Statistics and Computing

, Volume 27, Issue 4, pp 1111–1128 | Cite as

Parameter estimation of complex mixed models based on meta-model approach

  • Pierre Barbillon
  • Célia Barthélémy
  • Adeline Samson


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.


Mixed models Stochastic EM algorithm MCMC methods Gaussian process emulator 



Adeline Samson has been supported by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01). Les recherches menant aux présents résultats ont bénéficié d’un soutien financier du septiéme programme-cadre de l’Union européenne (7ePC/2007-2013) en vertu de la convention de subvention n 266638.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Pierre Barbillon
    • 1
  • Célia Barthélémy
    • 2
  • Adeline Samson
    • 3
    • 4
  1. 1.UMR MIA-ParisAgroParisTech, INRA, Université Paris-SaclayParisFrance
  2. 2.INRIA Saclay, Popix TeamOrsayFrance
  3. 3.Univ. Grenoble Alpes, LJKGrenobleFrance
  4. 4.CNRS, LJKGrenobleFrance

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