Large sample properties of Gibbs-type priors
Pierpaolo De Blasi, Antonio Lijoi, Igor Pruenster · 2012
Abstract In this paper we concisely summarize some recent findings that can be found in [1] and concern large sample properties of Gibbs-type priors. We shall specifically focus on consistency according to the frequentist approach which pos-tulates the existence of a “ true ” distribution P0 that generates the data. We show that the asymptotic behaviour of the posterior is completely determined by the probabil-ity 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 P0. Such findings are further illustrated by means of three specific priors admitting closed form expres-sions and exhibiting a wide range of asymptotic behaviours.