A discrete data augmentation scheme together with two different parameterizations yields two Gibbs samplers for sampling from the posterior distribution of the hyperparameters of the Dirichlet-multinomial hierarchical model under a default prior distribution. The finite-state space nature of...

This article proposes a set of categories, each one representing a particular distillation of important statistical ideas. Each category is labeled a “sense” because we think of these as essential in helping every statistical mind connect in constructive and insightful ways with statistical...

Doctors use statistics to advance medical knowledge; we use a medical analogy to build statistical inference “from scratch” and to highlight an improvement. A doctor, perhaps implicitly, predicts a treatment's effectiveness for an individual patient based on its performance in a clinical...

Bayesian inference for exponential mixtures is presented in the paper, including the choice of a non-informative prior based on a location-scale reparametrization of the mixture. Adapted control sheets are proposed for studying the convergence of the associated Gibbs sampler. They exhibit a...

The estimation of the noncentrality parameter of a chi-squared distribution, although simple to state, leads to difficulties, both for frequentist and Bayesian inferences. We propose in this paper a family of admissible improper Bayes estimators and study the minimax behavior of these estimators...

The estimation of quadratic functions of a multivariate normal mean is an inferential problem which, while being simple to state and often encountered in practice, leads to surprising complications both from frequentist and Bayesian points of view. The drawbacks of Bayesian inference using the...