Franco Taroni

How can the forensic scientist rationally justify performing a sequence of tests and analyses in a particular case? When is it worth performing a test or analysis on an item? Currently, there is a large void in logical frameworks for making rational decisions in forensic science. The aim of this paper is to fill this void by presenting a step-by-step guide on how to apply Bayesian decision theory to routine decision problems encountered by forensic scientists on performing or not performing a particular laboratory test or analysis. A decision-theoretic framework, composed of actions, states of nature, and utilities, models this problem, and an influence diagram translates its notions into a probabilistic graphical network. Within this framework, the expected value of information (EVOI) for the submission of an item to a particular test or analysis addresses the above questions. The development of a classical case example on whether to perform presumptive tests for blood before submitting the item for a DNA analysis illustrates the use of this model for source level questions in forensic biology (i.e., questions that ask whether a crime stain consisting of a particular body fluid comes from a particular person). We show how to construct an influence diagram for this example, and how sensitivity analyses lead to an optimal analytical sequence. The key idea is to show that such a Bayesian decisional approach provides a coherent framework for justifying the optimal analytical sequence for a particular case in forensic science.

The Bayesian perspective is based on conditioning related to reported evidence that is considered to be certain. What is called ‘Radical Probabilism’ replaces such an extreme view by introducing uncertainty on the reported evidence. How can such equivocal evidence be used in further inferences about a main hypothesis? The theoretical ground is introduced with the aim of offering to the readership an explanation for the generalization of the Bayes’ Theorem. This extension—that considers uncertainty related to the reporting of evidence—also has an impact on the assessment of the value of evidence through the Bayes’ factor. A generalization for such a logical measure of the evidence is also presented and justified.

The analysis of inferential interactions plays an important role in the description of the line of reasoning for a forensic evaluator in a case involving the cross-transfer of evidence. It is possible the two items of evidence may mean more to an evaluator when considered jointly than they do if considered separately. An approach to the evaluation of evidence, with particular attention to the factors that need to be considered, is described for a case involving the cross-transfer of evidence. A formula is given which may be used to define the possible interactions between the evidence transferred in each direction and hence ease the interpretation of such evidence. Numerical examples are given from a classical fibre evidence scenario.

This paper focuses on the normative analysis—in the sense of the classic decision-theoretic formulation—of decision problems that arise in connection with forensic expert reporting. We distinguish this analytical account from other common types of decision analyses, such as descriptive approaches. While decision theory is, since several decades, an extensively discussed topic in legal literature, its use in forensic science is more recent, and with an emphasis on goals such as the analysis of the logical structure of forensic expert conclusions regarding, for example, propositions of common source of evidential and known materials. Typical examples are so-called identification decisions, especially categorical conclusions according to which fingermarks come from a particular a person of interest. We will present and compare ways of stating forensic identification decisions in decision-theoretic terms and explain their underlying rationale. In particular, we will emphasize the importance of viewing this analysis as normative in the sense of providing a reflective rather than a prescriptive reference point against which people in charge of forensic identification decisions may compare their otherwise intuitive and informal reasoning, before acting. Normative decision analysis in forensic science thus provides a vector through which current practice can be articulated, scrutinized and rethought.

The use of the Bayes factor (BF) or likelihood ratio as a metric to assess the probative value of forensic traces is largely supported by operational standards and recommendations in different forensic disciplines. However, the progress towards more widespread consensus about foundational principles is still fragile as it raises new problems about which views differ. It is not uncommon e.g. to encounter scientists who feel the need to compute the probability distribution of a given expression of evidential value (i.e. a BF), or to place intervals or significance probabilities on such a quantity. The article here presents arguments to show that such views involve a misconception of principles and abuse of language. The conclusion of the discussion is that, in a given case at hand, forensic scientists ought to offer to a court of justice a given single value for the BF, rather than an expression based on a distribution over a range of values.

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 problem