Data Analysis in Forensic Science: A Bayesian Decision Perspective sets forth procedures for data analysis that rely on the decision–theoretic approach to inference. Emphasis is made on foundational philosophical tenets as well as the implications of the decision–theoretic approach in practice. This book discusses a range of statistical decision–theoretic methods that are useful in the analysis of forensic scientific data. Forensic scientific examples include point estimation, the comparison of means and proportions in populations, the choice of sample size and the classification of items of evidence of unknown origin into predefined populations.
- Comprehensive coverage of the analysis of forensic data from a Bayesian perspective, featuring numerous real–world examples and applications.
- Explanation and definition of key concepts and methods from historical, philosophical and theoretical points of view.
- An incremental approach for consideration of examples inspired and motivated by issues that may arise in routine forensic practice.
- Consideration of the arguments and methods, including those of decision theory, used at each stage of the analyses.
- Inclusion of code written in R to offer an opportunity for enhanced exploration of the ideas.
- The use of graphical models (e.g. Bayesian networks) to illustrate selected applications of Bayesian methodology.
I The Foundations of Inference and Decision in Forensic Science.
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.
4.2 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.
5.2 Credible Intervals.
5.3 Decision–Theoretic Evaluation of Credible Intervals.
5.4 R Code.
6 Hypothesis Testing.
6.2 Bayesian Hypothesis Testing.
6.3 One–sided testing.
6.4 Two–Sided Testing.
6.5 R Code.
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.
8.2 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.
9.2 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.