The Annals of Statistics

Some Aspects of Polya Tree Distributions for Statistical Modelling

Michael Lavine

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Abstract

Polya tree distributions are defined. They are generalizations of Dirichlet processes that allow for the possibility of putting positive mass on the set of continuous distributions. Predictive and posterior distributions are explained. A canonical construction of a Polya tree is given so that the Polya tree has any desired predictive distribution. Choices of the Polya tree parameters are discussed. Mixtures of Polya trees are defined and examples are given.

Article information

Source
Ann. Statist., Volume 20, Number 3 (1992), 1222-1235.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348767

Digital Object Identifier
doi:10.1214/aos/1176348767

Mathematical Reviews number (MathSciNet)
MR1186248

Zentralblatt MATH identifier
0765.62005

JSTOR
links.jstor.org

Subjects
Primary: 62A15
Secondary: 62G99: None of the above, but in this section

Keywords
Nonparametric Bayes Dirichlet processes tailfree processes

Citation

Lavine, Michael. Some Aspects of Polya Tree Distributions for Statistical Modelling. Ann. Statist. 20 (1992), no. 3, 1222--1235. doi:10.1214/aos/1176348767. https://projecteuclid.org/euclid.aos/1176348767


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