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 ».
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.
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@article{CRMATH_2002__335_1_79_0,
author = {Pieczynski, Wojciech},
title = {Arbres de {Markov} couple},
journal = {Comptes Rendus. Math\'ematique},
pages = {79--82},
publisher = {Elsevier},
volume = {335},
number = {1},
year = {2002},
doi = {10.1016/S1631-073X(02)02430-5},
language = {fr},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02430-5/}
}
TY - JOUR AU - Pieczynski, Wojciech TI - Arbres de Markov couple JO - Comptes Rendus. Mathématique PY - 2002 SP - 79 EP - 82 VL - 335 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02430-5/ DO - 10.1016/S1631-073X(02)02430-5 LA - fr ID - CRMATH_2002__335_1_79_0 ER -
Pieczynski, Wojciech. Arbres de Markov couple. Comptes Rendus. Mathématique, Tome 335 (2002) no. 1, pp. 79-82. doi : 10.1016/S1631-073X(02)02430-5. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02430-5/
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