Choosing a model in a Classification purpose.
We advocate the usefulness of taking into account the modelling purpose when selecting a model. Two situations are considered to support this idea: Choosing the number of components in a mixture model in a cluster analysis perspective, and choosing a probabilistic model in a supervised classification context. For this last situation we propose a new criterion, the Bayesian Entropy Criterion, and illustrate its behavior with numerical experiments. Those numerical experiments shows that this new criterion compares favorably with the classical BIC criterion to choose a model minimizing the classification error rate.