A class of measure-valued Markov chains and Bayesian nonparametrics

Measure-valued Markov chains have raised interest in Bayesian nonparametrics since the seminal paper by Feigin and Tweedie where a Markov chain having the law of the Dirichlet process as unique invariant measure has been introduced. In the present paper we propose and investigate a new class of measure-valued Markov chains defined via exchangeable sequences of random variables. Asymptotic properties for this new class are derived and applications related to Bayesian nonparametric mixture modelling, and to a generalization of the Markov chain proposed by [12], are discussed. These results and their applications highlight once again the interplay between Bayesian nonparametrics and the theory of measure-valued Markov chains.