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dc.contributor.authorSamson, Adeline
HAL ID: 9408
dc.contributor.authorDonnet, Sophie
HAL ID: 14568
ORCID: 0000-0003-4370-7316
dc.subjectBrownian bridgeen
dc.subjectSAEM algorithmen
dc.subjectNon-linear mixed effects modelen
dc.subjectMaximum likelihood estimationen
dc.subjectIncomplete data modelen
dc.subjectGibbs algorithmen
dc.subjectEuler-Maruyama approximationen
dc.subjectDiffusion processen
dc.titleParametric inference for mixed models defined by diffusion processesen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversité Paris Descartes - Paris V;France
dc.description.abstractenNon-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.
dc.relation.isversionofjnlnameESAIM. Probability and Statistics
dc.relation.isversionofjnlpublisherEDP Sciences
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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