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Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method

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  • C. P. Robert
  • T. Rydén
  • D. M. Titterington

Abstract

Hidden Markov models form an extension of mixture models which provides a flexible class of models exhibiting dependence and a possibly large degree of variability. We show how reversible jump Markov chain Monte Carlo techniques can be used to estimate the parameters as well as the number of components of a hidden Markov model in a Bayesian framework. We employ a mixture of zero‐mean normal distributions as our main example and apply this model to three sets of data from finance, meteorology and geomagnetism.

Suggested Citation

  • C. P. Robert & T. Rydén & D. M. Titterington, 2000. "Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 57-75.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:1:p:57-75
    DOI: 10.1111/1467-9868.00219
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    Cited by:

    1. Hartman, Brian M. & Heaton, Matthew J., 2011. "Accounting for regime and parameter uncertainty in regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 429-437.
    2. Deschamps, Philippe J., 2006. "A flexible prior distribution for Markov switching autoregressions with Student-t errors," Journal of Econometrics, Elsevier, vol. 133(1), pages 153-190, July.
    3. Salima El Kolei, 2013. "Parametric estimation of hidden stochastic model by contrast minimization and deconvolution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1031-1081, November.
    4. Ho, Remus K.W. & Hu, Inchi, 2008. "Flexible modelling of random effects in linear mixed models--A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1347-1361, January.
    5. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 433-465, September.
    6. McGrory, C.A. & Pettitt, A.N. & Faddy, M.J., 2009. "A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4311-4321, October.
    7. 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.
    8. Panagiotis Papastamoulis & George Iliopoulos, 2013. "On the Convergence Rate of Random Permutation Sampler and ECR Algorithm in Missing Data Models," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 293-304, June.
    9. Oscar M Rueda & Ramón Díaz-Uriarte, 2007. "Flexible and Accurate Detection of Genomic Copy-Number Changes from aCGH," PLOS Computational Biology, Public Library of Science, vol. 3(6), pages 1-8, June.
    10. Kobayashi, Kiyoshi & Kaito, Kiyoyuki & Lethanh, Nam, 2012. "A statistical deterioration forecasting method using hidden Markov model for infrastructure management," Transportation Research Part B: Methodological, Elsevier, vol. 46(4), pages 544-561.
    11. J. Vermaak & C. Andrieu & A. Doucet & S. J. Godsill, 2004. "Reversible Jump Markov Chain Monte Carlo Strategies for Bayesian Model Selection in Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 785-809, November.
    12. Christopher Nam & John Aston & Adam Johansen, 2014. "Parallel sequential Monte Carlo samplers and estimation of the number of states in a Hidden Markov Model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 553-575, June.
    13. Liu, Hefei & Song, Xinyuan & Zhang, Baoxue, 2022. "Varying-coefficient hidden Markov models with zero-effect regions," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    14. Francesco Bartolucci, 2002. "A recursive algorithm for Markov random fields," Biometrika, Biometrika Trust, vol. 89(3), pages 724-730, August.
    15. John Liechty & Rik Pieters & Michel Wedel, 2003. "Global and local covert visual attention: Evidence from a bayesian hidden markov model," Psychometrika, Springer;The Psychometric Society, vol. 68(4), pages 519-541, December.
    16. Yu Luo & David A. Stephens & Aman Verma & David L. Buckeridge, 2021. "Bayesian latent multi‐state modeling for nonequidistant longitudinal electronic health records," Biometrics, The International Biometric Society, vol. 77(1), pages 78-90, March.
    17. Jennifer Pohle & Roland Langrock & Floris M. Beest & Niels Martin Schmidt, 2017. "Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 270-293, September.
    18. McGrory, C.A. & Titterington, D.M., 2007. "Variational approximations in Bayesian model selection for finite mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5352-5367, July.
    19. Liu, Hefei & Song, Xinyuan, 2021. "Bayesian analysis of hidden Markov structural equation models with an unknown number of hidden states," Econometrics and Statistics, Elsevier, vol. 18(C), pages 29-43.
    20. Hugh Christensen & Simon Godsill & Richard E Turner, 2020. "Hidden Markov Models Applied To Intraday Momentum Trading With Side Information," Papers 2006.08307, arXiv.org.
    21. Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
    22. Nial Friel & Håvard Rue, 2007. "Recursive computing and simulation-free inference for general factorizable models," Biometrika, Biometrika Trust, vol. 94(3), pages 661-672.
    23. 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.
    24. Ting Wang & Jiancang Zhuang & Kazushige Obara & Hiroshi Tsuruoka, 2017. "Hidden Markov modelling of sparse time series from non-volcanic tremor observations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 691-715, August.

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