Taroni F., Bozza S., Biedermann A., Garbolino P., Aitken C. Data Analysis in Forensic Science: A Bayesian Decision Perspective

N.-Y.: Wiley, 2010.- 390 p.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 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.Throughout this practical appraisal there are a wide variety of examples taken from the routine work of forensic scientists. These applications are demonstrated in the ever-more popular R language. The reader is taken through these applied examples in a step-by-step approach, discussing the methods at each stage.The Foundations of Inference and Decision in Forensic ScienceThe Inevitability of Uncertainty
Desiderata in Evidential Assessment
The Importance of the Propositional Framework and the Nature of Evidential Assessment
From Desiderata to Applications
The Bayesian Core of Forensic Science
Structure of the BookCoherent Reasoning Under Uncertainty
A rational betting policy
A rational policy for combining degrees of belief
A rational policy for changing degrees of belief
A method for measuring the value of consequences
The consequences of rational preferences
Intermezzo: some more thoughts about rational preferences
The implementation of coherent decision making under uncertainty: Bayesian networks
The connection between pragmatic and epistemic standards of reasoning
Scientific Reasoning as Coherent Decision Making
Bayes’ theorem
The theories’ race
Statistical reasoning: the models’ race
Probabilistic model building: betting on random quantities
Likelihood ratios and the ‘weight of evidence’
The expected value of information
The hypotheses’ race in the lawUnivariate random variables
Multiple random variables
Statistical Inference and Decision Theory
Utility theory
Maximizing expected utility
The loss function
The Bayesian Paradigm
Sequential use of Bayes’ theorem
Principles of rational inference in statistics
Prior distributions
Predictive distributions
Markov Chain Monte Carlo methods (MCMC)
Bayesian Decision Theory
Optimal decisions
Standard loss functions
R CodeForensic Data AnalysisBayesian Decision for a Proportion
Estimation when there are zero occurrences in a sample
Prior probabilities
Prediction
Inference for in the presence of background data on the number of successes
Multinomial variables
Inference about the Poisson parameter in the absence of background events
Inference about the Poisson parameter in the presence of background events
Forensic inference using graphical models
Bayesian Decision for Normal Mean
Case with known variance
Case with unknown variance
Estimation of the mean in the presence of background data
R CodeCredible Intervals and Lower Bounds
Decision-Theoretic Evaluation of Credible Intervals
R CodePosterior odds and Bayes factors
Decision-theoretic testingProportion
A note on multinomial cases (k categories)
MeanProportion
Mean
R CodeLarge consignments
Small consignments
Bayesian network for sampling from large consignments
Bayesian network for sampling from small consignments
Fixed sample size
Sequential analysis
Sequential probability ratio test
R CodeStandards of Coherent Classification
Binomial distribution and cocaine on bank notes
Poisson distributions and firearms examination
Normal distribution and colour dye (case with known variance)
A note on the robustness of the likelihood ratio
Normal distribution and questioned documents (case with known variance)
Normal distribution and sex determination (case with unknown variance)
Non-Normal Distributions and Cocaine on Bank Notes
A Note on Multivariate Continuous Data
R CodeWhat is the Past and Current Position of Statistics in Forensic Science?
Why Should Forensic Scientists Conform to a Bayesian Framework for Inference and Decision Making?
Why Regard Probability as a Personal Degree of Belief?
Why Should Scientists be Aware of Decision Analysis?
How to Implement Bayesian Inference and Decision Analysis?Discrete Distributions
Continuous Distributions