I attended a fairly interesting forensic science session at SimStat 2019 in Salzburg as it concentrated on evidence and measures of evidence rather than on strict applications of Bayesian methodology to forensic problems. Even though American administrations like the FBI or various police departments were involved. It was a highly coherent session and I had a pleasant discussion with some of the speakers after the session. For instance, my friend Alicia Carriquiry presented an approach to determined from images of bullets whether or not they have been fired from the same gun, leading to an interesting case for a point null hypothesis where the point null makes complete sense. The work has been published in Annals of Applied Statistics and is used in practice. The second talk by Danica Ommen on fiducial forensics on IED, asking whether or not copper wires used in the bombs are the same, which is another point null illustration. Which also set an interesting questioning on the dependence of the alternative prior on the distribution of material chosen as it is supposed to cover all possible origins for the disputed item. But more interestingly this talk launched into a discussion of making decision based on finite samplers and unknown parameters, not that specific to forensics, with a definitely surprising representation of the Bayes factor as an expected likelihood ratio which made me first reminiscent of Aitkin’s (1991) infamous posterior likelihood (!) before it dawned on me this was a form of bridge sampling identity where the likelihood ratio only involved parameters common to both models, making it an expression well-defined under both models. This identity could be generalised to the general case by considering a ratio of integrated likelihoods, the extreme case being the ratio equal to the Bayes factor itself. The following two talks by Larry Tang and Christopher Saunders were also focused on the likelihood ratio and their statistical estimates, debating the coherence of using a score function and presenting a functional ABC algorithm where the prior is a Dirichlet (functional) prior. Thus a definitely relevant session from a Bayesian perspective!
