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Inference in Molecular Population Genetics

Abstract

Full likelihood-based inference for modern population genetics data presents methodological and computational challenges. The problem is of considerable practical importance and has attracted recent attention, with the development of algorithms based on importance sampling (IS) and Markov chain Monte Carlo (MCMC). Here we introduce a new importance sampling algorithm. The optimal proposal distribution for these problems can be characterised, and we exploit a detailed analysis of genealogical processes to develop a practicable approximation to it. We compare the new method with existing algorithms on a variety of genetic examples. Our approach substantially outperforms existing importance sampling algorithms, with efficiency typically improved by several orders of magnitude. The new method also compares favourably with existing MCMC methods in some problems, and less favourably in others, suggesting that both IS and MCMC have a continuing role to play in this area. We offer insights into the relative advantages of each approach, and discuss diagnostics in the importance sampling framework.

Keywords: Ancestral inference, Coalescent, Computationally intensive inference, Importance Sampling, MCMC, Population Genetics.

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