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Importance sampling and the two-locus model with subdivided population structure

Part of: Stochastic processes Stochastic systems and control

Published online by Cambridge University Press:  01 July 2016

Robert C. Griffiths ,
Paul A. Jenkins  and
Yun S. Song
Robert C. Griffiths*
Affiliation:
University of Oxford
Paul A. Jenkins*
Affiliation:
University of Oxford
Yun S. Song*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK.
∗ Postal address: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK.
∗∗ Postal address: Departments of EECS and Statistics, University of California, Berkeley, CA 94720, USA. Email address: yss@stat.berkeley.edu
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Abstract

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The diffusion-generator approximation technique developed by De Iorio and Griffiths (2004a) is a very useful method of constructing importance-sampling proposal distributions. Being based on general mathematical principles, the method can be applied to various models in population genetics. In this paper we extend the technique to the neutral coalescent model with recombination, thus obtaining novel sampling distributions for the two-locus model. We consider the case with subdivided population structure, as well as the classic case with only a single population. In the latter case we also consider the importance-sampling proposal distributions suggested by Fearnhead and Donnelly (2001), and show that their two-locus distributions generally differ from ours. In the case of the infinitely-many-alleles model, our approximate sampling distributions are shown to be generally closer to the true distributions than are Fearnhead and Donnelly's.

Keywords

Coalescent processrecombinationdiffusion processimportance samplingmigrationsubdivided population

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 93E25: Other computational methods 92D15: Problems related to evolution
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 2 , June 2008 , pp. 473 - 500
Copyright
Copyright © Applied Probability Trust 2008 

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