EM algorithm coupled with particle filter for maximum likelihood parameter estimation of stochastic differential mixed-effects models
Samson, Adeline; Donnet, Sophie (2010), EM algorithm coupled with particle filter for maximum likelihood parameter estimation of stochastic differential mixed-effects models. https://basepub.dauphine.fr/handle/123456789/4851
Type
Document de travail / Working paperLien vers un document non conservé dans cette base
http://hal.archives-ouvertes.fr/hal-00519576/fr/Date
2010Éditeur
Université Paris-Dauphine
Ville d’édition
Paris
Pages
37
Métadonnées
Afficher la notice complèteRésumé (EN)
Biological processes measured repeatedly among a series of individuals are standardly analyzed by mixed models. They use common regression function and error model, both depending on individual random parameters. Regression functions defined by parametric Stochastic Differential Equations (SDEs) model adequately biological processes. This results in a mixed-effects model defined by an SDE. We focus on the parameter maximum likelihood estimation of this model. As the likelihood is not explicit, we propose the use of a stochastic version of the Expectation- Maximization algorithm combined with the Particle Markov Chain Monte Carlo method. We prove the convergence of the proposed algorithm towards the maximum likelihood estimator. We illustrate the performance of this estimation method on simulated datasets. We consider two examples: the first one is based on an Ornstein-Uhlenbeck process with two random parameters and an additive error model; the second one is based on a time-inhomogeneous SDE (Gompertz SDE) with a stochastic volatility error model and three random parameters. We highlight the superiority of our estimator over an estimator based on the EM algorithm coupled with standard MCMC algorithms.Mots-clés
Stochastic Differential Equations; algorithmPublications associées
Affichage des éléments liés par titre et auteur.
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Samson, Adeline; Donnet, Sophie (2007) Article accepté pour publication ou publié
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Samson, Adeline; Donnet, Sophie (2008) Article accepté pour publication ou publié