The Annals of Statistics

Optional Pólya tree and Bayesian inference

Wing H. Wong and Li Ma

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We introduce an extension of the Pólya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data. The resulting “optional Pólya tree” distribution has large support in total variation topology and yields posterior distributions that are also optional Pólya trees with computable parameter values.

Article information

Ann. Statist., Volume 38, Number 3 (2010), 1433-1459.

First available in Project Euclid: 8 March 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F15: Bayesian inference 62G99: None of the above, but in this section
Secondary: 62G07: Density estimation

Pólya tree Bayesian inference nonparametric recursive partition density estimation


Wong, Wing H.; Ma, Li. Optional Pólya tree and Bayesian inference. Ann. Statist. 38 (2010), no. 3, 1433--1459. doi:10.1214/09-AOS755.

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