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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.


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

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

First available in Project Euclid: 21 August 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Sequential Monte Carlo high-order HMM smoothing filtering


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.

Export citation