Bayesian model comparison through posterior deviances  (2pm)

Murray Aitkin

Department of Mathematics and Statistics, University of Melbourne

This talk gives an overview of the use of the posterior distributions of likelihoods and likelihood ratios for model comparisons, as an alternative to frequentist likelihood ratio tests and Bayesian Bayes factors. Examples are given of a Bayesian version of the t-test, the goodness of fit of a Poisson model to count data, and an evaluation of the number of components needed for a mixture of normal distributions for the Roeder galaxy recession velocity data.

Prof. Murray Aitkin is a Professorial Fellow in the Department of Mathematics and Statistics at the University of Melbourne. He trained in Statistics at Sydney University and did postdoctoral work at the Thurstone Psychometric Laboratory at Chapel Hill. Since then he has held senior positions in Macquarie University, the Educational Testing Center, Lancaster University, Tel Aviv University, the University of Newcastle (UK), Australian National University and the University of Western Australia, Education Statistics Services Institute (US) and now at Melbourne University. He is a fellow of the American Statistical Association and an elected member of the International Statistical Institute. Prof. Aitkin has a range of research interests in theoretical and applied statistics, including Bayesian, frequentist and likelihood theories of inference, modelling in survey sampling and item-response modelling in large-scale testing.