Exact simulation of coupled Wright-Fisher diffusions

Sampling paths of a diffusion process remains a challenging problem. The major bottleneck is that its finite dimensional distributions are seldom available in closed form, and one often needs resorting to time-discretized numerical approximations. Exact rejection algorithms of diffusion processes have therefore become increasingly popular in recent years. In this setting, exact refers to the fact that samples can be drawn from the true distributions without approximation errors, up to computer precision.

In this talk I introduce an exact rejection algorithm for simulating paths of the coupled Wright-Fisher diffusion, which models the coevolution of interacting networks of genes, such as those encountered in studies of antibiotic resistance. Our work presents the first extension of exact rejection algorithms to the multivariate case for diffusion processes with non-unit coefficient. Candidate proposals in our rejection scheme are independent multivariate neutral Wright Fisher diffusions, whose transition density is only known in infinite series form but can be sampled exactly by means of a modification of the alternating series method. Our algorithm provides samples of the diffusion’s paths at a finite (random) number of time points, the so-called skeletons, and the remaining of the paths can be recovered without further reference to the target distribution by sampling from neutral multivariate Wright-Fisher bridges, for which an exact sampling strategy is also developed. Results on the algorithm’s complexity and its performance in a simulation study will also be discussed. To put this work in context, I will start presenting the type of population genetics’ problems that motivate the coupled Wright-Fisher model, as well as giving a brief introduction to exact rejection algorithms and how they compare to time-discretized approximations such as the Euler-Maruyama scheme.

This is a joint MATHICSE-STATS seminar