Bayes Factors for Forensic Decision Analyses with R

ISBN-13: 9783031098413 / Angielski / Miękka / 2023

Silvia Bozza;Franco Taroni;Alex Biedermann

Opis

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.

Spis treści

Part I - Introduction to the Bayes Factor (Likelihood Ratio)

Presents the principal statistic discussed throughout this book:  the Bayes factor, in the context of forensic science, more often known as the likelihood ratio.  Subsections of this part:

• clarify the different roles (known as, respectively, the ‘investigative’ and ‘evaluative’ role) that forensic scientists may assume in their daily work
  
• articulate the reasons why forensic scientists should adhere to a Bayesian framework of inference in order to ensure coherence in their inferential and decision-making tasks
  
• formally describe what the Bayes factor is and how it relates to coherent decision analysis
  
• describe the advantages that Bayes factors offer in assessing, articulating and communicating the value of scientific evidence in general, and in legal proceedings in particular
  

Part II - Bayes Factor for I

nvestigative Purposes

Deals with a peculiar task of the forensic scientist, known as the ‘investigative mode’ (i.e., one of the two main modes of functioning introduced in Part I). That is, in forensic settings, it may well be the case that a potential source (i.e., a suspect) is not available for comparative purposes, in particular in early stages of the legal process.  Notwithstanding, data and measurements on recovered material (e.g., seized on a crime scene) can be used for an investigative purpose.  In this mode of working, scientists can offer to investigative authorities (or, in a more general perspective, mandating parties) information to help discriminate between general propositions concerning, for instance, the characterizing features of the source that left the recovered material (e.g., gender, externally visible traits such as hair and eye color, handedness, etc.).  At this stage in the process, the scientist tries to help answer questions such

as ‘what  happened?’ in the case under investigation, or ‘what can we infer about the offender?’. In this context, the Bayes factor can be used as a statistic to measure and help decide how to classify, for example, objects and substances on which measurements have been made. This use of the Bayes factor will be explained through practical examples involving topics such as handwriting characteristics, toner from printers in questioned document examination, drugs of abuse, toxicology, forensic anthropology and forensic DNA profiling (listing is not exhaustive and may evolve during the writing of the book).  Both univariate and multivariate data will be considered, with or without replicates, and involving different statistical distributions (i.e. Binomial, Poisson, Normal, etc.).  The examples refer to realistic forensic applications as they may be encountered in judicial contexts and the forensic practitioner’s own field of activity.  Data will be selected from published literature or from the author’s own records.  R sample code will be specified and explanations will be included on how to interpret results in context and convey their meaning appropriately.

Part III - Bayes Factor for Evaluative Purposes

Focuses on the scientist’s role in a more advanced stage of the legal process.  That is, situations in which the evaluation of scientific findings will take into account a potential source of the recovered material (e.g., a suspect or an  object/tool).  This kind of reporting is typically required when scientists need to communicate their results for use at trial.  It is of utmost importance at this juncture that scientists express the value of the observed data and findings under competing hypotheses, focusing on a potential (i.e., known) source versus an  alternative source (e.g., propositions such as ‘the recovered item comes from the same source as the control

material’, and ‘the recovered item is from a source that is different from that of the control material’).  The Bayes factor is the central inferential concept for such expressions of weight of evidence.  In this part of the book, too, examples will be chosen with the intention to reflect realistic scenarios as they may arise in current judicial practice.  In particular, the outline will consider uni- and multi­-variate data from scenarios related to microtraces (e.g., glass and paint fragments), handwriting and drugs of abuse.  Besides computational R code, this chapter will also include (i) sensitivity analyses to provide readers with a means to further investigate the properties of the proposed evaluative procedures based on the Bayes factor, and (ii) decision theoretic extensions to outline how to interface expressions of weight of evidence with the broader perspective of coherent decision-making.  

Part IV - Conclusion

Summarizes the key messages developed throughout this book, emphasizing (i) the contribution of an extended use of the Bayes factor in a normative decision framework, and (ii) the role of the Bayes factor as the relevant statistic for both investigative and evaluative tasks that characterize current forensic science.

O autorze

Silvia Bozza is Associate Professor of Statistics at Ca' Foscari University of Venice (Italy), Department of Economics and Senior Researcher at the University of Lausanne (School of Criminal Justice). Her research interests are mainly focused on Bayesian modelling, decision theory and probabilistic graphical models with applications in forensic science. 

Franco Taroni is Full Professor of Forensic Statistics at the Faculty of Law, Criminal Justice and Public Administration, School of Criminal Justice, of the University of Lausanne (Switzerland). He publishes extensively in the area of probabilistic reasoning, decision making and data analysis in forensic science.

Alex Biedermann is Associate Professor at the Faculty of Law, Criminal Justice and Public Administration, School of Criminal Justice, of the University of Lausanne (Switzerland). He researches and teaches in the area of evidential reasoning and decision making at the intersection between forensic science and the law. His work is multidisciplinary and pertains to forensic science, law and topics in probability and decision theory.