In this paper we concisely summarize some recent findings that can be found in De Blasi, Lijoi and Pruenster (2012) and concern large sample properties of Gibbs-type priors. We shall specifically focus on consistency according to the frequentist approach which postulates the existence of a “ true ” distribution P_0 that generates the data. We show that the asymptotic behaviour of the posterior is completely determined by the probability of obtaining a new distinct observation. Exploiting the predictive structure of Gibbs-type priors, we are able to establish that consistency holds essentially always for discrete P0 , whereas inconsistency may occur for diffuse P_0. Such findings are further illustrated by means of three specific priors admitting closed form expressions and exhibiting a wide range of asymptotic behaviours.

Large sample properties of Gibbs-type priors

DE BLASI, Pierpaolo;PRUENSTER, Igor
2012

Abstract

In this paper we concisely summarize some recent findings that can be found in De Blasi, Lijoi and Pruenster (2012) and concern large sample properties of Gibbs-type priors. We shall specifically focus on consistency according to the frequentist approach which postulates the existence of a “ true ” distribution P_0 that generates the data. We show that the asymptotic behaviour of the posterior is completely determined by the probability of obtaining a new distinct observation. Exploiting the predictive structure of Gibbs-type priors, we are able to establish that consistency holds essentially always for discrete P0 , whereas inconsistency may occur for diffuse P_0. Such findings are further illustrated by means of three specific priors admitting closed form expressions and exhibiting a wide range of asymptotic behaviours.
46th Scientific Meeting of the Italian Statistical Society
Roma
20-22 Giugno 2012
Atti della XLVI Riunione Scientifica della Società Italiana di Statistica
CLEUP
1
4
9788861298828
http://meetings.sis-statistica.org/index.php/sm/sm2012/paper/view/2020
Asymptotics; Bayesian nonparametrics; Gibbs-type priors
Pierpaolo De Blasi; Antonio Lijoi; Igor Pruenster
File in questo prodotto:
File Dimensione Formato  
2020-3330-1-PB.pdf

Accesso aperto

Tipo di file: PREPRINT (PRIMA BOZZA)
Dimensione 84.56 kB
Formato Adobe PDF
84.56 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/2318/115385
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact