The Catch-up Phenomenon in Bayesian and MDL model selection

Jeudi 24 janvier 2013 14:00-15:00 - Van erven Tim - Orsay

Résumé : Bayesian and minimum description length (MDL) model selection and their 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 and MDL 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.
From an MDL point of view, the occurrence of the catch-up phenomenon implies that the code that corresponds to the switch distribution compresses the sample data substantially more than the standard two-part MDL code. From a Bayesian point of view, the occurrence of the catch-up phenomenon implies that the distribution of the data is not a random sample from the prior distribution.

Lieu : bât. 425 - 117-119

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