Deux modèles de Markov caché pour processus multiples et leur contribution à l’élaboration d’une notion de style postural
Journal de la société française de statistique, Tome 150 (2009) no. 1, pp. 73-100.

Nous décrivons dans cet article deux modèles de Markov caché (hmms) pour processus multiples que nous mettons au point à des fins d’application à un problème biomédical d’étude du maintien postural. Informellement, ces modèles sont des hmms standard considérant simultanément plusieurs processus individuels. Ceux-ci partagent les mêmes distributions de chaîne de Markov cachée et d’émission, avec l’ajout éventuel d’un effet de type mixte dans la partie conditionnelle du modèle. Nous discutons des aspects théoriques de l’estimation de l’ordre des deux modèles, ainsi que des aspects numériques. Nous contribuons enfin à l’élaboration d’une notion de “style postural”.

Two hidden Markov models (hmms) for multiple processes are introduced and applied to the biomedical study of how people maintain posture. Informally, they model simultaneously multiple processes by making them share the same hidden Markov and observed conditional distributions. One of them incorporates covariates and random effects in the conditional part. We discuss the theoretical issue of order estimation for both models as well as computational issues. Finally, we contribute to the definition of a notion of “postural style”.

Classification : 62M02, 62M05, 62P10
Mot clés : BIC, estimation de l’ordre, modèle de Markov caché (HMM), posture
Keywords: BIC, hidden Markov models (HMM), order estimation, posture 
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     journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
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Chambaz, Antoine; Bonan, Isabelle; Vidal, Pierre-Paul. Deux modèles de Markov caché pour processus multiples et leur contribution à l’élaboration d’une notion de style postural. Journal de la société française de statistique, Tome 150 (2009) no. 1, pp. 73-100. http://archive.numdam.org/item/JSFS_2009__150_1_73_0/

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