Bayesian segmentation of piecewise constant autoregressive processes using MCMC methods
In this paper we address the problem of the Bayesian segmentation of signals which are modelled as piecewise constant autoregressive (AR) processes excited by white Gaussian noise. We define a probabilistic model that takes into account the fact that the number of AR processes needed to represent the data, the model orders, the values of the parameters and the noise variances are unknown. The resulting posterior probability distributions and Bayesian estimators of the model parameters do not admit closed-form analytical expression. A stochastic algorithm based on a reversible jump Markov chain Monte Carlo (MCMC) method [11] is derived to estimate these quantities. Results are obtained for both synthetic and real data (a speech signal which has been examined in the literature previously [1], [4] and [14]) and confirm the applicability of both the model and the algorithm. ∗C Andrieu is sponsored by AT&T Laboratories, Cambridge, UK. †A.Doucet is sponsored by EPSRC, UK.