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Statistica Sinica 19 (2009), 707-720





BAYESIAN NONPARAMETRIC CONSTRUCTION OF

THE FLEMING-VIOT PROCESS WITH

FERTILITY SELECTION


Matteo Ruggiero and Stephen G. Walker


Università degli Studi di Pavia and University of Kent


09
Abstract: This paper provides a construction in the Bayesian framework of the Fleming-Viot measure-valued diffusion with diploid fertility selection, and highlights new connections between Bayesian nonparametrics and population genetics. Via a generalisation of the Blackwell-MacQueen Pólya-urn scheme, a Markov particle process is defined such that the associated process of empirical measures converges to the Fleming-Viot diffusion. The stationary distribution, known from Ethier and Kurtz (1994), is then derived through an application of the Dirichlet process mixture model and shown to be the de Finetti measure of the particle process. The Fleming-Viot process with haploid selection is derived as a special case.



Key words and phrases: Blackwell-MacQueen urn-scheme, Dirichlet process mixture, fertility selection, Fleming-Viot process, Gibbs sampler.

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