On the Use of the Fisher Information in Computing the Stochastic Complexity

Because the evaluation of the stochastic complexity is difficult for most of the models, various approximations have been proposed during the last two decades. In this article, we focus on two approximations that rely on the Fisher information, and we revisit some recent results that demonstrate the estimation performances of the two formulae in solving the following problems: order selection for autoregressive models, estimation of the number of sinewaves in gaussian noise, and order selection for Markov models.