Bayesian Nonparametric Construction of Fleming-Viot Models in Population Genetics
Matteo Ruggiero · 2007
This work provides an explicit construction in a Bayesian nonparametric framework of two Fleming-Viot processes, known in population genetics, and yields a previously unknown stationary distribution. In particular, by means of generalised Polya-urn schemes, two types of pure jump particle processes are introduced, describing the evolution in time of an exchangeable population. The process of empirical measures of the individuals converges weakly in the Skorohod space to a specific Fleming-Viot diusion, and the stationary distribution is shown to be the de Finetti measure of the infinite sequence of individuals. In presence of viability selection the stationary distribution turns out to be the two-parameter Poisson-Dirichlet process.