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Exact simulation of the Wright-Fisher diffusion

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Jenkins, Paul and Spanò, Dario (2017) Exact simulation of the Wright-Fisher diffusion. Annals of Applied Probability, 27 (3). pp. 1478-1509. doi:10.1214/16-AAP1236 ISSN 1050-5164.

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Official URL: http://doi.org/10.1214/16-AAP1236

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Abstract

The Wright–Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article, we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright–Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition function; this approach even applies to its infinite-dimensional analogue, the Fleming–Viot process. We then develop an exact rejection algorithm for processes with more general drift functions, including those modelling natural selection, using ideas from retrospective simulation. Our approach also yields methods for exact simulation of the moment dual of the Wright–Fisher diffusion, the ancestral process of an infinite-leaf Kingman coalescent tree. We believe our new perspective on diffusion simulation holds promise for other models admitting a transition eigenfunction expansion.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): Monte Carlo method, Diffusion processes, Perfect simulation (Statistics) , Population genetics
Journal or Publication Title: Annals of Applied Probability
Publisher: Institute of Mathematical Statistics
ISSN: 1050-5164
Official Date: 19 July 2017
Dates:
DateEvent
19 July 2017Published
22 July 2016Accepted
Volume: 27
Number: 3
Page Range: pp. 1478-1509
DOI: 10.1214/16-AAP1236
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 25 July 2016
Date of first compliant Open Access: 27 November 2017
Funder:
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/L018497/1Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
Related URLs:
  • https://projecteuclid.org/euclid.aoap/15...
Open Access Version:
  • ArXiv

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