Competing explanations in Bayesian networks - The small town murder problem revisited

The use of probability theory and statistical reasoning in legal contexts is controversial, with several well-known thought experiments highlighting perceived paradoxes. One example is the small town murder problem, recently discussed by de Zoete et al., who argued that the perceived paradoxes arise from a failure to properly distinguish between hypotheses and evidence, and can be resolved using Bayesian networks. While we agree with their general conclusions, we contend that their analysis of the small town murder problem overlooks a central issue and underutilizes the full potential of Bayesian modeling. In this note, we propose an alternative analysis of the problem, drawing on well-known results on conditioning on a common effect of two factors.