Setting bounds for the likelihood ratio when multiple hypotheses are postulated

The interpretation of mixtures of DNA in the forensic context presents particular challenges. The only logical means available for dealing with them is through Bayesian inference, which leads to the formulation, in most cases, of a likelihood ratio which weighs the evidence in favour of two competing hypotheses. However, situations can arise in which additional hypotheses are proposed and the authors discuss one such situation--that where the number of contributors to the mixture is in dispute. A way of dealing with the problem is presented.