survival convergence and mortality crossovers 385 9.5.2 Simulations 387 9.5.3 Explanations for survival convergence and the preceding mortality crossover 393 9.6 Sample size required and power analysis 398 9.6.1 Calculation of sample size required 399 9.6.2 Illustration: Calculating sample size required 401 9.7 Summary 403 Appendix A The delta method 405 Appendix B Approximation of the variance–covariance matrix for the predicted probabilities from results of the multinomial logit model 407 Appendix C Simulated patient data on treatment of PTSD (n = 255) 410 Appendix D SAS code for derivation of φ estimates in reduced-form equations 417 Appendix E The analytic result of κ*(x) 422 References 424 Index 438

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Book SynopsisA guide to the validation and risk management of quantitative models used for pricing and hedging Whereas the majority of quantitative finance books focus on mathematics and risk management books focus on regulatory aspects, this book addresses the elements missed by this literature--the risks of the models themselves. This book starts from regulatory issues, but translates them into practical suggestions to reduce the likelihood of model losses, basing model risk and validation on market experience and on a wide range of real-world examples, with a high level of detail and precise operative indications.Table of ContentsPreface xi Acknowledgements xix Part I Theory and Practice of Model Risk Management 1 Understanding Model Risk 3 1.1 What Is Model Risk? 3 1.1.1 The Value Approach 4 1.1.2 The Price Approach 6 1.1.3 A Quant Story of the Crisis 9 1.1.4 A Synthetic View on Model Risk 17 1.2 Foundations of Modelling and the Reality of Markets 22 1.2.1 The Classic Framework 22 1.2.2 Uncertainty and Illiquidity 30 1.3 Accounting for Modellers 38 1.3.1 Fair Value 38 1.3.2 The Liquidity Bubble and the Accountancy Boards 40 1.3.3 Level 1, 2, 3 .go? 41 1.3.4 The Hidden Model Assumptions in ‘vanilla’ Derivatives 42 1.4 What Regulators Said After the Crisis 48 1.4.1 Basel New Principles: The Management Process 49 1.4.2 Basel New Principles: The Model, The Market and The Product 51 1.4.3 Basel New Principles: Operative Recommendations 52 1.5 Model Validation and Risk Management: Practical Steps 53 1.5.1 A Scheme for Model Validation 54 1.5.2 Special Points in Model Risk Management 59 1.5.3 The Importance of Understanding Models 60 2 Model Validation and Model Comparison: Case Studies 63 2.1 The Practical Steps of Model Comparison 63 2.2 First Example: The Models 65 2.2.1 The Credit Default Swap 66 2.2.2 Structural First-Passage Models 67 2.2.3 Reduced-Form Intensity Models 69 2.2.4 Structural vs Intensity: Information 72 2.3 First Example: The Payoff. Gap Risk in a Leveraged Note 74 2.4 The Initial Assessment 77 2.4.1 First Test: Calibration to Liquid Relevant Products 77 2.4.2 Second Test: a Minimum Level of Realism 78 2.5 The Core Risk in the Product 81 2.5.1 Structural Models: Negligible Gap Risk 82 2.5.2 Reduced-Form Models: Maximum Gap Risk 82 2.6 A Deeper Analysis: Market Consensus and Historical Evidence 85 2.6.1 What to Add to the Calibration Set 85 2.6.2 Performing Market Intelligence 86 2.6.3 The Lion and the Turtle. Incompleteness in Practice 86 2.6.4 Reality Check: Historical Evidence and Lack of it 87 2.7 Building a Parametric Family of Models 88 2.7.1 Understanding Model Implications 93 2.8 Managing Model Uncertainty: Reserves, Limits, Revisions 95 2.9 Model Comparison: Examples from Equity and Rates 99 2.9.1 Comparing Local and Stochastic Volatility Models in Pricing Equity Compound and Barrier Options 99 2.9.2 Comparing Short Rate and Market Models in Pricing Interest Rate Bermudan Options 105 3 Stress Testing and the Mistakes of the Crisis 111 3.1 Learning Stress Test from the Crisis 111 3.1.1 The Meaning of Stress Testing 112 3.1.2 Portfolio Stress Testing 113 3.1.3 Model Stress Testing 116 3.2 The Credit Market and the ‘Formula that Killed Wall Street’ 118 3.2.1 The CDO Payoff 118 3.2.2 The Copula 119 3.2.3 Applying the Copula to CDOs 122 3.2.4 The Market Quotation Standard 124 3.3 Portfolio Stress Testing and the Correlation Mistake 125 3.3.1 From Flat Correlation Towards a Realistic Approach 126 3.3.2 A Correlation Parameterization to Stress the Market Skew 131 3.4 Payoff Stress and the Liquidity Mistake 136 3.4.1 Detecting the Problem: Losses Concentrated in Time 137 3.4.2 The Problem in Practice 139 3.4.3 A Solution. From Copulas to Real Models 145 3.4.4 Conclusions 150 3.5 Testing with Historical Scenarios and the Concentration Mistake 151 3.5.1 The Mapping Methods for Bespoke Portfolios 152 3.5.2 The Lehman Test 156 3.5.3 Historical Scenarios to Test Mapping Methods 157 3.5.4 The Limits of Mapping and the Management of Model Risk 164 3.5.5 Conclusions 168 4 Preparing for Model Change. Rates and Funding in the New Era 171 4.1 Explaining the Puzzle in the Interest Rates Market and Models 171 4.1.1 The Death of a Market Model: 9 August 2007 173 4.1.2 Finding the New Market Model 174 4.1.3 The Classic Risk-free Market Model 178 4.1.4 A Market Model with Stable Default Risk 182 4.1.5 A Market with Volatile Credit Risk 192 4.1.6 Conclusions 200 4.2 Rethinking the Value of Money: The Effect of Liquidity in Pricing 201 4.2.1 The Setting 204 4.2.2 Standard DVA: Is Something Missing? 206 4.2.3 Standard DVA plus Liquidity: Is Something Duplicated? 207 4.2.4 Solving the Puzzle 207 4.2.5 Risky Funding for the Borrower 208 4.2.6 Risky Funding for the Lender and the Conditions for Market Agreement 209 4.2.7 Positive Recovery Extension 210 4.2.8 Two Ways of Looking at the Problem: Default Risk or Funding Benefit? The Accountant vs the Salesman 211 4.2.9 Which Direction for Future Pricing? 214 Part II Snakes in the Grass: Where Model Risk Hides 5 Hedging 219 5.1 Model Risk and Hedging 219 5.2 Hedging and Model Validation: What is Explained by P&L Explain? 221 5.2.1 The Sceptical View 222 5.2.2 The Fundamentalist View and Black and Scholes 222 5.2.3 Back to Reality 224 5.2.4 Remarks: Recalibration, Hedges and Model Instability 226 5.2.5 Conclusions: from Black and Scholes to Real Hedging 228 5.3 From Theory to Practice: Real Hedging 229 5.3.1 Stochastic Volatility Models: SABR 231 5.3.2 Test Hedging Behaviour Leaving Nothing Out 232 5.3.3 Real Hedging for Local Volatility Models 238 5.3.4 Conclusions: the Reality of Hedging Strategies 241 6 Approximations 243 6.1 Validate and Monitor the Risk of Approximations 243 6.2 The Swaption Approximation in the Libor Market Model 245 6.2.1 The Three Technical Problems in Interest Rate Modelling 245 6.2.2 The Libor Market Model and the Swaption Market 247 6.2.3 Pricing Swaptions 250 6.2.4 Understanding and Deriving the Approximation 253 6.2.5 Testing the Approximation 257 6.3 Approximations for CMS and the Shape of the Term Structure 264 6.3.1 The CMS Payoff 265 6.3.2 Understanding Convexity Adjustments 266 6.3.3 The Market Approximation for Convexity Adjustments 267 6.3.4 A General LMM Approximation 269 6.3.5 Comparing and Testing the Approximations 271 6.4 Testing Approximations Against Exact. Dupire’s Idea 276 6.4.1 Perfect Positive Correlation 278 6.4.2 Perfect Negative Correlation 280 6.5 Exercises on Risk in Computational Methods 283 6.5.1 Approximation 283 6.5.2 Integration 285 6.5.3 Monte Carlo 285 7 Extrapolations 287 7.1 Using the Market to Complete Information: Asymptotic Smile 288 7.1.1 The Indetermination in the Asymptotic Smile 288 7.1.2 Pricing CMS with a Smile: Extrapolating to Infinity 292 7.1.3 Using CMS Information to Transform Extrapolation into Interpolation and Fix the Indetermination 293 7.2 Using Mathematics to Complete Information: Correlation Skew 295 7.2.1 The Expected Tranched Loss 295 7.2.2 Properties for Interpolation 298 7.2.3 Properties for Turning Extrapolation into Interpolation 298 8 Correlations 303 8.1 The Technical Difficulties in Computing Correlations 303 8.1.1 Correlations in Interest Rate Modelling 305 8.1.2 Cross-currency Correlations 307 8.1.3 Stochastic Volatility Correlations 312 8.2 Fundamental Errors in Modelling Correlations 315 8.2.1 The Zero-correlation Error 316 8.2.2 The 1-Correlation Error 319 9 Calibration 323 9.1 Calibrating to Caps/Swaptions and Pricing Bermudans 324 9.1.1 Calibrating Caplets 325 9.1.2 Understanding the Term Structure of Volatility 326 9.1.3 Different Parameterizations 329 9.1.4 The Evolution of the Term Structure of Volatility 332 9.1.5 The Effect on Early-Exercise Derivatives 334 9.1.6 Reducing Our Indetermination in Pricing Bermudans: Liquid European Swaptions 335 9.2 The Evolution of the Forward Smiles 340 10 When the Payoff is Wrong 347 10.1 The Link Between Model Errors and Payoff Errors 347 10.2 The Right Payoff at Default: The Impact of the Closeout Convention 348 10.2.1 How Much Will be Paid at Closeout, Really? 350 10.2.2 What the Market Says and What the ISDA Says 352 10.2.3 A Quantitative Analysis of the Closeout 353 10.2.4 A Summary of the Findings and Some Conclusions on Payoff Uncertainty 360 10.3 Mathematical Errors in the Payoff of Index Options 362 10.3.1 Too Much Left Out 364 10.3.2 Too Much Left In 365 10.3.3 Empirical Results with the Armageddon Formula 365 10.3.4 Payoff Errors and Armageddon Probability 367 11 Model Arbitrage 371 11.1 Introduction 371 11.2 Capital Structure Arbitrage 373 11.2.1 The Credit Model 373 11.2.2 The Equity Model 375 11.2.3 From Barrier Options to Equity Pricing 377 11.2.4 Capital-structure Arbitrage and Uncertainty 381 11.3 The Cap-Swaption Arbitrage 391 11.4 Conclusion: Can We Use No-Arbitrage Models to Make Arbitrage? 394 12 Appendix 397 12.1 Random Variables 397 12.1.1 Generating Variables from Uniform Draws 397 12.1.2 Copulas 397 12.1.3 Normal and Lognormal 398 12.2 Stochastic Processes 399 12.2.1 The Law of Iterated Expectation 399 12.2.2 Diffusions, Brownian Motions and Martingales 400 12.2.3 Poisson Process 403 12.2.4 Time-dependent Intensity 404 12.3 Useful Results from Quantitative Finance 405 12.3.1 Black and Scholes (1973) and Black (1976) 405 12.3.2 Change of Numeraire 407 Bibliography 409 Index 417

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Book SynopsisBayesian Networks This book should have a place on the bookshelf of every forensic scientist who cares about the science of evidence interpretation.Dr. Ian Evett, Principal Forensic Services Ltd, London, UK Bayesian Networksfor Probabilistic Inference and Decision Analysis in Forensic Science Second Edition Continuing developments in science and technology mean that the amounts of information forensic scientists are able to provide for criminal investigations is ever increasing. The commensurate increase in complexity creates diffculties for scientists and lawyers with regard to evaluation and interpretation, notably with respect to issues of inference and decision. Probability theory, implemented through graphical methods, and specifically Bayesian networks, provides powerful methods to deal with this complexity. Extensions of these methods to elements of decision theory provide further support and assistance to the judicial system. BayeTrade Review“The clear and accessible style of this second edition makes this book ideal for all forensic scientists, applied statisticians and graduate students wishing to evaluate forensic findings from the perspective of probability and decision analysis. It will also appeal to lawyers and other scientists and professionals interested in the evaluation and interpretation of forensic findings, including decision making based on scientific information.” (Zentralblatt MATH, 1 October 2014) Table of ContentsForeword xiii Preface to the second edition xvii Preface to the first edition xxi 1 The logic of decision 1 1.1 Uncertainty and probability 1 1.1.1 Probability is not about numbers, it is about coherent reasoning under uncertainty 1 1.1.2 The first two laws of probability 2 1.1.3 Relevance and independence 3 1.1.4 The third law of probability 5 1.1.5 Extension of the conversation 6 1.1.6 Bayes’ theorem 6 1.1.7 Probability trees 7 1.1.8 Likelihood and probability 9 1.1.9 The calculus of (probable) truths 10 1.2 Reasoning under uncertainty 12 1.2.1 The Hound of the Baskervilles 12 1.2.2 Combination of background information and evidence 13 1.2.3 The odds form of Bayes’ theorem 15 1.2.4 Combination of evidence 16 1.2.5 Reasoning with total evidence 16 1.2.6 Reasoning with uncertain evidence 18 1.3 Population proportions, probabilities and induction 19 1.3.1 The statistical syllogism 19 1.3.2 Expectations and population proportions 21 1.3.3 Probabilistic explanations 22 1.3.4 Abduction and inference to the best explanation 25 1.3.5 Induction the Bayesian way 26 1.4 Decision making under uncertainty 28 1.4.1 Bookmakers in the Courtrooms? 28 1.4.2 Utility theory 29 1.4.3 The rule of maximizing expected utility 33 1.4.4 The loss function 34 1.4.5 Decision trees 35 1.4.6 The expected value of information 38 1.5 Further readings 42 2 The logic of Bayesian networks and influence diagrams 45 2.1 Reasoning with graphical models 45 2.1.1 Beyond detective stories 45 2.1.2 Bayesian networks 46 2.1.3 A graphical model for relevance 48 2.1.4 Conditional independence 50 2.1.5 Graphical models for conditional independence: d-separation 51 2.1.6 A decision rule for conditional independence 53 2.1.7 Networks for evidential reasoning 53 2.1.8 The Markov property 56 2.1.9 Influence diagrams 58 2.1.10 Conditional independence in influence diagrams 60 2.1.11 Relevance and causality 61 2.1.12 The Hound of the Baskervilles revisited 63 2.2 Reasoning with Bayesian networks and influence diagrams 65 2.2.1 Divide and conquer 66 2.2.2 From directed to triangulated graphs 67 2.2.3 From triangulated graphs to junction trees 69 2.2.4 Solving influence diagrams 71 2.2.5 Object-oriented Bayesian networks 74 2.2.6 Solving object-oriented Bayesian networks 79 2.3 Further readings 82 2.3.1 General 82 2.3.2 Bayesian networks and their predecessors in judicial contexts 83 3 Evaluation of scientific findings in forensic science 85 3.1 Introduction 85 3.2 The value of scientific findings 86 3.3 Principles of forensic evaluation and relevant propositions 90 3.3.1 Source level propositions 92 3.3.2 Activity level propositions 94 3.3.3 Crime level propositions 97 3.4 Pre-assessment of the case 100 3.5 Evaluation using graphical models 103 3.5.1 Introduction 103 3.5.2 General aspects of the construction of Bayesian networks 103 3.5.3 Eliciting structural relationships 105 3.5.4 Level of detail of variables and quantification of influences 106 3.5.5 Deriving an alternative network structure 108 4 Evaluation given source level propositions 113 4.1 General considerations 113 4.2 Standard statistical distributions 115 4.3 Two stains, no putative source 117 4.3.1 Likelihood ratio for source inference when no putative source is available 117 4.3.2 Bayesian network for a two-trace case with no putative source 119 4.3.3 An alternative network structure for a two trace no putative source case 121 4.4 Multiple propositions 122 4.4.1 Form of the likelihood ratio 122 4.4.2 Bayesian networks for evaluation given multiple propositions 123 5 Evaluation given activity level propositions 129 5.1 Evaluation of transfer material given activity level propositions assuming a direct source relationship 130 5.1.1 Preliminaries 130 5.1.2 Derivation of a basic structure for a Bayesian network 131 5.1.3 Modifying the basic network 134 5.1.4 Further considerations about background presence 137 5.1.5 Background from different sources 139 5.1.6 An alternative description of the findings 142 5.1.7 Bayesian network for an alternative description of findings 145 5.1.8 Increasing the level of detail of selected propositions 147 5.1.9 Evaluation of the proposed model 149 5.2 Cross- or two-way transfer of trace material 150 5.3 Evaluation of transfer material given activity level propositions with uncertainty about the true source 154 5.3.1 Network structure 154 5.3.2 Evaluation of the network 154 5.3.3 Effect of varying assumptions about key factors 157 6 Evaluation given crime level propositions 159 6.1 Material found on a crime scene: A general approach 159 6.1.1 Generic network construction for single offender 159 6.1.2 Evaluation of the network 161 6.1.3 Extending the single-offender scenario 163 6.1.4 Multiple offenders 166 6.1.5 The role of the relevant population 168 6.2 Findings with more than one component: The example of marks 168 6.2.1 General considerations 168 6.2.2 Adding further propositions 169 6.2.3 Derivation of the likelihood ratio 170 6.2.4 Consideration of distinct components 172 6.2.5 An extension to firearm examinations 177 6.2.6 A note on the likelihood ratio 181 6.3 Scenarios with more than one trace: ‘Two stain-one offender’ cases 182 6.4 Material found on a person of interest 185 6.4.1 General form 185 6.4.2 Extending the numerator 187 6.4.3 Extending the denominator 189 6.4.4 Extended form of the likelihood ratio 190 6.4.5 Network construction and examples 190 7 Evaluation of DNA profiling results 196 7.1 DNA likelihood ratio 196 7.2 Network approaches to the DNA likelihood ratio 198 7.2.1 The ‘match’ approach 198 7.2.2 Representation of individual alleles 198 7.2.3 Alternative representation of a genotype 202 7.3 Missing suspect 203 7.4 Analysis when the alternative proposition is that a brother of the suspect left the crime stain 206 7.4.1 Revision of probabilities and networks 206 7.4.2 Further considerations on conditional genotype probabilities 212 7.5 Interpretation with more than two propositions 214 7.6 Evaluation with more than two propositions 217 7.7 Partially corresponding profiles 220 7.8 Mixtures 223 7.8.1 Considering multiple crime stain contributors 223 7.8.2 Bayesian network for a three-allele mixture scenario 225 7.9 Kinship analyses 227 7.9.1 A disputed paternity 227 7.9.2 An extended paternity scenario 230 7.9.3 A case of questioned maternity 232 7.10 Database search 234 7.10.1 Likelihood ratio after database searching 234 7.10.2 An analysis focussing on posterior probabilities 237 7.11 Probabilistic approaches to laboratory error 241 7.11.1 Implicit approach to typing error 241 7.11.2 Explicit approach to typing error 243 7.12 Further reading 246 7.12.1 A note on object-oriented Bayesian networks 246 7.12.2 Additional topics 246 8 Aspects of combining evidence 249 8.1 Introduction 249 8.2 A difficulty in combining evidence: The ‘problem of conjunction’ 250 8.3 Generic patterns of inference in combining evidence 252 8.3.1 Preliminaries 252 8.3.2 Dissonant evidence: Contradiction and conflict 252 8.3.3 Harmonious evidence: Corroboration and convergence 256 8.3.4 Drag coefficient 261 8.4 Examples of the combination of distinct items of evidence 262 8.4.1 Handwriting and fingermarks 262 8.4.2 Issues in DNA analyses 266 8.4.3 One offender and two corresponding traces 267 8.4.4 Firearms and gunshot residues 271 8.4.5 Comments 279 9 Networks for continuous models 281 9.1 Random variables and distribution functions 281 9.1.1 Normal distribution 283 9.1.2 Bivariate Normal distribution 287 9.1.3 Conditional expectation and variance 288 9.2 Samples and estimates 289 9.2.1 Summary statistics 289 9.2.2 The Bayesian paradigm 291 9.3 Continuous Bayesian networks 292 9.3.1 Propagation in a continuous Bayesian network 295 9.3.2 Background data 300 9.3.3 Intervals for a continuous entity 302 9.4 Mixed networks 306 9.4.1 Bayesian network for a continuous variable with a discrete parent 308 9.4.2 Bayesian network for a continuous variable with a continuous parent and a binary parent, unmarried 310 10 Pre-assessment 314 10.1 Introduction 314 10.2 General elements of pre-assessment 315 10.3 Pre-assessment in a fibre case: A worked through example 316 10.3.1 Preliminaries 316 10.3.2 Propositions and relevant events 317 10.3.3 Expected likelihood ratios 319 10.3.4 Construction of a Bayesian network 321 10.4 Pre-assessment in a cross-transfer scenario 321 10.4.1 Bidirectional transfer 321 10.4.2 A Bayesian network for a pre-assessment of a cross-transfer scenario 324 10.4.3 The value of the findings 325 10.5 Pre-assessment for consignment inspection 328 10.5.1 Inspecting small consignments 328 10.5.2 Bayesian network for inference about small consignments 330 10.5.3 Pre-assessment for inspection of small consignments 333 10.6 Pre-assessment for gunshot residue particles 335 10.6.1 Formation and deposition of gunshot residue particles 335 10.6.2 Bayesian network for grouped expected findings (GSR counts) 336 10.6.3 Examples for GSR count pre-assessment using a Bayesian network 339 11 Bayesian decision networks 343 11.1 Decision making in forensic science 343 11.2 Examples of forensic decision analyses 344 11.2.1 Deciding about whether or not to perform a DNA analysis 344 11.2.2 Probability assignment as a question of decision making 352 11.2.3 Decision analysis for consignment inspection 357 11.2.4 Decision after database searching 366 11.3 Further readings 368 12 Object-oriented networks 370 12.1 Object orientation 370 12.2 General elements of object-oriented networks 371 12.2.1 Static versus dynamic networks 371 12.2.2 Dynamic Bayesian networks as object-oriented networks 373 12.2.3 Refining internal class descriptions 374 12.3 Object-oriented networks for evaluating DNA profiling results 378 12.3.1 Basic disputed paternity case 378 12.3.2 Useful class networks for modelling kinship analyses 379 12.3.3 Object-oriented networks for kinship analyses 381 12.3.4 Object-oriented networks for inference of source 383 12.3.5 Refining internal class descriptions and further considerations 385 13 Qualitative, sensitivity and conflict analyses 388 13.1 Qualitative probability models 389 13.1.1 Qualitative influence 389 13.1.2 Additive synergy 392 13.1.3 Product synergy 394 13.1.4 Properties of qualitative relationships 396 13.1.5 Implications of qualitative graphical models 401 13.2 Sensitivity analyses 402 13.2.1 Preliminaries 402 13.2.2 Sensitivity to a single probability assignment 403 13.2.3 Sensitivity to two probability assignments 405 13.2.4 Sensitivity to prior distribution 408 13.3 Conflict analysis 410 13.3.1 Conflict detection 411 13.3.2 Tracing a conflict 414 13.3.3 Conflict resolution 415 References 419 Author index 433 Subject index 438

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Book Synopsis A simple and systematic guide to the planning and performance of investigations concerned with health and disease and with health care Offers researchers help in choosing a topic and to think about shaping objectives and ideas and to link these with the appropriate choice of method Fully updated with new sections on the use of the Web and computer programmes freely available in the planning, performance or analysis of studies Table of ContentsPreface vii 1. First steps 1 2. Types of investigation 13 3. Stages of an investigation 35 4. Formulating the objectives 39 5. The objectives of evaluative studies 49 6. The study population 61 7. Control groups 69 8. Sampling 77 9. Selecting cases and controls for case-control studies 91 10. The variables 101 11. Defining the variables 109 12. Definitions of diseases 117 13. Scales of measurement 125 14. Composite scales 133 15. Methods of collecting data 143 16. Reliability 151 17. Validity 161 18. Interviews and self-administered questionnaires 179 19. Constructing a questionnaire 193 20. Surveying the opinions of a panel: consensus methods 203 21. The use of documentary sources 209 22. Planning the records 225 23. Planning the handling of data 233 24. Pretests and other preparations 241 25. Collecting the data 247 26. Statistical analysis 251 27. Interpreting the findings 259 28. Making sense of associations 269 29. Application of the study findings 297 30. Writing a report 305 31. Rapid epidemiological methods 313 32. Clinical trials 325 33. Programme trials 345 34. Community-oriented primary care 357 35. Using the Web for health research 373 Appendix A Community appraisal: a checklist 383 Appendix B Random numbers 387 Appendix C Free computer programs 389 Index 407

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Book SynopsisThis is the only major text in the area of chemometrics published over the last decade focusing exclusively on pattern recognition. The coverage uses real world pattern recognition case studies, often involving quite large and complex datasets.Table of ContentsAcknowledgements. Preface. 1 Introduction. 1.1 Past, Present and Future. 1.2 About this Book. Bibliography. 2 Case Studies. 2.1 Introduction. 2.2 Datasets, Matrices and Vectors. 2.3 Case Study 1: Forensic Analysis of Banknotes. 2.4 Case Study 2: Near Infrared Spectroscopic Analysis of Food. 2.5 Case Study 3: Thermal Analysis of Polymers. 2.6 Case Study 4: Environmental Pollution using Headspace Mass Spectrometry. 2.7 Case Study 5: Human Sweat Analysed by Gas Chromatography Mass Spectrometry. 2.8 Case Study 6: Liquid Chromatography Mass Spectrometry of Pharmaceutical Tablets. 2.9 Case Study 7: Atomic Spectroscopy for the Study of Hypertension. 2.10 Case Study 8: Metabolic Profiling of Mouse Urine by Gas Chromatography of Urine Extracts. 2.11 Case Study 9: Nuclear Magnetic Resonance Spectroscopy for Salival Analysis of the Effect of Mouthwash. 2.12 Case Study 10: Simulations. 2.13 Case Study 11: Null Dataset. 2.14 Case Study 12: GCMS and Microbiology of Mouse Scent Marks. Bibliography. 3 Exploratory Data Analysis. 3.1 Introduction. 3.2 Principal Components Analysis. 3.2.1 Background. 3.2.2 Scores and Loadings. 3.2.3 Eigenvalues. 3.2.4 PCA Algorithm. 3.2.5 Graphical Representation. 3.3 Dissimilarity Indices, Principal Co-ordinates Analysis and Ranking. 3.3.1 Dissimilarity. 3.3.2 Principal Co-ordinates Analysis. 3.3.3 Ranking. 3.4 Self Organizing Maps. 3.4.1 Background. 3.4.2 SOM Algorithm. 3.4.3 Initialization. 3.4.4 Training. 3.4.5 Map Quality. 3.4.6 Visualization. Bibliography. 4 Preprocessing. 4.1 Introduction. 4.2 Data Scaling. 4.2.1 Transforming Individual Elements. 4.2.2 Row Scaling. 4.2.3 Column Scaling. 4.3 Multivariate Methods of Data Reduction. 4.3.1 Largest Principal Components. 4.3.2 Discriminatory Principal Components. 4.3.3 Partial Least Squares Discriminatory Analysis Scores. 4.4 Strategies for Data Preprocessing. 4.4.1 Flow Charts. 4.4.2 Level 1. 4.4.3 Level 2. 4.4.4 Level 3. 4.4.5 Level 4. Bibliography. 5 Two Class Classifiers. 5.1 Introduction. 5.1.1 Two Class Classifiers. 5.1.2 Preprocessing. 5.1.3 Notation. 5.1.4 Autoprediction and Class Boundaries. 5.2 Euclidean Distance to Centroids. 5.3 Linear Discriminant Analysis. 5.4 Quadratic Discriminant Analysis. 5.5 Partial Least Squares Discriminant Analysis. 5.5.1 PLS Method. 5.5.2 PLS Algorithm. 5.5.3 PLS-DA. 5.6 Learning Vector Quantization. 5.6.1 Voronoi Tesselation and Codebooks. 5.6.2 LVQ1. 5.6.3 LVQ3. 5.6.4 LVQ Illustration and Summary of Parameters. 5.7 Support Vector Machines. 5.7.1 Linear Learning Machines. 5.7.2 Kernels. 5.7.3 Controlling Complexity and Soft Margin SVMs. 5.7.4 SVM Parameters. Bibliography. 6 One Class Classifiers. 6.1 Introduction. 6.2 Distance Based Classifiers. 6.3 PC Based Models and SIMCA. 6.4 Indicators of Significance. 6.4.1 Gaussian Density Estimators and Chi-Squared. 6.4.2 Hotelling’s T2. 6.4.3 D-Statistic. 6.4.4 Q-Statistic or Squared Prediction Error. 6.4.5 Visualization of D- and Q-Statistics for Disjoint PC Models. 6.4.6 Multivariate Normality and What to do if it Fails. 6.5 Support Vector Data Description. 6.6 Summarizing One Class Classifiers. 6.6.1 Class Membership Plots. 6.6.2 ROC Curves. Bibliography. 7 Multiclass Classifiers. 7.1 Introduction. 7.2 EDC, LDA and QDA. 7.3 LVQ. 7.4 PLS. 7.4.1 PLS2. 7.4.2 PLS1. 7.5 SVM. 7.6 One against One Decisions. Bibliography. 8 Validation and Optimization. 8.1 Introduction. 8.1.1 Validation. 8.1.2 Optimization. 8.2 Classification Abilities, Contingency Tables and Related Concepts. 8.2.1 Two Class Classifiers. 8.2.2 Multiclass Classifiers. 8.2.3 One Class Classifiers. 8.3 Validation. 8.3.1 Testing Models. 8.3.2 Test and Training Sets. 8.3.3 Predictions. 8.3.4 Increasing the Number of Variables for the Classifier. 8.4 Iterative Approaches for Validation. 8.4.1 Predictive Ability, Model Stability, Classification by Majority Vote and Cross Classification Rate. 8.4.2 Number of Iterations. 8.4.3 Test and Training Set Boundaries. 8.5 Optimizing PLS Models. 8.5.1 Number of Components: Cross-Validation and Bootstrap. 8.5.2 Thresholds and ROC Curves. 8.6 Optimizing Learning Vector Quantization Models. 8.7 Optimizing Support Vector Machine Models. Bibliography. 9 Determining Potential Discriminatory Variables. 9.1 Introduction. 9.1.1 Two Class Distributions. 9.1.2 Multiclass Distributions. 9.1.3 Multilevel and Multiway Distributions. 9.1.4 Sample Sizes. 9.1.5 Modelling after Variable Reduction. 9.1.6 Preliminary Variable Reduction. 9.2 Which Variables are most Significant?. 9.2.1 Basic Concepts: Statistical Indicators and Rank. 9.2.2 T-Statistic and Fisher Weights. 9.2.3 Multiple Linear Regression, ANOVA and the F-Ratio. 9.2.4 Partial Least Squares. 9.2.5 Relationship between the Indicator Functions. 9.3 How Many Variables are Significant? 9.3.1 Probabilistic Approaches. 9.3.2 Empirical Methods: Monte Carlo. 9.3.3 Cost/Benefit of Increasing the Number of Variables. Bibliography. 10 Bayesian Methods and Unequal Class Sizes. 10.1 Introduction. 10.2 Contingency Tables and Bayes’ Theorem. 10.3 Bayesian Extensions to Classifiers. Bibliography. 11 Class Separation Indices. 11.1 Introduction. 11.2 Davies Bouldin Index. 11.3 Silhouette Width and Modified Silhouette Width. 11.3.1 Silhouette Width. 11.3.2 Modified Silhouette Width. 11.4 Overlap Coefficient. Bibliography. 12 Comparing Different Patterns. 12.1 Introduction. 12.2 Correlation Based Methods. 12.2.1 Mantel Test. 12.2.2 RV Coefficient. 12.3 Consensus PCA. 12.4 Procrustes Analysis. Bibliography. Index.

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Book SynopsisThere is a growing demand from institutional bodies for the justification of industrial methodologies and practices (e.g. safety criteria, environmental protection and control, maintenance and design optimization). Previous books in this area have either been too theoretical, or too specific in their scope.Table of ContentsPreface xiii Contributors and Acknowledgements xv Introduction xvii Notation – Acronyms and abbreviations xxi Part I Common Methodological Framework 1 1 Introducing the common methodological framework 3 1.1 Quantitative uncertainty assessment in industrial practice: a wide variety of contexts 3 1.2 Key generic features, notation and concepts 4 1.2.1 Pre-existing model, variables of interest and uncertain/fixed inputs 4 1.2.2 Main goals of the uncertainty assessment 6 1.2.3 Measures of uncertainty and quantities of interest 7 1.2.4 Feedback process 9 1.2.5 Uncertainty modelling 10 1.2.6 Propagation and sensitivity analysis processes 10 1.3 The common conceptual framework 11 1.4 Using probabilistic frameworks in uncertainty quantification – preliminary comments 13 1.4.1 Standard probabilistic setting and interpretations 13 1.4.2 More elaborate level-2 settings and interpretations 14 1.5 Concluding remarks 17 References 18 2 Positioning of the case studies 21 2.1 Main study characteristics to be specified in line with the common framework 21 2.2 Introducing the panel of case studies 21 2.3 Case study abstracts 27 Part II Case Studies 33 3 CO2 emissions: estimating uncertainties in practice for power plants 35 3.1 Introduction and study context 35 3.2 The study model and methodology 36 3.2.1 Three metrological options: common features in the preexisting models 36 3.2.2 Differentiating elements of the fuel consumption models 38 3.3 Underlying framework of the uncertainty study 39 3.3.1 Specification of the uncertainty study 39 3.3.2 Description and modelling of the sources of uncertainty 40 3.3.3 Uncertainty propagation and sensitivity analysis 42 3.3.4 Feedback process 44 3.4 Practical implementation and results 44 3.5 Conclusions 47 References 47 4 Hydrocarbon exploration: decision-support through uncertainty treatment 49 4.1 Introduction and study context 49 4.2 The study model and methodology 50 4.2.1 Basin and petroleum system modelling 50 4.3 Underlying framework of the uncertainty study 54 4.3.1 Specification of the uncertainty study 54 4.3.2 Description and modelling of the sources of uncertainty 56 4.3.3 Uncertainty propagation and sensitivity analysis 57 4.3.4 Feedback process 57 4.4 Practical implementation and results 59 4.4.1 Uncertainty analysis 59 4.4.2 Sensitivity analysis 62 4.5 Conclusions 63 References 64 5 Determination of the risk due to personal electronic devices (PEDs) carried out on radio-navigation systems aboard aircraft 65 5.1 Introduction and study context 65 5.2 The study model and methodology 66 5.2.1 Electromagnetic compatibility modelling and analysis 66 5.2.2 Setting the EMC problem 67 5.2.3 A model-based approach 68 5.2.4 Regulatory and industrial stakes 69 5.3 Underlying framework of the uncertainty study 71 5.3.1 Specification of the uncertainty study 71 5.3.2 Description and modelling of the sources of uncertainty 72 5.3.3 Uncertainty propagation and sensitivity analysis 75 5.3.4 Feedback process 76 5.4 Practical implementation and results 76 5.4.1 Limitations of the results of the study 76 5.4.2 Scenario no.1: effects of one emitter in the aircraft on ILS antenna (realistic data-set) 76 5.4.3 Scenario no. 2: effects of one emitter in the aircraft on ILS antenna with penalized susceptibility 78 5.4.4 Scenario no. 3: 10 coherent emitters in the aircraft, ILS antenna with a realistic data set 79 5.4.5 Scenario no. 4: new model considering the effect of one emitter in the aircraft on ILS antenna and safety factors 79 5.5 Conclusions 80 References 80 6 Safety assessment of a radioactive high-level waste repository – comparison of dose and peak dose 81 6.1 Introduction and study context 81 6.2 Study model and methodology 82 6.2.1 Source term model 83 6.2.2 Geosphere model 83 6.2.3 The biosphere model 84 6.3 Underlying framework of the uncertainty study 84 6.3.1 Specification of the uncertainty study 84 6.3.2 Sources of uncertainty, model inputs and uncertainty model developed 85 6.3.3 Uncertainty propagation and sensitivity analysis 86 6.3.4 Feedback process 87 6.4 Practical implementation and results 87 6.4.1 Uncertainty analysis 87 6.4.2 Sensitivity analysis 91 6.5 Conclusions 95 References 96 7 A cash flow statistical model for airframe accessory maintenance contracts 97 7.1 Introduction and study context 97 7.2 The study model and methodology 97 7.2.1 Generalities 97 7.2.2 Level-1 uncertainty 98 7.2.3 Computation 98 7.2.4 Stock size 100 7.3 Underlying framework of the uncertainty study 100 7.3.1 Specification of the uncertainty study 100 7.3.2 Description and modelling of the sources of uncertainty 101 7.3.3 Uncertainty propagation and sensitivity analysis 103 7.3.4 Feedback process 104 7.4 Practical implementation and results 104 7.4.1 Design of experiments results 105 7.4.2 Sobol’s sensitivity indices 107 7.4.3 Comparison between DoE and Sobol’ methods 108 7.5 Conclusions 108 References 109 8 Uncertainty and reliability study of a creep law to assess the fuel cladding behaviour of PWR spent fuel assemblies during interim dry storage 111 8.1 Introduction and study context 111 8.2 The study model and methodology 112 8.2.1 Failure limit strain and margin 113 8.2.2 The temperature scenario 113 8.3 Underlying framework of the uncertainty study 114 8.3.1 Specification of the uncertainty study 114 8.3.2 Description and modelling of the sources of uncertainty 115 8.3.3 Uncertainty propagation and sensitivity analysis 116 8.3.4 Feedback process 116 8.4 Practical implementation and results 117 8.4.1 Dispersion of the minimal margin 117 8.4.2 Sensitivity analysis 119 8.4.3 Exceedance probability analysis 120 8.5 Conclusions 121 References 122 9 Radiological protection and maintenance 123 9.1 Introduction and study context 123 9.2 The study model and methodology 124 9.3 Underlying framework of the uncertainty study 128 9.3.1 Specification of the uncertainty study 128 9.3.2 Description and modelling of the sources of uncertainty 129 9.3.3 Uncertainty propagation and sensitivity analysis 131 9.3.4 Feedback process 131 9.4 Practical implementation and results 132 9.5 Conclusions 134 References 134 10 Partial safety factors to deal with uncertainties in slope stability of river dykes 135 10.1 Introduction and study context 135 10.2 The study model and methodology 136 10.2.1 Slope stability models 136 10.2.2 Incorporating slope stability in dyke design 137 10.2.3 Uncertainties in design process 138 10.3 Underlying framework of the uncertainty study 138 10.3.1 Specification of the uncertainty study 139 10.3.2 Description and modelling of the sources of uncertainty 142 10.3.3 Uncertainty propagation and sensitivity analysis 144 10.3.4 Feedback process 149 10.4 Practical implementation and results 150 10.5 Conclusions 153 References 153 11 Probabilistic assessment of fatigue life 155 11.1 Introduction and study context 155 11.2 The study model and methodology 155 11.2.1 Fatigue criteria 155 11.2.2 System model 156 11.3 Underlying framework of the uncertainty study 157 11.3.1 Outline of current practice in fatigue design 157 11.3.2 Specification of the uncertainty study 158 11.3.3 Description and modelling of the sources of uncertainty 160 11.3.4 Uncertainty propagation and sensitivity analysis 161 11.3.5 Feedback process 161 11.4 Practical implementation and results 162 11.4.1 Identification of the macro fatigue resistance β(N) 162 11.4.2 Uncertainty analysis 164 11.5 Conclusions 167 References 167 12 Reliability modelling in early design stages using the Dempster-Shafer Theory of Evidence 169 12.1 Introduction and study context 169 12.2 The study model and methodology 170 12.2.1 The system 170 12.2.2 The system fault tree model 171 12.2.3 The IEC 61508 guideline: a framework for safety requirements 172 12.3 Underlying framework of the uncertainty study 173 12.3.1 Specification of the uncertainty study 173 12.3.2 Description and modelling of the sources of uncertainty 176 12.4 Practical implementation and results 178 12.5 Conclusions 182 References 182 Part III Methodological Review and Recommendations 185 13 What does uncertainty management mean in an industrial context? 187 13.1 Introduction 187 13.2 A basic distinction between ‘design’ and ‘in-service operations’ in an industrial estate 188 13.2.1 Design phases 188 13.2.2 In-service operations 189 13.3 Failure-driven risk management and option-exploring approaches at company level 190 13.4 Survey of the main trends and popular concepts in industry 191 13.5 Links between uncertainty management studies and a global industrial context 192 13.5.1 Internal/endogenous context 193 13.5.2 External/exogenous uncertainty 194 13.5.3 Layers of uncertainty 195 13.6 Developing a strategy to deal with uncertainties 195 References 197 14 Uncertainty settings and natures of uncertainty 199 14.1 A classical distinction 199 14.2 Theoretical distinctions, difficulties and controversies in practical applications 202 14.3 Various settings deemed acceptable in practice 205 References 210 15 Overall approach 213 15.1 Recalling the common methodological framework 213 15.2 Introducing the mathematical formulation and key steps of a study 214 15.2.1 The specification step – measure of uncertainty, quantities of interest and setting 214 15.2.2 The uncertainty modelling (or source quantification) step 215 15.2.3 The uncertainty propagation step 218 15.2.4 The sensitivity analysis step, or importance ranking 219 15.3 Links between final goals, study steps and feedback process 220 15.4 Comparison with applied system identification or command/control classics 221 15.5 Pre-existing or system model validation and model uncertainty 222 15.6 Links between decision theory and the criteria of the overall framework 223 References 224 16 Uncertainty modelling methods 225 16.1 Objectives of uncertainty modelling and important issues 225 16.2 Recommendations in a standard probabilistic setting 227 16.2.1 The case of independent variables 228 16.2.2 Building an univariate probability distribution via expert/engineering judgement 229 16.2.3 The case of dependent uncertain model inputs 234 16.3 Comments on level-2 probabilistic settings 236 References 237 17 Uncertainty propagation methods 239 17.1 Recommendations per quantity of interest 240 17.1.1 Variance, moments 240 17.1.2 Probability density function 243 17.1.3 Quantiles 245 17.1.4 Exceedance probability 247 17.2 Meta-models 250 17.2.1 Building a meta-model 251 17.2.2 Validation of a meta-model 252 17.3 Summary 253 References 256 18 Sensitivity analysis methods 259 18.1 The role of sensitivity analysis in quantitative uncertainty assessment 260 18.1.1 Understanding influence and ranking importance of uncertainties (goal U) 261 18.1.2 Calibrating, simplifying and validating a numerical model (goal A) 262 18.1.3 Comparing relative performances and decision support (goal S) 263 18.1.4 Demonstrating compliance with a criterion or a regulatory threshold (goal C) 264 18.2 Towards the choice of an appropriate Sensitivity Analysis framework 264 18.3 Scope, potential and limitations of the various techniques 269 18.3.1 Differential methods 269 18.3.2 Approximate reliability methods 270 18.3.3 Regression/correlation 271 18.3.4 Screening methods 273 18.3.5 Variance analysis of Monte Carlo simulations 274 18.3.6 Non-variance analysis of Monte Carlo simulations 276 18.3.7 Graphical methods 278 18.4 Conclusions 280 References 281 19 Presentation in a deterministic format 285 19.1 How to present in a deterministic format? 286 19.1.1 (Partial) safety factors in a deterministic approach 286 19.1.2 Safety factors in a probabilistic approach 287 19.2 On the reliability target 290 19.3 Final comments 291 References 292 20 Recommendations on the overall process in practice 293 20.1 Recommendations on the key specification step 293 20.1.1 Choice of the system model 294 20.1.2 Choice of the uncertainty setting 294 20.1.3 Choice of the quantity of interest 296 20.1.4 Choice of the model input representation (‘x’ and ‘d’) 297 20.2 Final comments regarding dissemination challenges 297 References 298 Conclusion 299 Appendices 303 Appendix A A selection of codes and standards 305 Appendix B A selection of tools and websites 307 Appendix C Towards non-probabilistic settings: promises and industrial challenges 313 Index 329

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Book SynopsisThis is the first text to examine the use of statistical methods in forensic science and bayesian statistics in combination. The book is split into two parts: Part One concentrates on the philosophies of statistical inference. Chapter One examines the differences between the frequentist, the likelihood and the Bayesian perspectives, before Chapter Two explores the Bayesian decision-theoretic perspective further, and looks at the benefits it carries. Part Two then introduces the reader to the practical aspects involved: the application, interpretation, summary and presentation of data analyses are all examined from a Bayesian decision-theoretic perspective. A wide range of statistical methods, essential in the analysis of forensic scientific data is explored. These include the comparison of allele proportions in populations, the comparison of means, the choice of sampling size, and the discrimination of items of evidence of unknown origin into predefined populations. TTable of ContentsForeword. Preface. I The Foundations of Inference and Decision in Forensic Science. 1 Introduction. 1.1 The Inevitability of Uncertainty. 1.2 Desiderata in Evidential Assessment. 1.3 The Importance of the Propositional Framework and the Nature of Evidential Assessment. 1.4 From Desiderata to Applications. 1.5 The Bayesian Core of Forensic Science. 1.6 Structure of the Book. 2 Scientific Reasoning and Decision Making. 2.1 Coherent Reasoning Under Uncertainty. 2.2 Coherent Decision Making Under Uncertainty of Reasoning. 2.3 Scientific Reasoning as Coherent Decision Making. 2.4 Forensic Reasoning as Coherent Decision Making. 3 Concepts of Statistical Science and Decision Theory. 3.1 Random Variables and Distribution Functions. 3.2 Statistical Inference and Decision Theory. 3.3 The Bayesian Paradigm. 3.4 Bayesian Decision Theory. 3.5 R Code. II Forensic Data Analysis. 4 Point Estimation. 4.1 Introduction. 4.2 Bayesian Decision for a Proportion. 4.3 Bayesian Decision for a Poisson Mean. 4.4 Bayesian Decision for Normal Mean. 4.5 R Code. 5 Credible Intervals. 5.1 Introduction. 5.2 Credible Intervals. 5.3 Decision-Theoretic Evaluation of Credible Intervals. 5.4 R Code. 6 Hypothesis Testing. 6.1 Introduction. 6.2 Bayesian Hypothesis Testing. 6.3 One-sided testing. 6.4 Two-Sided Testing. 6.5 R Code. 7 Sampling. 7.1 Introduction. 7.2 Sampling Inspection. 7.3 Graphical Models for Sampling Inspection. 7.4 Sampling Inspection under a Decision-Theoretic Approach. 7.5 R Code. 8 Classification of Observations. 8.1 Introduction. 8.2 Standards of Coherent Classification. 8.3 Comparing Models using Discrete Data. 8.4 Comparison of Models using Continuous Data. 8.5 Non-Normal Distributions and Cocaine on Bank Notes. 8.6 A note on Multivariate Continuous Data. 8.7 R Code. 9 Bayesian Forensic Data Analysis: Conclusions and Implications. 9.1 Introduction. 9.2 What is the Past and Current Position of Statistics in Forensic Science? 9.3 Why Should Forensic Scientists Conform to a Bayesian Framework for Inference and Decision Making? 9.4 Why Regard Probability as a Personal Degree of Belief? 9.5 Why Should Scientists be Aware of Decision Analysis? 9.6 How to Implement Bayesian Inference and Decision Analysis? A Discrete Distributions. B Continuous Distributions. Bibliography. Author Index. Subject Index.

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Book SynopsisAn introduction to the Calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.Table of ContentsI. Introduction Part 1. Historical Introduction Part 2. Some Basic Concepts of the theory of sets Part 3. A set of Axioms for the Real-Number System Part 4. Mathematical Induction, Summation Notation,and Related Topics 1. The Concepts of Integral Calculus 2. Some Applications of Integration 3. Continuous Functions 4. Differential Calculus 5. The Relation Between Integration and Differentiation 6. The Logarithm,the Exponential,and the Inverse Trigonmetric Functions 7. Polynomial Approximations to Functions 8. Introduction to Differential Equations 9. Complex Numbers 10. Sequences, Infinite Series, Improper Integrals 11. Sequences and Series of functions 12. Vector algebra 13. Applications of Vector Algebra to Analytic Geometry 14. Calculus of Vector Valued Functions 15. Linear Spaces 16. Linear Transformations and Matrices Answers to exercises 617 Index 657

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Book SynopsisThe volumes of Organic Reactions are collections of chapters each devoted to a single reaction, or a definite phase of a reaction, of wide applicability. The material is treated from a preparative viewpoint, with emphasis on limitations, interfering influences, effects of structure, and the selection of experimental techniques. Numerous detailed procedures illustrate the significant modifications of each method. Includes tables that contain all possible examples of the reaction under consideration.Table of Contents1. The Alkylation of Aromatic Compounds by the Friedel-Crafts Method--Charles C. Price 2. The Willgerodt Reaction--Marvin Carmack and M. A. Spielman 3. Preparation of Ketenes and Ketene Dimers--W. E. Hanford and John C. Sauer 4. Direct Sulfonation of Aromatic Hydrocarbons and Their Halogen Derivatives--C. M. Suter and Arthur W. Weston 5. Azlactones--H. E. Carter 6. Substitution and Addition Reactions of Thiocyanogen--John L. Wood 7. The Hofmann Reaction--Everett S. Wallis and John F. Lane 8. The Schmidt Reaction--Hans Wolff 9. The Curtius Reaction--Peter A. S. Smith Index

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Book SynopsisFinite mixture models are typically used where the population being studied is heterogeneous in composition. This work aims to offer an up-to-date account of the major issues involved with finite modelling. There is a practical emphasis on the applications of mixture models.Trade Review"This is an excellent book.... I enjoyed reading this book. I recommend it highly to both mathematical and applied statisticians." (Technometrics, February 2002) "This book will become popular to many researchers...the material covered is so wide that it will make this book a standard reference for the forthcoming years." (Zentralblatt MATH, Vol. 963, 2001/13) "the material covered is so wide that it will make this book a standard reference for the forthcoming years." (Zentralblatt MATH, Vol.963, No.13, 2001) "This book is excellent reading...should also serve as an excellent handbook on mixture modelling..." (Mathematical Reviews, 2002b) "...contains valuable information about mixtures for researchers..." (Journal of Mathematical Psychology, 2002) "...a masterly overview of the area...It is difficult to ask for more and there is no doubt that McLachlan and Peel's book will be the standard reference on mixture models for many years to come." (Statistical Methods in Medical Research, Vol. 11, 2002) "...they are to be congratulated on the extent of their achievement..." (The Statistician, Vol.51, No.3)Table of ContentsGeneral Introduction. ML Fitting of Mixture Models. Multivariate Normal Mixtures. Bayesian Approach to Mixture Analysis. Mixtures with Nonnormal Components. Assessing the Number of Components in Mixture Models. Multivariate t Mixtures. Mixtures of Factor Analyzers. Fitting Mixture Models to Binned Data. Mixture Models for Failure-Time Data. Mixture Analysis of Directional Data. Variants of the EM Algorithm for Large Databases. Hidden Markov Models. Appendices. References. Indexes.

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Book SynopsisThe volumes of Organic Reactions are collections of chapters each devoted to a single reaction, or a definite phase of a reaction, of wide applicability. The material is treated from a preparative viewpoint, with emphasis on limitations, interfering influences, effects of structure, and the selection of experimental techniques. Numerous detailed procedures illustrate the significant modifications of each method. Includes tables that contain all possible examples of the reaction under consideration.Table of Contents1. Catalytic Hydrogenation of Esters to Alcohols--The Late HomerAdkins 2. The Synthesis of Ketones from Acid Halides and OrganometallicCompounds of Magnesium, Zinc, and Cadmium--David A. Shirley 3. The Acylation of Ketones to form beta-Diketones or beta-KetoAldehydes--Charles R. Hauser, Frederic W. Swamer, and Joe T.Adams 4. The Sommelet Reaction--S. J. Angyal 5. The Synthesis of Aldehydes from Carboxylic Acids--ErichMosettig 6. The Metalation Reaction with Organolithium Compounds--HenryGilman and John W. Morton, Jr. 7. beta-Lactones--Harold E. Zaugg 8. The Reaction of Diazomethane and Its Derivatives with Aldehydesand Ketones--C. David Gutsche Index

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Book SynopsisH.S.M. Coxeter is one of the world''s best-known mathematicians who wrote several papers and books on geometry, algebra and topology, and finite mathematics. This book is being published in conjunction with the 50th anniversary of the Canadian Mathematical Society and it is a collection of 26 papers written by Dr. Coxeter.Table of ContentsPartial table of contents: The Nine Regular Solids. The Regular Sponges, or Skew Polyhedra. Two Aspects of the Regular 24-Cell. The Densities of the Regular Polytopes I. The Densities of theRegular Polytopes II. The Densities of the Regular Polytopes III. A Challenging Definite Integral. Groups Whose Fundamental Regions Are Simplexes. Discrete Groups Generated by Reflections. Finite Groups Generated by Reflections, and Their SubgroupsGenerated by Reflections. Orthogonal Trees. The Product of the Generators of a Finite Group Generated byReflections. Extreme Forms. Regular and Semi-Regular Polytopes I. Regular and Semi-RegularPolytopes II. Regular and Semi-Regular Polytopes III. Factor Groups of the Braid Group. Finite Groups Generated by Unitary Reflections. Index.

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Book SynopsisAnalysis of Ordinal Categorical Data Alan Agresti Statistical Science Now has its first coordinated manual of methods for analyzing ordered categorical data. This book discusses specialized models that, unlike standard methods underlying nominal categorical data, efficiently use the information on ordering.Table of ContentsModel Notation, Covariances, and Path Analysis. Causality and Causal Models. Structural Equation Models with Observed Variables. The Consequences of Measurement Error. Measurement Models: The Relation Between Latent and ObservedVariables. Confirmatory Factor Analysis. The General Model, Part I: Latent Variable and Measurement ModelsCombined. The General Model, Part II: Extensions. Appendices. Distribution Theory. References. Index.

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