Bayesian Networks and Influence Diagrams

Bayesian networks are graphical models that have been developed in the field of artificial intelligence as a framework to help researchers and practitioners apply probability theory to inference problems of substantive size as encountered in real-world applications. Influence diagrams (Bayesian decision networks) extend Bayesian networks to a modeling environment for coherent decision analysis under uncertainty. This article provides an overview of these methods and explains their contribution to the body of formal methods for the study, development and implementation of probabilistic procedures for assessing the probative value of scientific evidence and the coherent analysis of related questions of decision-making

Bayesian networks and dissonant items of evidence: A case study

The assessment of different items of evidence is a challenging process in forensic science, particularly when the relevant elements support different inferential directions. In this study, a model is developed to assess the joint probative value of three different analyses related to some biological material retrieved on an object of interest in a criminal case. The study shows the ability of probabilistic graphical models, say Bayesian networks, to deal with complex situations, those that one expects to face in real cases. The results obtained by the model show the importance of a conflict measure as an indication of inconsistencies in the model itself. A contamination event alleged by the defense is also introduced in the model to explain and solve the conflict. The study aims to give an insight in the application of a probabilistic model to real criminal cases

A probabilistic graphical model for assessing equivocal evidence

The Bayes’ theorem can be generalized to account for uncertainty on reported evidence. This has an impact on the value of the evidence, making the computation of the Bayes factor more demanding, as discussed by Taroni, Garbolino, and Bozza (2020). Probabilistic graphical models can however represent a suitable tool to assist the scientist in their evaluative task. A Bayesian network is proposed to deal with equivocal evidence and its use is illustrated through examples

The Role of the Bayes Factor in the Evaluation of Evidence

The use of the Bayes factor as a metric for the assessment of the probative value of forensic scientific evidence is largely supported by recommended standards in different disciplines. The application of Bayesian networks enables the consideration of problems of increasing complexity. The lack of a widespread consensus concerning key aspects of evidence evaluation and interpretation, such as the adequacy of a probabilistic framework for handling uncertainty or the method by which conclusions regarding how the strength of the evidence should be reported to a court, has meant the role of the Bayes factor in the administration of criminal justice has come under increasing challenge in recent years. We review the many advantages the Bayes factor has as an approach to the evaluation and interpretation of evidence

Bayes Factors for Forensic Decision Analyses with R

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

Statistical Interpretation of Evidence: Bayesian Analysis

Probability theory provides the general framework within which assignments of probabilities of past, present, and future events are coherently modified in the light of observed events or, more generally, new information. Forensic scientists, as an illustrative example, routinely face tasks of reasoning under uncertainty when they seek to assist members of the judiciary in evaluating or interpreting the meaning of items of scientific evidence. As a consequence of the laws of probability theory and related concepts, Bayes’ theorem is the key rule according to which to conduct such reasoning in order to comply with the requirement of rationality. This quantification, though, does not represent the end of the matter as the forensic scientist may also be confronted with questions of how to make a rational choice amongst alternative courses of action. This article presents the role of Bayes’ theorem, and its extension to decision analysis, in categorical and continuous data analysis in forensic science applications. It emphasizes the importance of propositional hierarchies, the role of background information, the interpretation of probability as personal degrees of belief and the personal quantification of the consequences of decisions. The discussion also includes a sketch of some common pitfalls of intuition associated with probabilistic reasoning in legal contexts

A generalised Bayes' factor formula for evidence evaluation under activity level propositions: variations around a fibres scenario

Generalised Bayes' factors and associated Bayesian networks are developed for the transfer of extrinsic evidence at the activity level, developments that extend previous work on activity level evaluation. A strategy for the assessment of extrinsic evidence is developed in stages with progressive increases in complexity. The final development is illustrated with an example involving fibres from clothing. This provides a list of factors involved in the consideration of a transfer case with activity level propositions and their roles in the determination of evidential value

Bayes Factors for Forensic Decision Analyses with R

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

Modeling the forensic two-trace problem with Bayesian networks

The forensic two-trace problem is a perplexing inference problem introduced by Evett (J Forensic Sci Soc 27:375-381, 1987). Different possible ways of wording the competing pair of propositions (i.e., one proposition advanced by the prosecution and one proposition advanced by the defence) led to different quantifications of the value of the evidence (Meester and Sjerps in Biometrics 59:727-732, 2003). Here, we re-examine this scenario with the aim of clarifying the interrelationships that exist between the different solutions, and in this way, produce a global vision of the problem. We propose to investigate the different expressions for evaluating the value of the evidence by using a graphical approach, i.e. Bayesian networks, to model the rationale behind each of the proposed solutions and the assumptions made on the unknown parameters in this proble