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...

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...

Random probability measures are the main tool for Bayesian nonparametric inference, with their laws acting as prior distributions. Many well–known priors used in practice admit different, though (in distribution) equivalent, representations. Some of these are convenient if one wishes to...

Species sampling problems have a long history in ecological and biological studies and a number of issues, including the evaluation of species richness, the design of sampling experiments, the estimation of rare species variety, are to be addressed. Such inferential problems have recently...

Most of the Bayesian nonparametric models for non-exchangeable data that are used in applications are based on some extension to the multivariate setting of the Dirichlet process, the best known being MacEachern’s dependent Dirichlet process. A comparison of two recently introduced classes of...

This paper studies a novel idea for constructing continuous-time stationary Markov models. The approach undertaken is based on a latent representation of the corresponding transition probabilities that conveys to appealing ways to study and simulate the dynamics of the constructed processes....

This paper is concerned with the construction of a continuous parameter sequence of random probability measures and its application for modeling random phenomena evolving in continuous time. At each time point we have a random probability measurewhich is generated by a Bayesian nonparametric...

An approach to constructing strictly stationary AR(1)-type models with arbitrary stationary distributions and a flexible dependence structure is introduced. Bayesian nonparametric predictive density functions, based on single observations, are used to construct the one-step ahead predictive...