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Pólya tree distributions for statistical modeling of censored data. (English) Zbl 1046.62009

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.
P. Muliere and 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.

MSC:

62E10 Characterization and structure theory of statistical distributions
62N01 Censored data models
62G99 Nonparametric inference

Citations:

Zbl 0888.62031
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