Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Accuracy of Laplace approximation for discrete response mixed models
Computational Statistics & Data Analysis
Computer Methods and Programs in Biomedicine
Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models
Computational Statistics & Data Analysis
Re-examination of the taper models by stochastic differential equations
GAVTASC'11 Proceedings of the 11th WSEAS international conference on Signal processing, computational geometry and artificial vision, and Proceedings of the 11th WSEAS international conference on Systems theory and scientific computation
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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.