  Statistical analysis of DNA mixtures is known to pose computational
challenges due to the enormous state space of possible DNA profiles. We propose
a Bayesian network representation for genotypes, allowing computations to be
performed locally involving only a few alleles at each step. In addition, we
describe a general method for computing the expectation of a product of
discrete random variables using auxiliary variables and probability propagation
in a Bayesian network, which in combination with the genotype network allows
efficient computation of the likelihood function and various other quantities
relevant to the inference. Lastly, we introduce a set of diagnostic tools for
assessing the adequacy of the model for describing a particular dataset.
