Optimal segmentation of random processes

Segmentation of a nonstationary process consists in assuming piecewise stationarity and in detecting the instants of change. We consider the case where all the data is available at the same time and perform a global segmentation instead of a sequential procedure. We build a change process and define arbitrarily its prior distribution. This allows us to propose the MAP estimate as well as some minimum contrast estimate as a solution. One of the interests of the method is its ability to give the best solution, according to the resolution level required by the user, that is, to the prior distribution chosen. The method can address a wide class of parametric and nonparametric models. Simulations and applications to real data are proposed