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Statistical Inference in Hidden Markov Models Using k -Segment Constraints

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  • Michalis K. Titsias
  • Christopher C. Holmes
  • Christopher Yau

Abstract

Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marginals using the forward--backward algorithm. In this article, we expand the amount of information we could obtain from the posterior distribution of an HMM by introducing linear-time dynamic programming recursions that, conditional on a user-specified constraint in the number of segments, allow us to (i) find MAP sequences, (ii) compute posterior probabilities, and (iii) simulate sample paths. We collectively call these recursions k -segment algorithms and illustrate their utility using simulated and real examples. We also highlight the prospective and retrospective use of k -segment constraints for fitting HMMs or exploring existing model fits. Supplementary materials for this article are available online.

Suggested Citation

  • Michalis K. Titsias & Christopher C. Holmes & Christopher Yau, 2016. "Statistical Inference in Hidden Markov Models Using k -Segment Constraints," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 200-215, March.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:513:p:200-215
    DOI: 10.1080/01621459.2014.998762
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    Cited by:

    1. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    2. Haeran Cho & Claudia Kirch, 2022. "Two-stage data segmentation permitting multiscale change points, heavy tails and dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 653-684, August.

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