Jayanta Ghosh, I.S.I and Purdue University

Model Selection---Overview and New Results

I will begin with a brief overview of model selection rules, focusing on BIC and AIC and their attractive properties as proved by Schwartz in 1978, Shibata in 1980 and 1981, and Jun Shao in 1997. A question that often comes up is which of the two should be used. There seems to be Bayesian preference for BIC and Frequentist preference for AIC. I will provide some history of this controversy and then go on to argue that this is an unfortunate controversy with its roots in confusion. New results indicate that one should think in terms of the Bayes Factor rather than BIC and that both the Bayes Factor and AIC have good Bayesian and Frequentist properties. However, they answer very different questions. If time permits Bayesian rules which do better than AIC (at least asymptotically) will be exhibited. The talk will be self-contained, requiring no previous background in model selection.