Practical estimation of high dimensional stochastic differential mixed-effects models

Umberto Picchini and Susanne Ditlevsen

Computational Statistics & Data Analysis, 2011, vol. 55, issue 3, 1426-1444

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.

Keywords: Automatic; differentiation; Closed; form; transition; density; expansion; Maximum; likelihood; estimation; Population; estimation; Stochastic; differential; equation; Cox-Ingersoll-Ross; process (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (10)

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