Open Access
June 2010 Optional Pólya tree and Bayesian inference
Wing H. Wong, Li Ma
Ann. Statist. 38(3): 1433-1459 (June 2010). DOI: 10.1214/09-AOS755


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.


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Wing H. Wong. Li Ma. "Optional Pólya tree and Bayesian inference." Ann. Statist. 38 (3) 1433 - 1459, June 2010.


Published: June 2010
First available in Project Euclid: 8 March 2010

zbMATH: 1189.62048
MathSciNet: MR2662348
Digital Object Identifier: 10.1214/09-AOS755

Primary: 62F15 , 62G99
Secondary: 62G07

Keywords: Bayesian inference , Density estimation , nonparametric , Pólya tree , recursive partition

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 3 • June 2010
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