An application of MCMC methods for the multiple change-points problem
Signal Processing - Special section on Markov Chain Monte Carlo (MCMC) methods for signal processing
Gaussian Markov Random Fields: Theory And Applications (Monographs on Statistics and Applied Probability)
Exact and efficient Bayesian inference for multiple changepoint problems
Statistics and Computing
Joint segmentation of wind speed and direction using a hierarchical model
Computational Statistics & Data Analysis
Computational methods for complex stochastic systems: a review of some alternatives to MCMC
Statistics and Computing
Bayesian curve fitting using MCMC with applications to signalsegmentation
IEEE Transactions on Signal Processing
Exact Bayesian curve fitting and signal segmentation
IEEE Transactions on Signal Processing
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We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches for models where the parameters are dependent. Under the assumption that the dependence is Markov, we propose an efficient online algorithm for sampling from an approximation to the posterior distribution of the number and position of the changepoints. In a simulation study, we show that the approximation introduced is negligible. We illustrate the power of our approach through fitting piecewise polynomial models to data, under a model which allows for either continuity or discontinuity of the underlying curve at each changepoint. This method is competitive with, or outperform, other methods for inferring curves from noisy data; and uniquely it allows for inference of the locations of discontinuities in the underlying curve.