  In forensic DNA calculations of relatedness of individuals and in DNA mixture
analyses, two sources of uncertainty are present concerning the allele
frequencies used for evaluating genotype probabilities when evaluating
likelihoods. They are: (i) imprecision in the estimates of the allele
frequencies in the population by using an inevitably finite database of DNA
profiles to estimate them; and (ii) the existence of population substructure.
Green and Mortera (2009) showed that these effects may be taken into account
individually using a common Dirichlet model within a Bayesian network
formulation, but that when taken in combination this is not the case; however
they suggested an approximation that could be used. Here we develop a slightly
different approximation that is shown to be exact in the case of a single
individual. We demonstrate the closeness of the approximation numerically using
a published database of allele counts, and illustrate the effect of
incorporating the approximation into calculations of a recently published
statistical model of DNA mixtures.
