Publication: Practical estimation of high dimensional stochastic differential mixed-effects models
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Practical estimation of high dimensional stochastic differential mixed-effects models

- Article in a journal -
 

Area
Stochastic DIfferential Equations

Author(s)
Umberto Picchini , Susanne Ditlevsen

Published in
Computational Statistics & Data Analysis

Year
2011

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.

AD Tools
ADiMat

BibTeX
@ARTICLE{
         Picchini2011Peo,
       author = "Umberto Picchini and Susanne Ditlevsen",
       title = "Practical estimation of high dimensional stochastic differential mixed-effects
         models",
       journal = "Computational Statistics \& Data Analysis",
       volume = "55",
       number = "3",
       pages = "1426--1444",
       year = "2011",
       issn = "0167-9473",
       doi = "10.1016/j.csda.2010.10.003",
       url = "http://www.sciencedirect.com/science/article/pii/S0167947310003774",
       keywords = "Automatic differentiation, Closed form transition density expansion, Maximum
         likelihood estimation, Population estimation, Stochastic differential equation, Cox--Ingersoll--Ross
         process",
       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.",
       ad_area = "Stochastic DIfferential Equations",
       ad_tools = "ADiMat"
}


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