On the normalized maximum likelihood and Bayesian decision theory

Under the principle of minimum description length, the optimal predictive model maximizes the normalized maximum likelihood (NML). While the Bayesian approach to model selection aims to identify the model that best describes the (unknown) true distribution that generated a set of data, the NML approach to model selection makes no reference to a true distribution, and this is seen as a significant advantage of the latter approach. In contrast, this article shows that, for a specific choice of utility function, the NML approach is equivalent to a Bayesian model selection under the Bayesian boostrap and with a specific penalty function for model complexity. This new characterization uncovers some statistical issues about the NML approach. (c) 2006 Elsevier Inc. All rights reserved.