Urn schemes and reinforced random walks

Abstract

We define a reinforced urn process (RUP) to be a reinforced random walk on a state space of urns and we show its partial exchangeability. When it is recurrent, a RUP is a mixture of Markov chains and we characterize its mixing distribution on the space of stochastic matrices. Many Bayesian nonparametric priors, like Pólya trees, the beta-Stacy process and, in general, neutral to the right processes can be derived from RUPs. Applications to survival data are examined.