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Importance sampling on coalescent histories. I

Part of: Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Maria De Iorio  and
Robert C. Griffiths
Maria De Iorio*
Affiliation:
Imperial College London
Robert C. Griffiths*
Affiliation:
University of Oxford
*
∗ Postal address: Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2BZ, UK
∗∗ Postal address: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK. Email address: [email protected]
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Abstract

Stephens and Donnelly (2000) constructed an efficient sequential importance-sampling proposal distribution on coalescent histories of a sample of genes for computing the likelihood of a type configuration of genes in the sample. In the current paper a characterization of their importance-sampling proposal distribution is given in terms of the diffusion-process generator describing the distribution of the population gene frequencies. This characterization leads to a new technique for constructing importance-sampling algorithms in a much more general framework when the distribution of population gene frequencies follows a diffusion process, by approximating the generator of the process.

Keywords

Coalescent processdiffusion processimportance sampling

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 93E25: Other computational methods 92D25: Population dynamics (general)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 2 , June 2004 , pp. 417 - 433
Copyright
Copyright © Applied Probability Trust 2004 

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Footnotes

Supported by BBSRC Bioinformatics grant 43/BIO14435.

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