This report is a collection of comments on the Read Paper of Fearnhead and Prangle (2011), to appear in the Journal of the Royal Statistical Society Series B, along with a reply from the authors.

This document is the aggregation of several discussions of Lopes et al. (2010) we submitted tothe proceedings of the Ninth Valencia Meeting, held in Benidorm, Spain, on June 3–8, 2010, inconjunction with Hedibert Lopes’ talk at this meeting. The main point in those discussions is...

Published nearly seventy years ago, Jeffreys' Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes school. In particular, its advances on the...

Nested sampling is a simulation method for approximating marginal likelihoods. We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is asymptotically Gaussian. It is shown that the asymptotic variance of the nested...

This chapter surveys advances in the field of Bayesian computation over the past twenty years, from a purely personnal viewpoint, hence containing some ommissions given the spectrum of the field. Monte Carlo, MCMC and ABC themes are thus covered here, while the rapidly expanding area of particle...

This paper discusses the dual interpretation of the Jeffreys–Lindley’s paradox associated with Bayesian posterior probabilities and Bayes factors, both as a differentiation between frequentist and Bayesian statistics and as a pointer to the difficulty of using improper priors while testing....

Ce chapitre vise à établir les fondements de l’approche bayésienne en statistique inférentielle, ses racines historiques et ses justifications philosophiques, ainsi qu’`a présenter des illustrations de sa mise en oeuvre pratique.

Evidence and Evolution: the Logic behind the Science was publishedin 2008 by Elliott Sober. It examines the philosophical foundations of the sta-tistical arguments used to evaluate hypotheses in evolutionary biology, based onsimple examples and likelihood ratios. The difficulty with reading the...

The book A Treatise on Probability was published by John MaynardKeynes in 1921. It contains a critical assessment of the foundations of probabilityand of the current statistical methodology. As a modern reader, we review herethe aspects that are most related with statistics, avoiding a...