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...

This chapter provides a overview of Bayesian inference, mostly emphasising that it is auniversal method for summarising uncertainty and making estimates and predictions usingprobability statements conditional on observed data and an assumed model (Gelman 2008).The Bayesian perspective is thus...

Every reversible Markov chain defines an operator whose spectrum encodes the convergenceproperties of the chain. When the state space is finite, the spectrum is just the set ofeigenvalues of the corresponding Markov transition matrix. However, when the state space isinfinite, the spectrum may be...

If, in the mid 1980's, one had asked the average statistician about the di-culties of using Bayesian Statistics, the most likely answer would have been\Well, there is this problem of selecting a prior distribution and then, evenif one agrees on the prior, the whole Bayesian inference is simply...

William Feller has a Note on Bayes’ rule in his classic probability bookin which he expresses doubts about the Bayesian approach to statistics and decriesit as a method of the past. We analyze in this note the motivations for Feller’sattitude, without aiming at a complete historical coverage...

The Search for Certainty was published in 2009 by Krzysztof Burdzy. Itexamines the “philosophical duopoly” of vonMises and de Finetti at the foundationof probability and statistics and find this duopoly missing. This review exposesthe weakness of the arguments presented in the book, it...

A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data simulated from the true process; exact inference being...