QUANTILE PYRAMIDS FOR BAYESIAN NONPARAMETRICS

• 成果类型: Article
• 署名作者: Hjort, Nils Lid; Walker, Stephen G.
• 署名单位: University of Oslo; University of Kent
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS553
• 发表日期: 2009
• 页码: 105-131
• 关键词: polya tree distributions; von-mises theorem; posterior distributions; inference; probability; Consistency; parameters; models

摘要

Polya trees fix partitions and use random probabilities in order to construct random probability measures. With quantile pyramids we instead fix probabilities and use random partitions. For nonparametric Bayesian inference we use a prior which supports piecewise linear quantile functions, based on the need to work with a finite set of partitions, yet we show that the limiting version of the prior exists. We also discuss and investigate an alternative model based on the so-called substitute likelihood, Both approaches factorize in a convenient way leading to relatively straightforward analysis via MCMC, since analytic summaries of posterior distributions are too complicated. We give conditions securing the existence of an absolute continuous quantile process, and discuss consistency and approximate normality for the sequence of posterior distributions. Illustrations are included.