Posterior likelihood ratios for evaluation of forensic trace evidence given a two-level model on the data

In forensic science, in order to determine whether sets of traces are from the same source or not, it is widely advocated to evaluate evidential value of similarity of the traces by likelihood ratios (LRs). If traces are expressed by measurements following a two-level model with random effects and known variances, closed LR formulas are available given normality, or kernel density distributions, on the effects. For the known variances estimators are used though, which leads to uncertainty on the resulting LRs which is hard to quantify. The above is analyzed in an approach in which both effects and variances are random, following standard prior distributions on univariate data, leading to posterior LRs. For non-informative and conjugate priors, closed LR formulas are obtained that are interesting in structure and generalize a known result given fixed variance. A semi-conjugate prior on the model seems usable in many applications. It is described how to obtain credible intervals using Monte Carlo Markov Chain and regular simulation, and an example is described for comparison of XTC tablets based on MDMA content. In this way, uncertainty on LR estimation is expressed more clearly which makes the evidential value more transparent in a judicial context.