Aic Scores as Evidence: A Bayesian Interpretation

Publisher Summary Akaike helped to launch the field in statistics now known as model selection theory by describing a goal, proposing a criterion, and proving a theorem. The goal is to figure out how accurately models will predict new data when fitted to old. The criterion came to be called the Akaike Information Criterion (AIC). The theorem that Akaike proved made it natural to understand AIC as a frequentist construct. AIC is a device for estimating the predictive accuracy of models. Bayesians assess an estimator by determining whether the estimates it generates are probably true or probably close to the truth. This chapter shows that it is an estimator whose estimates should be taken seriously by Bayesians, its frequentist pedigree notwithstanding. Frequentists often maintain that the question of how an individual estimate should be interpreted is meaningless—that the only legitimate question concerns the long-term behavior of estimators. Bayesians prove that interpretation of individual estimates is pressing in view of the fact that a given estimate might be produced by any number of different estimation procedures.