We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian nonparametric estimators, which can be readily exploited for...

We provide a new approach to the sampling of the well known mixture of Dirichlet process model. Recent attention has focused on retention of the random distribution function in the model, but sampling algorithms have then suffered from the countably infinite representation these distributions...

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...

In this paper we show that particular Gibbs sampler Markov processes can be modified to an autoregressive Markov process. The procedure allows the easy derivation of the innovation variables which provide strictly stationary autoregressive processes with fixed marginals. In particular, we...

We introduce approaches to performing Bayesian nonparametric statistical inference for distribution functions exhibiting a stochastic ordering. We consider Pólya tree prior distributions, and Bernstein polynomial prior distributions, and each prior provides an appealing and simple way of...

A new simulation method, "auxiliary random functions" is introduced. When used within a Gibbs sampler, this method enables a unified treatment of exact, right-censored, left-censored, left-truncated and interval censored data, with and without covariates in survival models. The models and...