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...

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...

In Templeton (2010), the Approximate Bayesian Compu-tation (ABC) algorithm (see, e.g., Pritchard et al., 1999,Beaumont et al., 2002,Marjoram et al., 2003, Ratmann et al.,2009) is criticised on mathematical and logical grounds: “the[Bayesian] inference is mathematically incorrect and...

This introduction to Bayesian statistics presents themain concepts as well as the principal reasons advocatedin favour of a Bayesian modelling. We coverthe various approaches to prior determination as wellas the basis asymptotic arguments in favour of usingBayes estimators. The testing aspects...

We propose a global noninformative approach for Bayesian variable selection that builds onZellner’s g-priors and is similar to Liang et al. (2008). Our proposal does not require any kindof calibration. In the case of a benchmark, we compare Bayesian and frequentist regularizationapproaches...

In this paper, we consider the implications of the fact that parallel raw-power canbe exploited by a generic Metropolis{Hastings algorithm if the proposed values areindependent. In particular, we present improvements to the independent Metropolis{Hastings algorithm that signicantly decrease the...