Pólya tree distributions for statistical modeling of censored data (Q1430416)

Summary: 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. \textit{P. Muliere} and \textit{S. Walker} [Scand. J. Stat. 24, 331--340 (1997; Zbl 0888.62031)] 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.