Beta approximation for the two alleles Moran model by Stein's method
Jason Fulman
TL;DR
This paper provides a precise error estimate for approximating the stationary distribution of the two alleles Moran model with a Beta distribution, using Stein's method of exchangeable pairs.
Contribution
It introduces a sharp error bound for the Beta approximation in the Moran model, fitting into Doebler's Stein's method framework.
Findings
Sharp error term for Beta approximation derived
The approximation fits well within Stein's exchangeable pairs framework
Improves understanding of distributional accuracy in population genetics models
Abstract
In work on the two alleles Moran model, Ewens showed that the stationary distribution for the number of genes of one type can be approximated by a Beta distribution. In this short note, we provide a sharp error term for this approximation. We show that this example fits perfectly into Doebler's framework for Beta approximation by Stein's method of exchangeable pairs.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Gene Regulatory Network Analysis · Stochastic processes and statistical mechanics