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Bayes Factors for Forensic Decision Analyses with R

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Bayes Factors for Forensic Decision Analyses with R provides a self-contained introduction to computational Bayesian statistics using R. With its primary focus on Bayes factors supported by data sets, this book features an operational perspective, practical relevance, and applicability―keeping theoretical and philosophical justifications limited. It offers a balanced approach to three naturally interrelated topics:

  • Probabilistic Inference - Relies on the core concept of Bayesian inferential statistics, to help practicing forensic scientists in the logical and balanced evaluation of the weight of evidence.
  • Decision Making - Features how Bayes factors are interpreted in practical applications to help address questions of decision analysis involving the use of forensic science in the law.
  • Operational Relevance - Combines inference and decision, backed up with practical examples and complete sample code in R, including sensitivity analyses and discussion on how to interpret results in context.

Over the past decades, probabilistic methods have established a firm position as a reference approach for the management of uncertainty in virtually all areas of science, including forensic science, with Bayes' theorem providing the fundamental logical tenet for assessing how new information―scientific evidence―ought to be weighed. Central to this approach is the Bayes factor, which clarifies the evidential meaning of new information, by providing a measure of the change in the odds in favor of a proposition of interest, when going from the prior to the posterior distribution. Bayes factors should guide the scientist's thinking about the value of scientific evidence and form the basis of logical and balanced reporting practices, thus representing essential foundations for rational decision making under uncertainty.

This book would be relevant to students, practitioners, and applied statisticians interested in inference and decision analyses in the critical field of forensic science. It could be used to support practical courses on Bayesian statistics and decision theory at both undergraduate and graduate levels, and will be of equal interest to forensic scientists and practitioners of Bayesian statistics for driving their evaluations and the use of R for their purposes.

This book is Open Access.


Author(s): Silvia Bozza, Franco Taroni, Alex Biedermann
Series: Springer Texts in Statistics
Publisher: Springer
Year: 2022

Language: English
Pages: 195
City: Cham

Preface
Contents
1 Introduction to the Bayes Factor and Decision Analysis
1.1 Introduction
1.2 Statistics in Forensic Science
1.3 Bayesian Thinking and the Value of Evidence
1.4 Bayes Factor for Model Choice
1.5 Bayes Factor in the Evaluative Setting
1.5.1 Feature-Based Models
1.5.2 Score-Based Models
1.6 Bayes Factor in the Investigative Setting
1.7 Bayes Factor Interpretation
1.8 Computational Aspects
1.9 Bayes Factor and Decision Analysis
1.10 Choice of the Prior Distribution
1.11 Sensitivity Analysis
1.12 Using R
2 Bayes Factor for Model Choice
2.1 Introduction
2.2 Proportion
2.2.1 Inference About a Proportion
2.2.2 Background Elements Affecting Counting Processes
2.2.2.1 Sensitivity to Monte Carlo Approximation
2.2.2.2 Unknown Expected Value of the Number of Background Elements
2.2.3 Decision for a Proportion
2.3 Normal Mean
2.3.1 Inference About a Normal Mean
2.3.1.1 Choosing the Parameters of the Normal Prior for the Mean
2.3.1.2 Sensitivity to the Choice of the Prior Distribution
2.3.2 Continuous Measurements Affected by Errors
2.3.3 Decision for a Mean
2.4 Summary of R Functions
Functions Available in the Base Package
Functions Available in Other Packages
Functions Developed in This Chapter
3 Bayes Factor for Evaluative Purposes
3.1 Introduction
3.2 Evidence Evaluation for Discrete Data
3.2.1 Binomial Model
3.2.2 Multinomial Model
3.2.3 Poisson Model
3.2.3.1 Choosing the Parameters of the Gamma Prior
3.2.3.2 Sensitivity to Prior Probabilities of Competing Propositions
3.3 Evidence Evaluation for Continuous Data
3.3.1 Normal Model with Known Variance
3.3.2 Normal Model with Both Parameters Unknown
Choosing the Parameters of the Normal Prior
3.3.3 Normal Model for Inference of Source
More Than Two Propositions
3.3.4 Score-Based Bayes Factor
3.4 Multivariate Data
3.4.1 Two-Level Models
3.4.1.1 Normal Distribution for the Between-Source Variability
3.4.1.2 Non-normal Distribution for the Between-Source Variability
3.4.1.3 Non-constant Within-Source Variability
3.4.2 Assessment of Method Performance
3.4.3 On the Assumption of Independence Under H2
3.4.4 Three-Level Models
3.5 Summary of R Functions
4 Bayes Factor for Investigative Purposes
4.1 Introduction
4.2 Discrete Data
4.2.1 Binomial Model
4.2.2 Multinomial Model
4.2.2.1 Choosing the Parameters of the Dirichlet Prior
4.2.2.2 More than Two Populations
4.3 Continuous Data
4.3.1 Normal Model and Known Variance
4.3.2 Normal Model and Unknown Variance
4.3.3 Non-Normal Model
Sensitivity to the Choice of the Smoothing Parameter
4.4 Multivariate Data
4.4.1 Normal Multivariate Data
4.4.1.1 Prior Distribution for the Unknown Mean and Variance
4.4.1.2 Classification as a Decision
4.4.2 Two-Level Models
4.4.2.1 Normal Distribution for the Between-Source Variation
4.4.2.2 Non-normal Distribution for the Between-Source Variation
4.4.2.3 Assessing Model Performance
4.5 Summary of R Functions
References
Index