Likelihood-free approaches for Bayesian hierarchical models: applications in population genetics

Mark Beaumont (University of Bristol)

Friday 24th February, 2012 15:00-16:00 Maths 203

Abstract

Many problems in population genetics are usefully addressed through a hierarchical modelling structure. Loci can often be regarded as conditionally independent, with parameters describing mutation rate or selection coefficients, for example, drawn from some common distribution that we wish to characterize. Hierarchical models can pose a problem for likelihood-free techniques, such as approximate Bayesian computation (ABC), because one may be interested in the hyper-parameters and also the parameters describing, for example, each of many loci or populations. It would seem reasonable to require summary statistics for each locus or population in these examples, which can potentially lead to a 'curse of dimensionality' problem in estimation. A general method is developed for addressing these problems efficiently. An application in population genetics, to detect locally adaptive selection, is described.

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