Posterior distributions for likelihood ratios in forensic science

Evaluation of evidence in forensic science is discussed using posterior distributions for likelihood ratios. Instead of eliminating the uncertainty by integrating (Bayes factor) or by conditioning on parameter values, uncertainty in the likelihood ratio is retained by parameter uncertainty derived from posterior distributions. A posterior distribution for a likelihood ratio can be summarised by the median and credible intervals. Using the posterior mean of the distribution is not recommended. An analysis of forensic data for body height estimation is undertaken. The posterior likelihood approach has been criticised both theoretically and with respect to applicability. This paper addresses the latter and illustrates an interesting application area.