Maximized log-likelihood updating and model selection

Abstract

On the basis of simple algebraic identities, we derive a new updating formula for the maximized log-likelihoods. This formula enables us to decompose the predictive minimum description length (PMDL) criterion of Rissanen J. Roy. Statist. Soc. Ser. B 49 (1987) 1 into maximized log-likelihood and a penalty term representing model complexity. Statistical implications for model selection problems are discussed. © 2003 Elsevier B.V. All rights reserved.