Setting the boundaries of prior influence on kinship relation testing: the case of many hypotheses

Kinship relation and, in particular, paternity probability estimation using a Bayesian approach require the input of a priori probabilities of different hypotheses. In practical case work, a priori probabilities or priors, for short, must often be estimated using only common sense and symmetry arguments because in most cases, there is no evidence-based information on which the priors may be determined. In contrast to the accuracy of the likelihood probabilities or the likelihood ratios, the precision of the priors is usually very poor. Thus, a quantitative estimation of the priors' influence on the paternity probability is desirable. This article presents exact formulae to define sharp minimum and maximum boundaries of posterior probabilities as a function of prior boundaries which may be applied in kinship cases with varying numbers of hypotheses and also presents two case examples.