Exact simulation of coupled Wright–Fisher diffusions. (December 2021)

• Record Type: Journal Article
• Authors: García-Pareja, Celia; Hult, Henrik; Koski, Timo
• Is Part Of: Advances in applied probability. Volume 53:Number 4(2021)
• Page Start: 923
• Page End: 950
• Publication Date: 2021-12
• Subjects: Exact simulation -- rejection algorithm -- multivariate diffusions -- population genetics -- coupled Wright–Fisher model -- epistasis; 60J60 -- 65C30 -- 60H35 -- 65C05; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2021.9
• Languages: English
• ISSNs: 0001-8678

Abstract

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.