Empirical Bayes methods are often thought of as a bridge between classical and Bayesian inference. In fact, in the literature the term empirical Bayes is used in quite diverse contexts and with different motivations. In this article, we provide a brief overview of empirical Bayes methods...

The original Studentization was the conversion of a sample mean departure into the familiar t-statistic, plus the derivation of the corresponding Student distribution function; the observed value of the distribution function is the observed p-value, as presented in an elemental form. We examine...

We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a non-parametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities.

Empirical Bayes procedures are commonly used based on the supposed asymptotic equivalence with fully Bayesian procedures, which, however, has not so far received full theoretical support in terms of uncertainty quantification. In this note, we provide some results on contraction rates of...

We present a dependent Bayesian nonparametric model for the proba- bilistic modelling of species-by-site data, i.e. population data where observations at different sites are classified into distinct species. We use a dependent version of the Griffiths-Engen-McCloskey distribution, the...

Although there have been a lot of developpements in the recent years on estimation in Bayesian nonparametric models, from a theoretical point view as well as from a methodological point of view, little has been done on Bayesian testing in nonparametric frameworks. In this talk I will be...

In this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on [0, 1]. We consider a parametrization of Beta distributions in terms of mean and scale parameters and construct a mixture of these Betas in the mean parameter,...

We have a statistic for assessing an observed data point relative to a statistical model but find that its distribution function depends on the parameter. To obtain the corresponding p-value, we require the minimally modified statistic that is ancillary; this process is called Studentization. We...