OPTIONAL POLYA TREE AND BAYESIAN INFERENCE

被引：52

作者：

Wong, Wing H. ^{[1
]}

Ma, Li ^{[1
]}

机构：

[1] Stanford Univ, Dept Stat, Stanford, CA 94305 USA

来源：

ANNALS OF STATISTICS | 2010年 / 38卷 / 03期

基金：

美国国家科学基金会;

关键词：

Polya tree; Bayesian inference; nonparametric; recursive partition; density estimation; ASYMPTOTIC-BEHAVIOR; DISTRIBUTIONS;

D O I：

10.1214/09-AOS755

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We introduce an extension of the Polya 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 Polya tree" distribution has large support in total variation topology and yields posterior distributions that are also optional Polya trees with computable parameter values.

引用

页码：1433 / 1459

页数：27

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