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arXiv · 1909.11626

Exact simulation of coupled Wright-Fisher diffusions

Celia García-Pareja·Henrik Hult·Timo Koski
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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 multidimensional Wright-Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of interacting genes' networks as those encountered in studies of antibiotic resistance. Our algorithm uses independent neutral Wright-Fisher diffusions as candidate proposals, which can be sampled exactly by means of existing algorithms and are only needed at a finite number of points. Once a candidate is accepted, the remaining of the path can be recovered by sampling from a neutral multivariate Wright-Fisher bridge, for which we also provide an exact sampling strategy. The technique relies on a modification of the alternating series method and extends existing algorithms that are currently available for the one-dimensional case. Finally, the algorithm's complexity is derived and its performance demonstrated in a simulation study.

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Celia García-Pareja, Henrik Hult, Timo Koski. 2019-09-25. Exact simulation of coupled Wright-Fisher diffusions. https://arxiv.org/abs/1909.11626

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