Data Analysis in Forensic Science A Bayesian Decision Perspective

• Main Authors: Taroni, Franco, Aitken, Colin, Biedermann, Alex, Bozza, Silvia, Garbolino, Paolo
• Format: eBook
• Language: English
• Published: Newark Wiley 2010; WILEY; John Wiley & Sons, Incorporated; Wiley-Blackwell
• Edition: 1. Aufl.
• Series: Statistics in practice
• Subjects: Bayesian statistical decision theory; Forensic sciences; MATHEMATICS; Probability & Statistics; Statistical methods; Technik; Wissen Statistik
• ISBN: 9780470998359; 0470998350; 0470665076; 9780470665077
• DOI: 10.1002/9780470665084

This 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 likeliho...

Table of Contents:

• Data analysis in forensic science : a bayesian decision perspective -- Contents -- Foreword -- Preface -- Part I: The Foundations of Inference and Decision in Forensic Science -- 1. Introduction -- 2. Scientific Reasoning and Decision Making -- Part II: Forensic Data Analysis -- 4. Point Estimation -- 5. Credible Intervals -- 6. Hypothesis Testing -- 7. Sampling -- 8. Classification of Observations -- 9. Bayesian Forensic Data Analysis: Conclusions and Implications -- Appendix A: Discrete Distributions -- Appendix B: Continuous Distributions -- Bibliography -- Author Index -- Subject Index
• 3.3 The Bayesian Paradigm -- 3.3.1 Sequential use of Bayes' theorem -- 3.3.2 Principles of rational inference in statistics -- 3.3.3 Prior distributions -- 3.3.4 Predictive distributions -- 3.3.5 Markov Chain Monte Carlo methods (MCMC) -- 3.4 Bayesian Decision Theory -- 3.4.1 Optimal decisions -- 3.4.2 Standard loss functions -- 3.5 R Code -- II Forensic Data Analysis -- 4 Point Estimation -- 4.1 Introduction -- 4.2 Bayesian Decision for a Proportion -- 4.2.1 Estimation when there are zero occurrences in a sample -- 4.2.2 Prior probabilities -- 4.2.3 Prediction -- 4.2.4 Inference for 0 in the presence of background data on the number of successes -- 4.2.5 Multinomial variables -- 4.3 Bayesian Decision for a Poisson Mean -- 4.3.1 Inference about the Poisson parameter in the absence of background events -- 4.3.2 Inference about the Poisson parameter in the presence of background events -- 4.3.3 Forensic inference using graphical models -- 4.4 Bayesian Decision for Normal Mean -- 4.4.1 Case with known variance -- 4.4.2 Case with unknown variance -- 4.4.3 Estimation of the mean in the presence of background data -- 4.5 R Code -- 5 Credible Intervals -- 5.1 Introduction -- 5.2 Credible Intervals and Lower Bounds -- 5.3 Decision-Theoretic Evaluation of Credible Intervals -- 5.4 R Code -- 6 Hypothesis Testing -- 6.1 Introduction -- 6.2 Bayesian Hypothesis Testing -- 6.2.1 Posterior odds and Bayes factors -- 6.2.2 Decision-theoretic testing -- 6.3 One-Sided Testing -- 6.3.1 Background -- 6.3.2 Proportion -- 6.3.3 A note on multinomial cases (k categories) -- 6.3.4 Mean -- 6.4 Two-Sided Testing -- 6.4.1 Background -- 6.4.2 Proportion -- 6.4.3 Mean -- 6.5 R Code -- 7 Sampling -- 7.1 Introduction -- 7.2 Sampling inspection -- 7.2.1 Background -- 7.2.2 Large consignments -- 7.2.3 Small consignments -- 7.3 Graphical Models for Sampling Inspection
• 7.3.1 Preliminaries -- 7.3.2 Bayesian network for sampling from large consignments -- 7.3.3 Bayesian network for sampling from small consignments -- 7.4 Sampling Inspection under a Decision-Theoretic Approach -- 7.4.1 Fixed sample size -- 7.4.2 Sequential analysis -- 7.4.3 Sequential probability ratio test -- 7.5 R Code -- 8 Classification of Observations -- 8.1 Introduction -- 8.2 Standards of Coherent Classification -- 8.3 Comparing Models using Discrete Data -- 8.3.1 Binomial distribution and cocaine on bank notes -- 8.3.2 Poisson distributions and firearms examination -- 8.4 Comparison of Models using Continuous Data -- 8.4.1 Normal distribution and colour dye (case with known variance) -- 8.4.2 A note on the robustness of the likelihood ratio -- 8.4.3 Normal distribution and questioned documents (case with known variance) -- 8.4.4 Normal distribution and sex determination (case with unknown variance) -- 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
• Intro -- Data Analysis in Forensic Science -- Contents -- Foreword -- 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 -- 2.1.1 A rational betting policy -- 2.1.2 A rational policy for combining degrees of belief -- 2.1.3 A rational policy for changing degrees of belief -- 2.2 Coherent Decision Making Under Uncertainty -- 2.2.1 A method for measuring the value of consequences -- 2.2.2 The consequences of rational preferences -- 2.2.3 Intermezzo: some more thoughts about rational preferences -- 2.2.4 The implementation of coherent decision making under uncertainty: Bayesian networks -- 2.2.5 The connection between pragmatic and epistemic standards of reasoning -- 2.3 Scientific Reasoning as Coherent Decision Making -- 2.3.1 Bayes' theorem -- 2.3.2 The theories' race -- 2.3.3 Statistical reasoning: the models' race -- 2.3.4 Probabilistic model building: betting on random quantities -- 2.4 Forensic Reasoning as Coherent Decision Making -- 2.4.1 Likelihood ratios and the 'weight of evidence' -- 2.4.2 The expected value of information -- 2.4.3 The hypotheses' race in the law -- 3 Concepts of Statistical Science and Decision Theory -- 3.1 Random Variables and Distribution Functions -- 3.1.1 Univariate random variables -- 3.1.2 Measures of location and variability -- 3.1.3 Multiple random variables -- 3.2 Statistical Inference and Decision Theory -- 3.2.1 Utility theory -- 3.2.2 Maximizing expected utility -- 3.2.3 The loss function