Exact simulation of coupled Wright-Fisher diffusions

TL;DR

This paper introduces an exact rejection algorithm for simulating coupled Wright-Fisher diffusions, enabling precise modeling of interacting gene networks with applications in antibiotic resistance research.

Contribution

It presents a novel exact simulation method for multidimensional coupled Wright-Fisher diffusions, extending existing algorithms to higher dimensions with proven efficiency.

Findings

Algorithm accurately simulates coupled Wright-Fisher paths

Provides exact sampling strategies for multivariate Wright-Fisher bridges

Demonstrates efficiency through simulation results

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.