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 Investigative PurposesDeals 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 PurposesFocuses 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 - ConclusionSummarizes 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.
