Parametric inference for mixed models defined by diffusion processes
Samson, Adeline; Donnet, Sophie (2008), Parametric inference for mixed models defined by diffusion processes, ESAIM. Probability and Statistics, 12, p. 196-218. http://dx.doi.org/10.1051/ps:2007045
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00263515/fr/
Journal nameESAIM. Probability and Statistics
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Abstract (EN)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.
Subjects / KeywordsBrownian bridge; SAEM algorithm; Non-linear mixed effects model; Maximum likelihood estimation; Incomplete data model; Gibbs algorithm; Euler-Maruyama approximation; Diffusion process
Showing items related by title and author.
Bayesian analysis of growth curves using mixed models defined by stochastic differential equations Foulley, Jean-Louis; Samson, Adeline; Donnet, Sophie (2010) Article accepté pour publication ou publié
EM algorithm coupled with particle filter for maximum likelihood parameter estimation of stochastic differential mixed-effects models Samson, Adeline; Donnet, Sophie (2010) Document de travail / Working paper
Discussion on "Parameter estimation for differential equations: a generalized smoothing approach" (by Ramsay JO, Hooker G, Campbell D and Cao J), Samson, Adeline; Donnet, Sophie (2007) Article accepté pour publication ou publié