Recently the class of normalized random measures with independent increments, which contains the Dirichlet process as a particular case, has been introduced. Here a new technique for deriving moments of these random probability measures is proposed. It is shown that, "a priori", most of the...

One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. In this paper, we provide a comprehensive Bayesian non-parametric analysis of random probabilities which are obtained by normalizing random measures with...

The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are known by now for random Dirichlet means but little is known, especially in terms of posterior distributions, for...

Bayesian nonparametric inference is a relatively young area of research and it has recently undergone a strong development. Most of its success can be explained by the considerable degree of flexibility it ensures in statistical modelling, if compared to parametric alternatives, and by the...

The present paper provides a review of the results concerning distributional properties of means of random probability measures. Our interest in this topic has originated from inferential problems in Bayesian Nonparametrics. Nonetheless, it is worth noting that these random quantities play an...

The present paper provides exact expressions for the probability distribution of linear functionals of the two–parameter Poisson–Dirichlet process. Distributional results that follow from the application of an inversion formula for a (generalized) Cauchy–Stieltjes transform are achieved....