Dependent Completely Random Measures and Statistical Applications

• Activity Number: 346
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Bernardo Nipoti*+
• Companies: University of Turin and Collegio Carlo Alberto, Italy
• Keywords: Bayesian nonparametrics ; Completely random measures ; Dependent processes ; Normalized random measures ; Hazard rate mixtures

Abstract

The construction of dependent random probability measures for Bayesian inference has attracted considerable attention in the last decade. We introduce and investigate a new class of vector nonparametric priors obtained by following an approach that makes use of completely random measures. By resorting to a construction of vectors of Poisson random measures provided in Griffiths and Milne (1978), we propose the definition of a class of vectors of dependent completely random measures. This leads us to define, via suitable transformations, vectors of dependent normalized random measures with independent increments and vectors of dependent random hazard rates. The analytical tractability of these objects allows us to prove results that turn out to be meaningful for both theoretical and practical purposes: indeed they let us gain some insight on the dependence structure of the priors defined and lead us to construct efficient Gibbs sampling algorithms. Possible applications to problems of density estimation or estimation of non-proportional survival functions are illustrated.