Annals of Statistics

Polya Trees and Random Distributions

R. Daniel Mauldin, William D. Sudderth, and S. C. Williams

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Trees of Polya urns are used to generate sequences of exchangeable random variables. By a theorem of de Finetti each such sequence is a mixture of independent, identically distributed variables and the mixing measure can be viewed as a prior on distribution functions. The collection of these Polya tree priors forms a convenient conjugate family which was mentioned by Ferguson and includes the Dirichlet processes of Ferguson. Unlike Dirichlet processes, Polya tree priors can assign probability 1 to the class of continuous distributions. This property and a few others are investigated.

Article information

Ann. Statist., Volume 20, Number 3 (1992), 1203-1221.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62A15
Secondary: 62G99: None of the above, but in this section 60G09: Exchangeability 60G57: Random measures

Prior distributions random measures Polya urns Derechlet distributions


Mauldin, R. Daniel; Sudderth, William D.; Williams, S. C. Polya Trees and Random Distributions. Ann. Statist. 20 (1992), no. 3, 1203--1221. doi:10.1214/aos/1176348766.

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