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Bayesian estimation of hidden Markov chains: a stochastic implementation

Author

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  • Robert, Christian P.
  • Celeux, Gilles
  • Diebolt, Jean

Abstract

Hidden Markov models lead to intricate computational problems when considered directly. In this paper, we propose an approximation method based on Gibbs sampling which allows an effective derivation of Bayes estimators for these models.

Suggested Citation

  • Robert, Christian P. & Celeux, Gilles & Diebolt, Jean, 1993. "Bayesian estimation of hidden Markov chains: a stochastic implementation," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 77-83, January.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:1:p:77-83
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    Citations

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    Cited by:

    1. Rosychuk, Rhonda J. & Shofiqul Islam, 2009. "Parameter estimation in a model for misclassified Markov data -- a Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3805-3816, September.
    2. S. Özekici & R. Soyer, 2003. "Network reliability assessment in a random environment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 574-591, September.
    3. Gilles Celeux & Jean-Baptiste Durand, 2008. "Selecting hidden Markov model state number with cross-validated likelihood," Computational Statistics, Springer, vol. 23(4), pages 541-564, October.
    4. Chih-chiang Yang, 2007. "Confirmatory and Structural Categorical Latent Variables Models," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(6), pages 831-849, December.
    5. Tao, Laifa & Ma, Jian & Cheng, Yujie & Noktehdan, Azadeh & Chong, Jin & Lu, Chen, 2017. "A review of stochastic battery models and health management," Renewable and Sustainable Energy Reviews, Elsevier, vol. 80(C), pages 716-732.
    6. Savannah Wei Shi & Michel Wedel & F. G. M. (Rik) Pieters, 2013. "Information Acquisition During Online Decision Making: A Model-Based Exploration Using Eye-Tracking Data," Management Science, INFORMS, vol. 59(5), pages 1009-1026, May.
    7. McLachlan, Geoffrey J. & Krishnan, Thriyambakam & Ng, See Ket, 2004. "The EM Algorithm," Papers 2004,24, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    8. Chris Sherlock & Tatiana Xifara & Sandra Telfer & Mike Begon, 2013. "A coupled hidden Markov model for disease interactions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 609-627, August.
    9. Richard J. Boys & Daniel A. Henderson, 2004. "A Bayesian Approach to DNA Sequence Segmentation," Biometrics, The International Biometric Society, vol. 60(3), pages 573-581, September.
    10. Shuai Liu & Xiao-Yu Xu & Kai Zhao & Li-Ming Xiao & Qi Li, 2021. "Understanding the Complexity of Regional Innovation Capacity Dynamics in China: From the Perspective of Hidden Markov Model," Sustainability, MDPI, vol. 13(4), pages 1-22, February.
    11. Wang, Jiangzhou & Cui, Tingting & Zhu, Wensheng & Wang, Pengfei, 2023. "Covariate-modulated large-scale multiple testing under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    12. Wang, Xia & Shojaie, Ali & Zou, Jian, 2019. "Bayesian hidden Markov models for dependent large-scale multiple testing," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 123-136.
    13. Pierre-Julien Trombe & Pierre Pinson & Henrik Madsen, 2012. "A General Probabilistic Forecasting Framework for Offshore Wind Power Fluctuations," Energies, MDPI, vol. 5(3), pages 1-37, March.
    14. Ralf van der Lans & Rik Pieters & Michel Wedel, 2008. "—Competitive Brand Salience," Marketing Science, INFORMS, vol. 27(5), pages 922-931, 09-10.
    15. Rosella Castellano & Luisa Scaccia, 2014. "Can CDS indexes signal future turmoils in the stock market? A Markov switching perspective," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 285-305, June.

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