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...

In 1996, Propp and Wilson introduced coupling from the past (CFTP), an algorithm for generating a sample from the exact stationary distribution of a Markov chain. In 1998, Fill proposed another so–called perfect sampling algorithm. These algorithms have enormous potential in Markov Chain Monte...

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...

Hidden Markov models lead to intricate computational problems when considered directly. In this paper, we propose an approximation method based on Gibbs sampling which allows an effective derivation of Bayes estimators for these models.