Explicit specification of the prior probability of the prosecutor’s hypothesis in Bayesian networks

Bayesian networks are increasingly popular tools to model legal evidence due to their flexibility, transparency, and intuitive causal interpretation. However, an important challenge is that the prior probability of the prosecutor’s hypothesis—the probability before evidence is considered—is not explicitly specified in the standard framework, but only implicitly through conditional probability tables. This is problematic both for normative reasons, such as the presumption of innocence, and for practical reasons, such as cases where the perpetrator is known to belong to a small suspect group. The only existing approach to address this issue, the ‘reason model’ proposed by Dahlman and Kolflaath, modifies the network so that the variable corresponding to the prosecutor’s hypothesis has no parents. While this makes the prior probability of the prosecutor’s hypothesis explicit, we argue that it introduces artificial independencies that may lead to errors in the analysis. We propose two alternative methods for explicitly specifying the prior probability of the prosecutor’s hypothesis: the direct method and the odds ratio method. The direct method allows analysts to define the prior by reordering probability specifications, while the odds ratio method reparameterizes the conditional distribution of the prosecutor’s hypothesis. We show that both approaches avoid the main pitfalls of reason models, though each introduces its own trade-offs.