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Abstract:
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Bayesian model averaging, model selection and its approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates of convergence in prediction of future data than other methods such as AIC and leave-one-out cross-validation. On the other hand, these other methods can be inconsistent. This is sometimes called the AIC-BIC dilemma. I will present the catch-up phenomenon, which is a new explanation for the slow convergence of Bayesian methods. Based on this explanation I will define the switch distribution, a modification of the Bayesian marginal distribution. Under broad conditions, model selection and prediction based on the switch distribution is both consistent and achieves optimal convergence rates, thereby resolving the AIC-BIC dilemma. This is joint work with Peter Grunwald and Steven de Rooij.
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