Bayesian nonparametric analysis of Kingman's coalescent

TL;DR

This paper introduces a Bayesian nonparametric method for ancestral inference in population genetics using Kingman's coalescent, providing new estimators for genealogy-related quantities based on Fleming-Viot processes.

Contribution

It proposes a novel Bayesian nonparametric predictive framework for ancestral inference under Kingman's coalescent, including new estimators akin to Good-Turing estimators.

Findings

Introduces a Bayesian nonparametric approach for ancestral inference.

Develops estimators for genealogy quantities based on Fleming-Viot processes.

Illustrates the method with genetic data application.

Abstract

Kingman's coalescent is one of the most popular models in population genetics. It describes the genealogy of a population whose genetic composition evolves in time according to the Wright-Fisher model, or suitable approximations of it belonging to the broad class of Fleming-Viot processes. Ancestral inference under Kingman's coalescent has had much attention in the literature, both in practical data analysis, and from a theoretical and methodological point of view. Given a sample of individuals taken from the population at time $t>0$, most contributions have aimed at making frequentist or Bayesian parametric inference on quantities related to the genealogy of the sample. In this paper we propose a Bayesian nonparametric predictive approach to ancestral inference. That is, under the prior assumption that the composition of the population evolves in time according to a neutral Fleming-Viot process, and given the information contained in an initial sample of $m$ individuals taken from the population at time $t>0$, we estimate quantities related to the genealogy of an additional unobservable sample of size $m^{\prime}\geq1$. As a by-product of our analysis we introduce a class of Bayesian nonparametric estimators (predictors) which can be thought of as Good-Turing type estimators for ancestral inference. The proposed approach is illustrated through an application to genetic data.