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 .
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 in the infinite population limit, termed the Wright-Fisher diffusion. In this article we show that the diffusion is ergodic uniformly in the selection and mutation parameters, and that the measures induced by the solution to the stochastic differential equation are uniformly locally asymptotically normal. Subsequently these two results are used to analyse the statistical properties of the Maximum Likelihood and Bayesian estimators for the selection parameter , when both selection and mutation are acting on the population. In particular, it is shown that these estimators are uniformly over compact sets consistent, display uniform in the selection parameter asymptotic normality and convergence of moments over compact sets, and are asymptotically efficient for a suitable class of loss functions .
A
in the infinite population
A
show that the diffusion is ergodic uniformly in the selection and mutation parameters, and that the measures induced by the solution to the stochastic differential equation are uniformly locally asymptotically normal. Subsequently these two results are used to
R
Bayesian estimator
Maximum Likelihood and Bayesian estimators
R
coefficient in this model
parameter
R
this estimator is uniformly consistent
these estimators are uniformly
R
, uniformly asymptotically normal, and displays uniform
consistent, display uniform in the selection parameter asymptotic normality and
R
on compact sets
over compact sets, and are asymptotically efficient for a suitable class of loss functions