Bayesian networks and probabilistic reasoning about scientific evidence when there is a lack of data

Abstract

Bayesian networks (BNs) are a kind of graphical model that formally combines elements of graph and probability theory. BNs are a mathematically and statistically rigorous technique allowing their user to define a pictorial representation of assumed dependencies and influences among a set of variables deemed to be relevant for a particular inferential problem. The formalism allows one to process newly acquired evidence according to the rules of probability calculus. Applications of BNs have been reported in various forensic disciplines. However, there seems to be some reluctance to consider BNs as a more general framework for representing and evaluating sources of uncertainties associated with scientific evidence. Notably, BNs are widely thought of as an essentially numerical method, requiring “exact” numbers with a high “accuracy”. The present paper aims to draw the reader's attention to the point that the availability of hard numerical data is not a necessary requirement for using BNs in forensic science. An abstraction of quantitative BNs, known as qualitative probabilistic networks (QPNs), and sensitivity analyses are presented and their potential applications discussed. As a main difference to their quantitative counterpart, QPNs contain qualitative probabilistic relationships instead of numerical relations. Sensitivity analyses consist of varying the probabilities assigned to one or more variables and evaluating the effect on one or more other variables of interest. Both QPNs and sensitivity analyses appear to be useful concepts that permit one to work in contexts with acute lack of numerical data and where reasoning consistent with the laws of probability should nevertheless be performed.