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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
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Official URL: http://doi.org/10.1214/16-AAP1236
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 | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of 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 | ||||||
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| Date of first compliant deposit: | 25 July 2016 | ||||||
| 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 | ||||||
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