Quantile pyramids for Bayesian nonparametrics

Hjort, N.L. and Walker, S.G. (2009) Quantile pyramids for Bayesian nonparametrics. Annals of Statistics, 37 (1). pp. 105-131. ISSN 0090-5364 . (Full text available)

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http://dx.doi.org/10.1214/07-AOS553

Abstract

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.

Item Type: Article
Uncontrolled keywords: Consistency; Dirichlet process; nonparametric Bayes; Bernshtein-von Mises theorem; quantile pyramids; random quantiles
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Judith Broom
Date Deposited: 27 Mar 2009 18:45
Last Modified: 06 Sep 2011 00:58
Resource URI: http://kar.kent.ac.uk/id/eprint/12613 (The current URI for this page, for reference purposes)
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