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"
}