Construction and Stationary Distribution of the Fleming-Viot Process with Viability Selection

Abstract

This paper provides an explicit construction of the Fleming-Viot process with viability selection in a Bayesian nonparametric framework, and derives its stationary distribution. The measure-valued diffusion is obtained as the infinite population limit of the empirical measures of a semi-Markov process of exchangeable particles. In the limit the stationary distribution is shown to be the two-parameter Poisson-Dirichlet process, also known as the Pitman-Yor process.Fleming-Viot process; semi-Markov process; viability selection; stationary distribution; two-parameter Poisson-Dirichlet process.