Urn schemes and reinforced random walks

We define a reinforced um process (RUP) to be a reinforced random walk on a state space of urns and we show its partial exchangeability. When it is re current, a RUP is a mixture of Markov chains and we characterize its mixing distribution on the space of stochastic matrices. Many Bayesian nonparamet ric priors, like Polya trees, the beta-Stacy process and, in general, neutr al to the right processes can be derived from RUPs. Applications to surviva l data are examined. (C) 2000 Elsevier Science B.V. All rights reserved. MS G, primary 62C10; secondary 62G99.