The specificity of the Bayesian paradigm is nowhere clearer than when considering hypothesis testing and model choice, as the proposed procedures greatly differ from the Neyman-Pearson and Fisher alternatives. While, historically (Wrinch and Jeffreys, 1919), the central tool for conducting testing is the Bayes factor, with decision-theoretic support, its implementation faces difficulties that makes its adoption by practitioners a challenge. After exhibiting these difficulties, we examine several Bayesian testing alternatives proposed in the more recent Bayesian literature.(Part of this talk is covering joint work with K. Kamary, K. Mergersen, and J. Rousseau in arXiv:1412.2044.)
Christian Robert is a very eminent Bayesian Statistician at the Research Centre in Mathematics of Decision (CEREMADE) in Paris. His dozen books include ‘Bayesian choice’ (for which he won the De Groot Prize) and ‘Monte Carlo statistical methods’. Some of his numerous publications are: ‘On the Jeffreys-Lindley paradox’; ‘The expected demise of the Bayes factor’; and ‘Abandon statistical significance’. His research interests include Bayesian statistics, MCMC and Approximate Bayesian Calculation.
O. Behnke, L. Lyons, L. Moneta, N. Wardle