Computational aspects of DNA mixture analysis - Exact inference using auxiliary variables in a Bayesian network

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.