OPTIONAL POLYA TREE AND BAYESIAN INFERENCE

• 成果类型: Article
• 署名作者: Wong, Wing H.; Ma, Li
• 署名单位: Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS755
• 发表日期: 2010
• 页码: 1433-1459
• 关键词: ASYMPTOTIC-BEHAVIOR; distributions

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.