AIC Scores as Evidence – a Bayesian Interpretation
نویسنده
چکیده
Bayesians often reject the Akaike Information Criterion (AIC) because it introduces ideas that do not fit into their philosophy of statistical inference. Here we show that a difference in the AIC scores that two models receive is evidence that they differ in their degrees of predictive accuracy, where evidence is understood in terms of the Law of Likelihood. Since the Law of Likelihood is a central Bayesian principle, Bayesians have reason to take AIC scores seriously.
منابع مشابه
Scoring functions for learning Bayesian networks
The aim of this work is to benchmark scoring functions used by Bayesian network learning algorithms in the context of classification. We considered both information-theoretic scores, such as LL, AIC, BIC/MDL, NML and MIT, and Bayesian scores, such as K2, BD, BDe and BDeu. We tested the scores in a classification task by learning the optimal TAN classifier with benchmark datasets. We conclude th...
متن کاملCatching Up Faster by Switching Sooner: A Prequential Solution to the AIC-BIC Dilemma
Bayesian model averaging, model selection and its 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...
متن کاملAn Nml-based Method for Learning Bayesian Networks
Bayesian networks are among most popular model classes for discrete vector-valued i.i.d data. Currently the most popular model selection criterion for Bayesian networks follows Bayesian paradigm. However, this method has recently been reported to be very sensitive to the choice of prior hyper-parameters [1]. On the other hand, the general model selection criteria, AIC [2] and BIC [3], are deriv...
متن کاملCatching Up Faster by Switching Sooner: A predictive approach to adaptive estimation with an application to the AIC-BIC Dilemma
Prediction and estimation based on Bayesian model selection and model averaging, and derived methods such as BIC, do not always converge at the fastest possible rate. We identify the catch-up phenomenon as a novel explanation for the slow convergence of Bayesian methods, and use it to define a modification of the Bayesian predictive distribution, called the switch distribution. When used as an ...
متن کاملFactor Analysis and Aic
The information criterion AIC was introduced to extend the method of maximum likelihood to the multimodel situation. It was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis. The use of the AIC criterion in the factor analysis is particularly interesting whe...
متن کامل