Bayesian curve fitting using MCMC with applications to signal segmentation

• Published in: IEEE transactions on signal processing Vol. 50; no. 3; pp. 747 - 758
• Main Authors: Punskaya, E., Andrieu, C., Doucet, A., Fitzgerald, W.J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-03-2002; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Bayesian analysis; Bayesian methods; Computer simulation; Curve fitting; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Exact solutions; Gaussian noise; Information, signal and communications theory; Linear regression; Mathematical analysis; Mathematical models; Monte Carlo methods; Parameter estimation; Probability distribution; Regression; Segmentation; Signal and communications theory; Signal processing; Signal, noise; Speech processing; Telecommunications and information theory; Working environment noise; Bayes estimation; Performance evaluation; Monte Carlo method; Segmentation; Noise reduction; Algorithm; Markov chain; Model matching; Simulation; Regression model; Signal processing; Curve fitting; Speech processing
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.984776

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.