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Quantile pyramids for Bayesian nonparametrics

Hjort, Nils Lid, Walker, Stephen G. (2009) Quantile pyramids for Bayesian nonparametrics. Annals of Statistics, 37 (1). pp. 105-131. ISSN 0090-5364. (doi:10.1214/07-AOS553) (KAR id:12613)


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
DOI/Identification number: 10.1214/07-AOS553
Uncontrolled keywords: Consistency; Dirichlet process; nonparametric Bayes; Bernshtein-von Mises theorem; quantile pyramids; random quantiles
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: Engineering and Physical Sciences Research Council (
Depositing User: Judith Broom
Date Deposited: 27 Mar 2009 18:45 UTC
Last Modified: 12 Jul 2022 10:39 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Walker, Stephen G..

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