A minimum description length approach to hidden Markov models with Poisson and Gaussian emissions. Application to order identification |
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Authors: | A. Chambaz A. Garivier E. Gassiat |
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Affiliation: | 1. MAP5, Université Paris Descartes, France;2. CNRS & TELECOM ParisTech, France;3. Laboratoire de Mathématiques, Université Paris-Sud, France |
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Abstract: | We address the issue of order identification for hidden Markov models with Poisson and Gaussian emissions. We prove information-theoretic BIC-like mixture inequalities in the spirit of Finesso [1991. Consistent estimation of the order for Markov and hidden Markov chains. Ph.D. Thesis, University of Maryland]; Liu and Narayan [1994. Order estimation and sequential universal data compression of a hidden Markov source by the method of mixtures. Canad. J. Statist. 30(4), 573–589]; Gassiat and Boucheron [2003. Optimal error exponents in hidden Markov models order estimation. IEEE Trans. Inform. Theory 49(4), 964–980]. These inequalities lead to consistent penalized estimators that need no prior bound on the order. A simulation study and an application to postural analysis in humans are provided. |
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Keywords: | BIC Infinite alphabet Model selection Order estimation |
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