Parameter estimation of complex mixed models based on meta-model approach |
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Authors: | Pierre Barbillon Célia Barthélémy Adeline Samson |
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Affiliation: | 1.UMR MIA-Paris,AgroParisTech, INRA, Université Paris-Saclay,Paris,France;2.INRIA Saclay, Popix Team,Orsay,France;3.Univ. Grenoble Alpes, LJK,Grenoble,France;4.CNRS, LJK,Grenoble,France |
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Abstract: | Complex biological processes are usually experimented along time among a collection of individuals, longitudinal data are then available. The statistical challenge is to better understand the underlying biological mechanisms. A standard statistical approach is mixed-effects model where the regression function is highly-developed to describe precisely the biological processes (solutions of multi-dimensional ordinary differential equations or of partial differential equation). A classical estimation method relies on coupling a stochastic version of the EM algorithm with a Monte Carlo Markov Chain algorithm. This algorithm requires many evaluations of the regression function. This is clearly prohibitive when the solution is numerically approximated with a time-consuming solver. In this paper a meta-model relying on a Gaussian process emulator is proposed to approximate the regression function, that leads to what is called a mixed meta-model. The uncertainty of the meta-model approximation can be incorporated in the model. A control on the distance between the maximum likelihood estimates of the mixed meta-model and the maximum likelihood estimates of the exact mixed model is guaranteed. Eventually, numerical simulations are performed to illustrate the efficiency of this approach. |
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