Convergence of Bayesian Estimators for Diffusions in Genetics

A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process limit, termed the Wright-Fisher diffusion. In this article we analyse the statistical properties of the Bayesian estimator for the selection coefficient in this model, when both selection and mutation are acting on the population. In particular, it is shown that this estimator is uniformly consistent over compact sets, uniformly asymptotically normal, and displays uniform convergence of moments on compact sets.