Catching Up Faster by Switching Sooner: A Prequential Solution to the AIC-BIC Dilemma

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dc.creatorvan Erven, Tim
dc.creatorGrunwald, Peter
dc.creatorde Rooij, Steven
dc.date2008-07-07
dc.date.accessioned2026-07-07T10:03:09Z
dc.date.available2026-07-07T10:03:09Z
dc.descriptionBayesian model averaging, model selection and its approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates og convergence than other methods such as AIC and leave-one-out cross-validation. On the other hand, these other methods can br 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 show that, 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. The method is practical; we give an efficient implementation. The switch distribution has a data compression interpretation, and can thus be viewed as a "prequential" or MDL method; yet it is different from the MDL methods that are usually considered in the literature. We compare the switch distribution to Bayes factor model selection and leave-one-out cross-validation.
dc.descriptionA preliminary version of a part of this paper appeared at the NIPS 2007 conference
dc.identifierhttps://arxiv.org/abs/0807.1005
dc.identifierhttp://arxiv.org/abs/0807.1005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169185
dc.subjectStatistics Theory
dc.subjectInformation Theory
dc.subjectMachine Learning
dc.subjectMethodology
dc.subject62G99; 94A99
dc.titleCatching Up Faster by Switching Sooner: A Prequential Solution to the AIC-BIC Dilemma
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