Afrika Statistika

On some Extensions of the Sequential Monte Carlo methods in high-order Hidden Markov Models

Mouhamad Mounirou ALLAYA, Alioune COULIBALY, El Hadj DÈME, Mouhamadou Moustapha KÂ, and Babacar SÈNE

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Abstract

We analyze some extensions of the Sequential Monte Carlo (SMC) methods in the context of nonlinear state space models. Namely, we tailor the SMC methods to handle high-order HMM through the customary recursions of posterior distributions. It proceeds on mimicking the two-step procedure that is, the prediction step and the update step, in the derivation of the filter distribution. Once stated, we extend some smoothing recursions as the Forward-Backward algorithm and the Backward smoother to deal with the actual smoothing distributions in high-order HMM. Finally, we give few examples as an application of these extensions.

Résumé

Nous analysons quelques extensions des méthodes de Monte Carlo séquentielles (SMC) dans le contexte des modèles à espace d'états non-linéaires. Précisément,, nous adaptons les méthodes SMC pour traiter les HMM d'ordre supérieur à travers les récursions habituelles des distributions à posteriori. Cela procède par mimer la procédure en deux étapes, c'est-à-dire l'étape de prédiction et l'étape de mise à jour, dans la dérivation de la distribution du filtre. Une fois obtenu, nous étendons certaines récursions de lissage comme l'algorithme Forward-Backward et l'algorithme Backward Smoother pour traiter les distributions de lissage dans les HMM d'ordre supérieur. Enfin, nous donnons quelques exemples de l'application de ces extensions.

Article information

Source
Afr. Stat., Volume 14, Number 2 (2019), 1977-1998.

Dates
First available in Project Euclid: 21 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.as/1566353035

Digital Object Identifier
doi:10.16929/as/2019.1977.145

Mathematical Reviews number (MathSciNet)
MR3995012

Zentralblatt MATH identifier
07104736

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 62M05: Markov processes: estimation 65C05: Monte Carlo methods

Keywords
Sequential Monte Carlo high-order HMM smoothing filtering

Citation

ALLAYA, Mouhamad Mounirou; COULIBALY, Alioune; DÈME, El Hadj; KÂ, Mouhamadou Moustapha; SÈNE, Babacar. On some Extensions of the Sequential Monte Carlo methods in high-order Hidden Markov Models. Afr. Stat. 14 (2019), no. 2, 1977--1998. doi:10.16929/as/2019.1977.145. https://projecteuclid.org/euclid.as/1566353035


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