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 σ ∈ (0, 1), are equivalent to σ–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 σ–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.
Investigating nonparametric priors with Gibbs structure
LIJOI, ANTONIO;PRUENSTER, IGOR;
2008
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 σ ∈ (0, 1), are equivalent to σ–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 σ–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.File | Dimensione | Formato | |
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