Fitting multiple change-point models to data
Computational Statistics & Data Analysis
Inference in Hidden Markov Models (Springer Series in Statistics)
Inference in Hidden Markov Models (Springer Series in Statistics)
Using penalized contrasts for the change-point problem
Signal Processing
Exact and efficient Bayesian inference for multiple changepoint problems
Statistics and Computing
Exploring the state sequence space for hidden Markov and semi-Markov chains
Computational Statistics & Data Analysis
Continuously variable duration hidden Markov models for automatic speech recognition
Computer Speech and Language
IEEE Transactions on Signal Processing
Optimal segmentation of random processes
IEEE Transactions on Signal Processing
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This paper addresses the retrospective or off-line multiple change-point detection problem. Multiple change-point models are here viewed as latent structure models and the focus is on inference concerning the latent segmentation space. Methods for exploring the space of possible segmentations of a sequence for a fixed number of change points may be divided into two categories: (i) enumeration of segmentations, (ii) summary of the possible segmentations in change-point or segment profiles. Concerning the first category, a dynamic programming algorithm for computing the top $$N$$N most probable segmentations is derived. Concerning the second category, a forward-backward dynamic programming algorithm and a smoothing-type forward-backward algorithm for computing two types of change-point and segment profiles are derived. The proposed methods are mainly useful for exploring the segmentation space for successive numbers of change points and provide a set of assessment tools for multiple change-point models that can be applied both in a non-Bayesian and a Bayesian framework. We show using examples that the proposed methods may help to compare alternative multiple change-point models (e.g. Gaussian model with piecewise constant variances or global variance), predict supplementary change points, highlight overestimation of the number of change points and summarize the uncertainty concerning the position of change points.