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Exact simulation of coupled Wright–Fisher diffusions

Part of: Stochastic analysis Markov processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  22 November 2021

Celia García-Pareja Open the ORCID record for Celia García-Pareja [Opens in a new window] ,
Henrik Hult  and
Timo Koski
Celia García-Pareja*
Affiliation:
KTH Royal Institute of Technology
Henrik Hult*
Affiliation:
KTH Royal Institute of Technology
Timo Koski*
Affiliation:
KTH Royal Institute of Technology and University of Helsinki
*
*Postal address: Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, 114 28 Stockholm, Sweden.
*Postal address: Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, 114 28 Stockholm, Sweden.
*Postal address: Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, 114 28 Stockholm, Sweden.
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Abstract

In this paper an exact rejection algorithm for simulating paths of the coupled Wright–Fisher diffusion is introduced. The coupled Wright–Fisher diffusion is a family of multivariate Wright–Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of networks of interacting genes. The proposed rejection algorithm uses independent neutral Wright–Fisher diffusions as candidate proposals, which are only needed at a finite number of points. Once a candidate is accepted, the remainder of the path can be recovered by sampling from neutral multivariate Wright–Fisher bridges, for which an exact sampling strategy is also provided. Finally, the algorithm’s complexity is derived and its performance demonstrated in a simulation study.

Keywords

Exact simulationrejection algorithmmultivariate diffusionspopulation geneticscoupled Wright–Fisher modelepistasis

MSC classification

Primary: 60J60: Diffusion processes 65C30: Stochastic differential and integral equations
Secondary: 60H35: Computational methods for stochastic equations 65C05: Monte Carlo methods
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 4 , December 2021 , pp. 923 - 950
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Copyright
© The Author(s) 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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