The Neutral Population Model and Bayesian Non- Parametrics

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 diffusion model, with no arbitrary assumptions. We study the atomic structure of the neutral diffusion model, and elicit a finite 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.