Lijoi, A. and Prunster, I. and Walker, S.G. (2008) Investigating nonparametric priors with Gibbs structure. Statistica Sinica, 18 (4). pp. 1653-1668. ISSN 1017-0405 .
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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.
|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:||17 Apr 2009 08:41|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/12612 (The current URI for this page, for reference purposes)|
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