Convergence of likelihood ratios and estimators for selection in nonneutral Wright–Fisher diffusions

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 termed the Wright–Fisher diffusion. This diffusion evolves on a bounded interval, such that many standard resu...

Full description

Saved in:
Bibliographic Details
Published in:Scandinavian journal of statistics 2022-12, Vol.49 (4), p.1728-1760
Main Authors: Sant, Jaromir, A. Jenkins, Paul, Koskela, Jere, Spanò, Dario
Format: Article
Language:English
Subjects:
Asymptotic properties
asymptotic theory
Convergence
Differential equations
Diffusion theory
Ergodic processes
inference for diffusions
Likelihood ratio
Maximum likelihood estimators
Mutation
Parameters
selection
Wright–Fisher diffusion
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 termed the Wright–Fisher diffusion. This diffusion evolves on a bounded interval, such that many standard results in diffusion theory, assuming evolution on the real line, no longer apply. In this article we derive conditions to establish ϑ‐uniform ergodicity for diffusions on bounded intervals, and use them to prove that the Wright–Fisher diffusion is uniformly in the selection and mutation parameters ergodic, and that the measures induced by the solution to the stochastic differential equation are uniformly locally asymptotically normal. We subsequently use these results to show that the maximum likelihood and Bayesian estimators for the selection parameter are uniformly over compact sets consistent, asymptotically normal, display moment convergence, and are asymptotically efficient for a suitable class of loss functions.
ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12572