On a Gibbs sampler based random process in Bayesian nonparametrics

Abstract

We define and investigate a new class of measure-valued Markov chains by resorting to ideas formulated in Bayesian nonparametrics related to the Dirichlet process and the Gibbs sampler. Dependent random probability measures in this class are shown to be stationary and ergodic with respect to the law of a Dirichlet process and to converge in distribution to the neutral diffusion model.Random probability measure; Dirichlet process; Blackwell-MacQueen Pólya urn scheme; Gibbs sampler; Bayesian nonparametrics