A two-color, randomly reinforced urn


Statistical learning
A two-color, randomly reinforced urn
Wednesday 19th May 2004
Muliere, Pietro; Paganoni, Anna Maria; Secchi, Piercesare
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We study an urn containing balls of two or more colors. The urn is sequentially sampled. Each time a ball is extracted from the urn it is reintroduced in it togheter with a random number of balls of the same color: the distribution of the number of added balls may depend on the color extracted. We prove asymptotic results for the process of its compositions. Applications to sequential clinical trials are considered as well as connections with adaptive design of experiments in Bayesian framework.
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P.Muliere, A.M.Paganoni, P.Secchi (2006), A randomly reinforced urn, Journal of Statistical Planning and Inference, 136, 1853-1874