This article addresses issues of model choice in Bayesian contexts, and focusses on the use of the so-called posterior predictive p-values (ppp values). These involve a general discrepancy or conflict measure and depend ...

This Statistical Research Report contains the complete written discussion generated by the two papers “Frequentist Model Average Estimators”, by Hjort and Claeskens, and “The Focussed Information Criterion”, by Claeskens ...

Pólya trees fix partitions and use random probabilities in order to construct random probability measures. With quantile pyramids we instead fix probabilities and use random partitions. For nonparametric Bayesian inference, ...

The Dirichlet process has been extensively studied over the last thirty years, along with various generalisations, and remains a fundamental tool for nonparametric Bayesian statistics. The probabilistic structure of its ...

Two characterisations of a random mean from a Dirichlet process, as a limit of finite sums of a simple symmetric form and as a solution of certain stochastic equations, are investigated. These are used to reach results on ...

The intersection set of Bayesian and nonparametric statistics was almost empty until about 1973, but now seems to be growing at a healthy rate. This chapter gives an overview of various theoretical and applied research ...