This paper addresses the problem of the signal segmentation within a hierarchical Bayesian framework by using reversible jump MCMC sampling. The signal is modelled by piecewise constant MA processes where the numbers of segments, the position of abrupt, the order and the coefficients of  the MA processes for each segment are unknown.

The reversible jump MCMC algorithm is then used to generate samples distributed according to the joint posterior distribution of the unknown parameters. These samples allow to compute some interesting features of the a posterior distribution. Main advantage of the algorithm reversible jump MCMC algorithm is produce the joint estimators for the parameter and hyper parameter in hierarchical Bayesian.  The performance of the this methodology is illustrated via several simulation results.

Keywords :     Hierarchical Bayesian model, Reversible Jump MCMC methods, Signal  Segmentation, piecewise constant Moving-Average (MA) processes