S Favaro, M Ruggiero, D Spano and SG Walker

The Neutral population model and Bayesian non-parametrics

Abstract: Fleming-Viot processes are a wide class of probability-measure-valued diffusions which often arise as large population limits of so-called particle processes. Here we invert the procedure and show that a countable population process can be derived directly from the neutral di®usion model, with no arbitrary assumptions. We study the atomic structure of the neutral diffusion model, and elicit dimensional particle process from the time-dependent random measure, for any chosen population size. The static properties are consequences of the fact that its stationary distribution is the Dirichlet process, and rely on a new representation for it. The dynamics are derived directly from the transition function of the neutral diffusion model.

Keywords: Neutral diffusion model; particle process; Dirichlet process; Blackwell-MacQueen urn-scheme; transition function.