Catching up faster in Bayesian model selection and model averaging
Tim Erven, van, Peter Grünwald and Steven de Rooij
In: Advances in Neural Information Processing Systems 20 (NIPS 2007), 3-8 Dec 2007, Vancouver, Canada.
Bayesian model averaging, model selection and their approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates of convergence than other methods such as AIC and leave-one-out cross-validation. On the other hand, these other methods can be inconsistent. We identify the catch-up phenomenon as a novel explanation for the slow convergence of Bayesian methods. Based on this analysis we define the switch-distribution, a modification of the Bayesian marginal distribution. We prove that in many situations model selection and prediction based on the switch-distribution is both consistent and achieves optimal convergence rates, thereby resolving the AIC-BIC dilemma. The method is practical; we give an efficient implementation.