Title: Exact simulation of Wright-Fisher diffusions

Abstract

The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this talk I will illustrate a strategy for exact simulation from a broad class of Wright-Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, the key idea is to exploit an eigenfunction expansion of the transition function; this approach even applies to its infinite-dimensional analogue, the Fleming-Viot process. I will also describe an exact rejection algorithm for processes with more general drift functions, including those modelling natural selection, using ideas from retrospective simulation. This approach also yields methods for exact simulation of the moment dual of the Wright-Fisher diffusion, the ancestral process of an infinite-leaf Kingman coalescent tree. Joint work with Paul Jenkins (Warwick)