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Practical estimation of high dimensional stochastic differential mixed-effects models

  • Picchini, Umberto
  • Ditlevsen, Susanne
Registered author(s):

    Stochastic differential equations (SDEs) are established tools for modeling physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE, intrinsic randomness of a system around its drift can be identified and separated from the drift itself. When it is of interest to model dynamics within a given population, i.e. to model simultaneously the performance of several experiments or subjects, mixed-effects modelling allows for the distinction of between and within experiment variability. A framework for modeling dynamics within a population using SDEs is proposed, representing simultaneously several sources of variation: variability between experiments using a mixed-effects approach and stochasticity in the individual dynamics, using SDEs. These stochastic differential mixed-effects models have applications in e.g. pharmacokinetics/pharmacodynamics and biomedical modelling. A parameter estimation method is proposed and computational guidelines for an efficient implementation are given. Finally the method is evaluated using simulations from standard models like the two-dimensional Ornstein-Uhlenbeck (OU) and the square root models.

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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 3 (March)
    Pages: 1426-1444

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1426-1444
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Tang, Cheng Yong & Chen, Song Xi, 2009. "Parameter estimation and bias correction for diffusion processes," Journal of Econometrics, Elsevier, vol. 149(1), pages 65-81, April.
    2. Foulley, Jean-Louis & Samson, Adeline & Donnet, Sophie, 2010. "Bayesian analysis of growth curves using mixed models defined by stochastic differential equations," Economics Papers from University Paris Dauphine 123456789/1124, Paris Dauphine University.
    3. Skaug, Hans J. & Fournier, David A., 2006. "Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 699-709, November.
    4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    5. Umberto Picchini & Andrea De Gaetano & Susanne Ditlevsen, 2010. "Stochastic Differential Mixed-Effects Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 67-90.
    6. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
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