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...

Gibbs sampling has had great success in the analysis of mixture models. In particular, the “latent variable” formulation of the mixture model greatly reduces computational complexity. However, one failing of this approach is the possible existence of almost-absorbing states, called trapping...

Many authors have considered the problem of estimating a covariance matrix in small samples. In this framework the sample covariance matrix is not robust, the solution is to impose some ad hoc structure on the covariance matrix to force it to be well-conditioned. This method is known as...

This thesis presents contributions to the Monte Carlo methodology used in Bayesian statistics. The Bayesian framework is one of the main approaches to statistics and includes a rich methodology to perform inference and model choice. However, as statistical models become more realistic and drift...

Gibbs sampling has had great success in the analysis of mixture models. In particular, the “latent variable” formulation of the mixture model greatly reduces computational complexity. However, one failing of this approach is the possible existence of almost-absorbing states, called trapping...

In this essay, I argue about the relevance and the ultimate unity of the Bayesian approach in a neutral and agnostic manner. My main theme is that Bayesian data analysis is an effective tool for handling complex models, as proven by the increasing proportion of Bayesian studies in the applied...

In Chib (1995), a method for approximating marginal densities in a Bayesian setting is proposed, with one proeminent application being the estimation of the number of components in a normal mixture. As pointed out in Neal (1999) and Fruhwirth-Schnatter (2004), the approximation often fails short...

This note is made of four book reviews of Brooks et al. (2011), Karian and Dudewicz (2011), McGrayne (2010), and Ziliak and Mc- Closkey (2008), respectively. They are scheduled to appear in the next issue of CHANCE.

Simulation has become a standard tool in statistics because it may be the only tool available for analysing some classes of probabilistic models. We review in this paper simulation tools that have been specifically derived to address statistical challenges and, in particular, recent advances in...

Also known as likelihood-free methods, approximate Bayesian computational (ABC) methods have appeared in the past ten years as the most satisfactory approach to untractable likelihood problems, first in genetics then in a broader spectrum of applications. However, these methods suffer to some...