Les Chaı̂nes de Markov Cachées (CMC), qui permettent l'estimation des variables d'intérêt dans les cas des quantités importantes des données, sont largement utilisées dans les problèmes le plus divers. Ces modèles ont été récemment généralisés aux Chaı̂nes de Markov Couple (CMCouple), qui permettent des modélisations plus complètes des liens entre les processus caché et observé. Nous proposons dans cette Note de généraliser ces derniers aux modèles « Chaı̂nes de Markov Triplet » (CMT) dans lesquels la loi du couple (processus caché, processus observé) est la loi marginale d'un triplet Markovien. Nous montrons la calculabilité des estimations Bayésiennes du processus caché et présentons une CNS pour qu'une CMT soit une CMCouple, montrant en particulier que les modèles CMT sont strictement plus généraux que les modèles CMCouple. Nous précisons également un lien avec la fusion de Dempstert–Shafer.
The Hidden Markov Chains (HMC) are widely applied in various problems. This succes is mainly due to the fact that the hidden process can be recovered even in the case of very large set of data. These models have been recetly generalized to ‘Pairwise Markov Chains’ (PMC) model, which admit the same processing power and a better modeling one. The aim of this note is to propose further generalization called Triplet Markov Chains (TMC), in which the distribution of the couple (hidden process, observed process) is the marginal distribution of a Markov chain. Similarly to HMC, we show that posterior marginals are still calculable in Triplets Markov Chains. We provide a necessary and sufficient condition that a TMC is a PMC, which shows that the new model is strictly more general. Furthermore, a link with the Dempster–Shafer fusion is specified.
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Wojciech Pieczynski 1
@article{CRMATH_2002__335_3_275_0,
author = {Wojciech Pieczynski},
title = {Cha{\i}̂nes de {Markov} {Triplet}},
journal = {Comptes Rendus. Math\'ematique},
pages = {275--278},
publisher = {Elsevier},
volume = {335},
number = {3},
year = {2002},
doi = {10.1016/S1631-073X(02)02462-7},
language = {fr},
}
Wojciech Pieczynski. Chaı̂nes de Markov Triplet. Comptes Rendus. Mathématique, Volume 335 (2002) no. 3, pp. 275-278. doi : 10.1016/S1631-073X(02)02462-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02462-7/
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