Casella and Robert (1996) presented a general Rao--Blackwellisation principle for accept-reject and Metropolis-Hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at a high cost in computing and storage. Adopting a completely different...

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.

Monte Carlo methods are now an essential part of the statistician's toolbox, to the point of being more familiar to graduate students than the measure theoretic notions upon which they are based! We recall in this note some of the advances made in the design of Monte Carlo techniques towards...

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...

Missing variable models are typical benchmarks for new computational techniques in that the ill-posed nature of missing variable models offer a challenging testing ground for these techniques. This was the case for the EM algorithm and the Gibbs sampler, and this is also true for importance...

In this note we attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940's through its use today. We see how the earlier stages of the Monte Carlo (MC, not MCMC) research have led to the algorithms currently in use. More...

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...