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Fast exact filtering in generalized conditionally observed Markov switching models with copulas

Fei Zheng 1 Stéphane Derrode 1 Wojciech Pieczynski 2, 3
1 imagine - Extraction de Caractéristiques et Identification
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
2 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications
SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
Abstract : We deal with the problem of statistical filtering in the context of Markov switching models. For X_1^N hidden continuous process, R_1^N hidden finite Markov process, and Y_1^N observed continuous one, the problem is to sequentially estimate X_1^N and R_1^N from Y_1^N. In the classical " conditional Gaussian Linear state space model " (CGLSSM), where (R_1^N, X_1^N) is a hidden Gaussian Markov chain, fast exact filtering is not workable. Recently, " conditionally Gaussian observed Markov switching model " (CGOMSM) has been proposed, in which (R_1^N, Y_1^N) is a hidden Gaussian Markov chain instead. This model allows fast exact filtering. In this paper, using copula, we extend CGOMSM to a more general one, in which (R_1^N, Y_1^N) is a hidden Markov chain (HMC) with noise of any form and the regimes are no need to be all Gaussian, while the exact filtering is still workable. Experiments are conducted to show how the exact filtering results based on CGOMSM can be improved by the use of the new model.
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Fei Zheng, Stéphane Derrode, Wojciech Pieczynski. Fast exact filtering in generalized conditionally observed Markov switching models with copulas. TAIMA 2018: Traitement et Analyse de l'Information Méthodes et Applications, Apr 2018, Hammamet, Tunisia. ⟨hal-01786221⟩

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