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Comptes Rendus Mathématique
Volume 335, n° 1
pages 79-82 (2002)
Doi : S1631-073X(02)02430-5
Received : 14 November 2001 ; 
Arbres de Markov couple
Pairwise Markov trees
 

Wojciech Pieczynski
Institut National des Télécommunications, Département CITI, 9, rue Charles Fourier, 91000 Evry, France 

Note présentée par Paul Deheuvels

Résumé

Les modélisations par chaı̂nes de Markov cachées (CMC), dont la possibilité de calcul explicite de la loi Markovienne du processus caché conditionnelle aux observations est le principal intérêt, trouvent de très nombreuses applications dans les domaines les plus divers. Ce modèle a été récemment généralisé aux chaı̂nes de Markov « Couple », présentant les mêmes avantages que les CMC au niveau des traitements et proposant un pouvoir modélisant plus important. L'objet de cette Note est préciser comment les Arbres de Markov cachés, qui sont des extensions des CMC, peuvent également être généralisés aux modèles originaux appelés « Arbres de Markov couple ». Pour citer cet article : W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 79-82.

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Abstract

The Hidden Markov Chain (HMC) models are widely applied in various problems. This succes is mainly due to the fact that the hidden model distribution conditional on observations remains a Markov chain distribution, and thus different processings, like Bayesian restorations, are handleable. These models have been recetly generalized to “Pairwise” Markov chains, which admit the same processing power and a better modeling one. The aim of this Note is to show that the Hidden Markov trees, which can be seen as extensions of the HMC models, can also be generalized to “Pairwise” Markov trees, which present the same processing advantages and better modelling power. To cite this article: W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 79-82.

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