Consistent estimation of Y STR haplotype probabilities

Many methods have been proposed to estimate Y-STR haplotype probabilities in a population, but no consensus has been achieved. In this paper a consistency principle for statistical models to provide such probabilities is proposed, in which it is required that the probability of a given haplotype profile on n loci cannot exceed that of any sub-haplotype matching on any n - 1 or fewer loci. If this consistency principle is violated by a Y haplotype probability model, then it could render the presentation of such probabilities highly problematic in a courtroom setting. We show, using publicly available datasets and two recently proposed graphical models for estimating probabilities of Y-STR haplotypes for illustration, that such violations can occur, and that the violations can in some instances be quite large. Some implications of this are discussed.