An 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 fo r estimating the hyperparameters of the model. Furthermore, a slight modifi cation of the algorithm allows one to compute the change-points sequences o f highest probabilities. The so-called reversible jump algorithm is not nec essary in this framework, and a very much simpler and faster procedure of s imulation is proposed. We show that different interesting statistics can be derived from the posterior distribution. Indeed, MCMC is powerful for simu lating joint distributions, and its use should not be restricted to the est imation of marginal posterior distributions, or posterior means. (C) 2001 E lsevier Science B.V. All rights reserved.