Bayesian curve fitting using MCMC with applications to signal segmentation

We propose some Bayesian methods to address the problem of fitting a signal modeled by a sequence of piecewise constant linear (in the parameters) regression models, for example, autoregressive or Volterra models. A joint prior distribution is set up over the number of the changepoints/knots, their positions, and over the orders of the linear regression models within each segment if these are unknown. Hierarchical priors are developed and, as the resulting posterior probability distributions and Bayesian estimators do not admit closed-form analytical expressions, reversible jump Markov chain Monte Carlo (MCMC) methods are derived to estimate these quantities. Results are obtained for standard denoising and segmentation of speech data problems that have already been examined in the literature. These results demonstrate the performance of our methods.