En génétique des populations, les modèles sont souvent complexes ce qui rend l'évaluation de la vraisemblance difficile, si ce n'est impossible. En revanche, des mécanismes de génération de données sont parfois disponibles ce qui explique pourquoi les méthodes d'inférence bayésienne...

Managers in the fundraising and public sectors face the constant challenge of soliciting donations from a population who may or may not have donated before. Rather than merely asking respondents what they wish to donate, it is standard practice to present a set of suggested amounts – the...

The article discusses the views of statistics professors Andrew Gelman and Christian P. Robert about the intemperate anti-Bayesian statement appeared on the book of probability theory by mathematician William Feller. It notes that they explore Feller's words along with similar remarks by others...

The missionary zeal of many Bayesians of old has been matched, in the other direction, by an attitude among some theoreticians that Bayesian methods were absurd—not merely misguided but obviously wrong in principle. We consider several examples, beginning with Feller's classic text on...

We consider finite state space stationary hidden Markov models (HMMs) in the situation where the number of hidden states is unknown. We provide a frequentist asymptotic evaluation of Bayesian analysis methods. Our main result gives posterior concentration rates for the marginal densities, that...

We consider finite state space stationary hidden Markov models (HMMs) in the situation where the number of hidden states is unknown. We provide a frequentist asymptotic evaluation of Bayesian analysis methods. Our main result gives posterior concentration rates for the marginal densities, that...

The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce a valid outcome. We derive necessary and sufficient conditions on those statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true...

The issue of using informative priors for estimation of mixtures at multiple time points is examined. Several different informative priors and an independent prior are compared using samples of actual and simulated aerosol particle size distribution (PSD) data. Measurements of aerosol PSDs refer...

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...

Mixture models may be a useful and flexible tool to describe data with a complicated structure, for instance characterized by multimodality or asymmetry. In a Bayesian setting, it is a well established fact that one need to be careful in using improper prior distributions, since the posterior...