Transformations of dependent completely random measures

Abstract

We introduce 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 devised in [1], we propose the definition of a class of bivariate vectors of dependent completely random measures that have the nice property of being jointly infinitely divisible. This leads us to define, via suitable transformations, vectors of dependent normalized random measures with independent increments, dependent neutral–to–the–right processes and dependent random hazard rates. These proposals appear in the
author’s Ph.D. thesis [2]: here one can find a thorough investigation of their theoretical properties as well as an illustration of their use for the statistical analysis of partially exchangeable data.