Using penalized contrasts for the change-point problem

A methodology for model selection based on a penalized contrast is developed. This methodology is applied to the change-point problem, for estimating the number of change points and their location. We aim to complete previous asymptotic results by constructing algorithms that can be used in diverse practical situations. First, we propose an adaptive choice of the penalty function for automatically estimating the dimension of the model, i.e., the number of change points. In a Bayesian framework, we define the posterior distribution of the change-point sequence as a function of the penalized contrast. MCMC procedures are available for sampling this posterior distribution. The parameters of this distribution are estimated with a stochastic version of EM algorithm (SAEM). An application to EEG analysis and some Monte-Carlo experiments illustrate these algorithms.