To test if a density <I>f</I> is equal to a specified <I>f</I><SUB>0</SUB>, one knows by the Neyman-Pearson lemma the form of the optimal test at a specified alternative <I>f</I><SUB>1</SUB>. Any nonparametric density ...

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 traditional use of model selection methods in practice is to proceed as if the final selected model had been chosen in advance, without acknowledging the additional uncertainty introduced by model selection. This often ...

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 ...

Generalising the standard frailty models of survival analysis, we propose to model frailty as a weighted Lévy process. Hence the frailty of an individual is not a given quantity, but develops over time. Formulae for the ...

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 ...