Statistical Interpretation of Evidence: Bayesian Analysis

Résumé 0

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.