This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. Crucially, no sieve or entropy measures are required and so rates do not depend on the rate of convergence...

Consistency of Bayesian nonparametric procedures has been the focus of a considerable amount of research. Here we deal with strong consistency for Bayesian density estimation. An awkward consequence of inconsistency is pointed out. We investigate reasons for inconsistency and precisely identify...

The past decade has seen a remarkable development in the area of Bayesian nonparametric inference both from a theoretical and applied perspective. As for the latter, the celebrated Dirichlet process has been successfully exploited within Bayesian mixture models leading to many interesting...

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....

In this work we propose a Bayesian nonparametric approach for tackling statistical problems related to EST surveys. In particular, we provide estimates for: a) the coverage, defined as the proportion of unique genes in the library represented in the given sample of reads; b) the number of new...

In recent years the Dirichlet process prior has experienced a great success in the context of Bayesian mixture modelling. The idea of overcoming discreteness of its realizations by exploiting it in hierarchical models, combined with the development of suitable sampling techniques, represent one...

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...

A Bayesian nonparametric methodology has been recently proposed in order to deal with the issue of prediction within species sampling problems. Such problems concern the evaluation, conditional on a sample of size n, of the species variety featured by an additional sample of size m. Genomic...