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Estimation of Viterbi path in Bayesian hidden Markov models

Author

Listed:
  • Jüri Lember

    (University of Tartu)

  • Dario Gasbarra

    (University of Helsinki)

  • Alexey Koloydenko

    (Royal Holloway, University of London)

  • Kristi Kuljus

    (University of Tartu)

Abstract

The article studies different methods for estimating the Viterbi path in the Bayesian framework. The Viterbi path is an estimate of the underlying state path in hidden Markov models (HMMs), which has a maximum joint posterior probability. Hence it is also called the maximum a posteriori (MAP) path. For an HMM with given parameters, the Viterbi path can be easily found with the Viterbi algorithm. In the Bayesian framework the Viterbi algorithm is not applicable and several iterative methods can be used instead. We introduce a new EM-type algorithm for finding the MAP path and compare it with various other methods for finding the MAP path, including the variational Bayes approach and MCMC methods. Examples with simulated data are used to compare the performance of the methods. The main focus is on non-stochastic iterative methods and our results show that the best of those methods work as well or better than the best MCMC methods. Our results demonstrate that when the primary goal is segmentation, then it is more reasonable to perform segmentation directly by considering the transition and emission parameters as nuisance parameters.

Suggested Citation

  • Jüri Lember & Dario Gasbarra & Alexey Koloydenko & Kristi Kuljus, 2019. "Estimation of Viterbi path in Bayesian hidden Markov models," METRON, Springer;Sapienza Università di Roma, vol. 77(2), pages 137-169, August.
    • Handle: RePEc:spr:metron:v:77:y:2019:i:2:d:10.1007_s40300-019-00152-7
    DOI: 10.1007/s40300-019-00152-7
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/1906 is not listed on IDEAS
    2. Same, Allou & Ambroise, Christophe & Govaert, Gerard, 2006. "A classification EM algorithm for binned data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 466-480, November.
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    Cited by:

    1. Jan Bulla & Roland Langrock & Antonello Maruotti, 2019. "Guest editor’s introduction to the special issue on “Hidden Markov Models: Theory and Applications”," METRON, Springer;Sapienza Università di Roma, vol. 77(2), pages 63-66, August.

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