Application of MCMC methods for the multiple change-points problem

We present in this paper a multiple change-point analysis for which an MCMC sampler plays a fundamental role. It is used for estimating the posterior distribution of the unknown sequence of change-points instants, and also for estimating the hyperparameters of the model. Furthermore, a slight modification of the algorithm allows one to compute the change-points sequences of highest probabilities. The so-called reversible jump algorithm is not necessary in this framework, and a very much simpler and faster procedure of simulation is proposed. We show that different interesting statistics can be derived from the posterior distribution. Indeed, MCMC is powerful for simulating joint distributions, and its use should not be restricted to the estimation of marginal posterior distributions, or posterior means.