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September, 1992 Polya Trees and Random Distributions
R. Daniel Mauldin, William D. Sudderth, S. C. Williams
Ann. Statist. 20(3): 1203-1221 (September, 1992). DOI: 10.1214/aos/1176348766

Abstract

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.

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R. Daniel Mauldin. William D. Sudderth. S. C. Williams. "Polya Trees and Random Distributions." Ann. Statist. 20 (3) 1203 - 1221, September, 1992. https://doi.org/10.1214/aos/1176348766

Information

Published: September, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0765.62006
MathSciNet: MR1186247
Digital Object Identifier: 10.1214/aos/1176348766

Subjects:
Primary: 62A15
Secondary: 60G09, 60G57, 62G99

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 3 • September, 1992
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