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Modèles à structure cachée : inférence, estimation, sélection de modèles et applications

Jean-Baptiste Durand 1
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558
Abstract : In this study, we present some inference algorithms and selection methods for the analysis of hidden Markov models. Properties of their structure are derived and lead us to define a family of models. These ones can be easily parameterized and interpreted. For these models, we propose inference algorithms based on backward-forward-like recursions which are efficient, numerically stable and which allow analytic calculus. Then, we investigate various order selection methods, among which the multifold cross validation, BIC, AIC and some criteria based on the marginal likelihood penalization. The existence of dependencies between variables complicates the implementation of half-sampling technics and leads to appropriate algorithms. These selection methods are compared through experimentations on simulated and on real data sets, the latter being related to software reliability. The importance of the hidden Markov chains and trees is also illustrated by applications in signal processing.
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https://tel.archives-ouvertes.fr/tel-00002754
Contributor : Jean-Baptiste Durand <>
Submitted on : Thursday, September 11, 2003 - 2:05:20 PM
Last modification on : Monday, February 10, 2020 - 4:36:45 PM
Long-term archiving on: : Thursday, September 23, 2010 - 3:51:43 PM

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  • HAL Id : tel-00002754, version 3

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Jean-Baptiste Durand. Modèles à structure cachée : inférence, estimation, sélection de modèles et applications. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2003. Français. ⟨tel-00002754v3⟩

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