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An expectation maximization algorithm for the hidden markov models with multiparameter student-t observations

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  • Emna Ghorbel

    (ESPRIT School of Engineering)

  • Mahdi Louati

    (Digital Research Center of Sfax)

Abstract

Hidden Markov models are a class of probabilistic graphical models used to describe the evolution of a sequence of unknown variables from a set of observed variables. They are statistical models introduced by Baum and Petrie in Baum (JMA 101:789–810) and belong to the class of latent variable models. Initially developed and applied in the context of speech recognition, they have attracted much attention in many fields of application. The central objective of this research work is upon an extension of these models. More accurately, we define multiparameter hidden Markov models, using multiple observation processes and the Riesz distribution on the space of symmetric matrices as a natural extension of the gamma one. Some basic related properties are discussed and marginal and posterior distributions are derived. We conduct the Forward-Backward dynamic programming algorithm and the classical Expectation Maximization algorithm to estimate the global set of parameters. Using simulated data, the performance of these estimators is conveniently achieved by the Matlab program. This allows us to assess the quality of the proposed estimators by means of the mean square errors between the true and the estimated values.

Suggested Citation

  • Emna Ghorbel & Mahdi Louati, 2024. "An expectation maximization algorithm for the hidden markov models with multiparameter student-t observations," Computational Statistics, Springer, vol. 39(6), pages 3287-3301, September.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:6:d:10.1007_s00180-023-01432-7
    DOI: 10.1007/s00180-023-01432-7
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    References listed on IDEAS

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    1. Kammoun, Kaouthar & Louati, Mahdi & Masmoudi, Afif, 2017. "Maximum likelihood estimator of the scale parameter for the Riesz distribution," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 127-131.
    2. Andersson, Steen A. & Klein, Thomas, 2010. "On Riesz and Wishart distributions associated with decomposable undirected graphs," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 789-810, April.
    3. Louati, Mahdi & Masmoudi, Afif, 2015. "Moment for the inverse Riesz distributions," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 30-37.
    4. Douc, R. & Fort, G. & Moulines, E. & Priouret, P., 2009. "Forgetting the initial distribution for Hidden Markov Models," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1235-1256, April.
    5. Lin, Pi-Erh, 1972. "Some characterizations of the multivariate t distribution," Journal of Multivariate Analysis, Elsevier, vol. 2(3), pages 339-344, September.
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