This paper aims at investigating nonparametric priors which 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 in (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, which 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.

Investigating nonparametric priors with Gibbs structure

PRUENSTER, Igor;
2008-01-01

Abstract

This paper aims at investigating nonparametric priors which 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 in (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, which 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.
2008
18
1653
1668
http://www3.stat.sinica.edu.tw/statistica/
Bayesian nonparametrics; Gibbs exchangeable partitions; Generalized gamma process; Normalized random measures with independent increments; Recursive equation; Stable distribution.
A. LIJOI; I. PRUENSTER; S.G. WALKER
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/8573
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