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Journal of Applied Mathematics and Decision Sciences
Volume 7, Issue 3, Pages 175-186
http://dx.doi.org/10.1155/S1173912603000166

Polya tree distributions for statistical modeling of censored data

Department of Mathematics and Statistics, Southern Illinois University Edwardsville, IL, USA

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.