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.
2008
2008
Lijoi, Antonio; Pruenster, Igor; Walker, Stephen G.
File in questo prodotto:
File Dimensione Formato  
sinica_published.pdf

non disponibili

Descrizione: Articolo principale
Tipologia: Documento in Post-print (Post-print document)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 191.97 kB
Formato Adobe PDF
191.97 kB Adobe PDF   Visualizza/Apri

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

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/3991402
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 27
  • ???jsp.display-item.citation.isi??? 25
social impact