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 P ́olya-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.

Bayesian non parametric construction of the Fleming-Viot process with fertility selection

RUGGIERO, MATTEO;
2009-01-01

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 P ́olya-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.
2009
19
707
720
http://www3.stat.sinica.edu.tw/statistica/
Blackwell-MacQueen urn-scheme; Dirichlet process mix- ture; fertility selection; Fleming-Viot process; Gibbs sampler.
M. RUGGIERO;WALKER STEPHEN G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/85324
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