Analysis and rejection sampling of Wright-Fisher diffusion bridges

TL;DR

This paper studies Wright-Fisher diffusion bridges, providing new theoretical insights and a rejection sampling method for simulating these processes under selection, aiding genetic variation analysis.

Contribution

It introduces a novel rejection sampling scheme for Wright-Fisher bridges under selection and analyzes their properties, advancing methods for genetic inference.

Findings

Distributional properties of neutral Wright-Fisher bridges

A new rejection sampling method for selected bridges

Insights into allele frequency dynamics under selection

Abstract

We investigate the properties of a Wright-Fisher diffusion process started from frequency x at time 0 and conditioned to be at frequency y at time T. Such a process is called a bridge. Bridges arise naturally in the analysis of selection acting on standing variation and in the inference of selection from allele frequency time series. We establish a number of results about the distribution of neutral Wright-Fisher bridges and develop a novel rejection sampling scheme for bridges under selection that we use to study their behavior.