Investigating nonparametric priors with Gibbs structure

Lijoi, Antonio and Prunster, Igor and Walker, Stephen G. (2008) Investigating nonparametric priors with Gibbs structure. Statistica Sinica, 18 (4). pp. 1653-1668. ISSN 1017-0405 . (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Abstract

This paper investigates nonparametric priors that induce infinite Gibbs-type partitions; such a feature is desirable both from a conceptual and a mathematical point of view. Recently it has been shown that Gibbs-type priors, with sigma is an element of (0, 1), are equivalent to sigma-stable Poisson-Kingman models. By looking at solutions to a recursive equation arising through Gibbs partitions, we provide an alternative proof of this fundamental result. Since practical implementation of general sigma-stable Poisson-Kingman models is difficult, we focus on a related class of priors, namely normalized random measures with independent increments; these are easily implementable in complex Bayesian models. We establish the result that the only Gibbs-type priors within this class are those based on a generalized gamma random measure.

Item Type: Article
Uncontrolled keywords: Bayesian nonparametrics; Gibbs exchangeable partitions; generalized gamma process; normalized random measures with independent increments; recursive equation; stable distribution
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: 17 Apr 2009 08:41
Last Modified: 25 Jun 2014 10:40
Resource URI: https://kar.kent.ac.uk/id/eprint/12612 (The current URI for this page, for reference purposes)
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