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.
LIJOI, ANTONIO;
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
