Advances in Decision Sciences
Volume 7 (2003), Issue 3, Pages 175-186
doi:10.1155/S1173912603000166

Polya tree distributions for statistical modeling of censored data

Abstract

Polya tree distributions extend the idea of the Dirichlet process as a prior for Bayesian nonparametric problems. Finite dimensional distributions are defined through conditional probabilities in P. This allows for a specification of prior information which carries greater weight where it is deemed appropriate according to the choice of a partition of the sample space. Muliere and Walker[7] construct a partition so that the posterior from right censored data is also a Polya tree. A point of contention is that the specification of the prior is partially dependent on the data. In general, the posterior from censored data will be a mixture of Polya trees. This paper will present a straightforward method for determining the mixing distribution.