Talk Title: Analyzing genetic mixtures using reversible-jump Markov chain Monte Carlo

Presenter: Eric C. Anderson

Affil: University of Washington, Seattle, WA USA.

 I will describe my work in progress of using RJMCMC to do Bayesian inference on genetic mixtures with an unknown number of components. We assume that each individual in the mixture arose from a single, randomly-mating component population in which there is no linkage disequilibrium. The number of such components, $k$ is unknown, and the allele frequencies in the component populations are also unknown. Our first goal is to compute posterior probabilities for $k$. Additionally, for each value of $k$, we desire posterior probabilities for the allele frequencies and mixture proportions of the component populations and for the posterior probability that any individual in the mixture originated from a particular component.

The bulk of the talk will deal with the implementation of a split-combine sort of reversible-jump move. I will first describe this in the context of a toy problem (which is essentially the ``single-diallelic-locus" case), and then demonstrate some of the problems encountered while extending the method to situations with multiple loci and multiple alleles. I propose an approach for overcoming these problems which may be useful for implementing RJMCMC in other mixture problems in which the component-specific parameters are of high dimension.