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Practical estimation of high dimensional stochastic differential mixed-effects models

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  • Picchini, Umberto
  • Ditlevsen, Susanne

Abstract

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.

Suggested Citation

  • Picchini, Umberto & Ditlevsen, Susanne, 2011. "Practical estimation of high dimensional stochastic differential mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1426-1444, March.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:3:p:1426-1444
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    1. repec:dau:papers:123456789/1124 is not listed on IDEAS
    2. 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.
    3. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 390-455.
    4. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    5. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    6. Hyejin KO & Marie Davidian, 2000. "Correcting for Measurement Error in Individual-Level Covariates in Nonlinear Mixed Effects Models," Biometrics, The International Biometric Society, vol. 56(2), pages 368-375, June.
    7. repec:dau:papers:123456789/4642 is not listed on IDEAS
    8. Sophie Donnet & Jean-Louis Foulley & Adeline Samson, 2010. "Bayesian Analysis of Growth Curves Using Mixed Models Defined by Stochastic Differential Equations," Biometrics, The International Biometric Society, vol. 66(3), pages 733-741, September.
    9. 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.
    10. 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, March.
    11. Benjamin Favetto & Adeline Samson, 2010. "Parameter Estimation for a Bidimensional Partially Observed Ornstein–Uhlenbeck Process with Biological Application," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 200-220, June.
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    Cited by:

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    5. Maud Delattre & Valentine Genon-Catalot & Adeline Samson, 2013. "Maximum Likelihood Estimation for Stochastic Differential Equations with Random Effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 322-343, June.
    6. Fabienne Comte & Nicolas Marie, 2021. "Nonparametric estimation for I.I.D. paths of fractional SDE," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 669-705, October.
    7. Wiqvist, Samuel & Golightly, Andrew & McLean, Ashleigh T. & Picchini, Umberto, 2021. "Efficient inference for stochastic differential equation mixed-effects models using correlated particle pseudo-marginal algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    8. Delattre, Maud & Genon-Catalot, Valentine & Larédo, Catherine, 2018. "Parametric inference for discrete observations of diffusion processes with mixed effects," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1929-1957.
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