Contributors are a nuisance (parameter) for DNA mixture evidence evaluation

Recently, a debate has arisen around the number of contributors postulated in hypotheses for the purpose of weight of evidence calculations on DNA mixture profiles. Specifically the issue at stake is whether or not one should have the same number of contributors under both hypotheses for which a likelihood ratio is calculated. In this paper we aim to clarify this issue. We take the general approach of considering the number of contributors as a nuisance parameter. Two central assumptions then determine the form of the overall likelihood ratio: whether the prior distributions of the nuisance parameter are equivalent given both hypotheses and whether they depend on the hypotheses. Examples are given for both scenarios where we have either independence or strong dependence between the prior distributions of the number of contributors and the hypotheses. Moreover, examples for different kinship scenarios are presented. In conclusion, the overall likelihood ratio does not only depend on likelihood ratios for fixed values of the nuisance parameter but may also vary considerably with different prior distributions.