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Practical estimation of high dimensional stochastic differential mixed-effects models

Picchini, Umberto LU and Ditlevsen, Susanne (2011) In Computational Statistics & Data Analysis 55(3). p.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... (More)
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. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Automatic differentiation, Closed form transition density expansion, Maximum likelihood estimation, Population estimation, Stochastic differential equation, Cox–Ingersoll–Ross process
in
Computational Statistics & Data Analysis
volume
55
issue
3
pages
1426 - 1444
publisher
Elsevier
external identifiers
  • scopus:78649325422
ISSN
0167-9473
DOI
10.1016/j.csda.2010.10.003
language
English
LU publication?
no
id
559dd93f-682f-4469-85f3-74b7b96db5a2 (old id 4215973)
date added to LUP
2014-01-13 13:05:29
date last changed
2017-05-28 03:19:16
@article{559dd93f-682f-4469-85f3-74b7b96db5a2,
  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.},
  author       = {Picchini, Umberto and Ditlevsen, Susanne},
  issn         = {0167-9473},
  keyword      = {Automatic differentiation,Closed form transition density expansion,Maximum likelihood estimation,Population estimation,Stochastic differential equation,Cox–Ingersoll–Ross process},
  language     = {eng},
  number       = {3},
  pages        = {1426--1444},
  publisher    = {Elsevier},
  series       = {Computational Statistics & Data Analysis},
  title        = {Practical estimation of high dimensional stochastic differential mixed-effects models},
  url          = {http://dx.doi.org/10.1016/j.csda.2010.10.003},
  volume       = {55},
  year         = {2011},
}