HAL : hal-00263515, version 1

DOI : 10.1051/ps:2007045

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ESAIM P&S 12 (2008) 196-218

Parametric inference for mixed models defined by stochastic differential equations

Sophie Donnet 1, Adeline Samson 2, 3

(2008)

Non-linear mixed models defined by stochastic differential equations (SDEs) are consid- ered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measure- ment instants. A tuned hybrid Gibbs algorithm based on conditional Brownian bridges simulations of the unobserved process paths is included in this algorithm. The convergence is proved and the error induced on the likelihood by the Euler-Maruyama approximation is bounded as a function of the step size of the approximation. Results of a pharmacokinetic simulation study illustrate the accuracy of this estimation method. The analysis of the Theophyllin real dataset illustrates the relevance of the SDE approach relative to the deterministic approach.

1 :	SELECT (INRIA Futurs)
	INRIA – Université Paris XI - Paris Sud
2 :	Mathématiques appliquées Paris 5 (MAP5)
	CNRS : UMR8145 – Université Paris V - Paris Descartes
3 :	Modèles et méthodes de l'évaluation thérapeutique des maladies chroniques
	INSERM : U738 – Université Paris VII - Paris Diderot

Domaine

:

Mathématiques/Statistiques Statistiques/Théorie

Mots Clés : Brownian bridge – diffusion process – Euler-Maruyama approximation – Gibbs algorithm – incomplete data model – maximum likelihood estimation – non-linear mixed effects model – SAEM algorithm

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Contributeur : Adeline Samson <>

Soumis le : Mardi 31 Mars 2009, 17:44:35

Dernière modification le : Dimanche 3 Octobre 2010, 21:07:19