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...

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...

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

Abstract For many decades, statisticians have made attempts to prepare the Bayesian omelette without breaking the Bayesian eggs; that is, to obtain probabilistic likelihood-based inferences without relying on informative prior distributions. A recent example is Murray Aitkin´s recent book,...

type="main" xml:id="rssb12056-abs-0001" <title type="main">Summary</title> <p>The choice of the summary statistics that are used in Bayesian inference and in particular in approximate Bayesian computation algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used...</p>

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...

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...