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Stochastic differential mixed-effects models

Picchini, Umberto LU ; De Gaetano, Andrea and Ditlevsen, Susanne (2010) In Scandinavian Journal of Statistics 37(1). p.67-90
Abstract
Stochastic differential equations have been shown useful in describing random continuous time processes. Biomedical experiments often imply repeated measurements on a series of experimental units and differences between units can be represented by incorporating random effects into the model. When both system noise and random effects are considered, stochastic differential mixed-effects models ensue. This class of models enables the simultaneous representation of randomness in the dynamics of the phenomena being considered and variability between experimental units, thus providing a powerful modelling tool with immediate applications in biomedicine and pharmacokinetic/pharmacodynamic studies. In most cases the likelihood function is not... (More)
Stochastic differential equations have been shown useful in describing random continuous time processes. Biomedical experiments often imply repeated measurements on a series of experimental units and differences between units can be represented by incorporating random effects into the model. When both system noise and random effects are considered, stochastic differential mixed-effects models ensue. This class of models enables the simultaneous representation of randomness in the dynamics of the phenomena being considered and variability between experimental units, thus providing a powerful modelling tool with immediate applications in biomedicine and pharmacokinetic/pharmacodynamic studies. In most cases the likelihood function is not available, and thus maximum likelihood estimation of the unknown parameters is not possible. Here we propose a computationally fast approximated maximum likelihood procedure for the estimation of the non-random parameters and the random effects. The method is evaluated on simulations from some famous diffusion processes and on real data sets (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
biomedical applications, Brownian motion with drift, CIR process, closed-form transition density expansion, Gaussian quadrature, geometric Brownian motion, maximum likelihood estimation, Ornstein–Uhlenbeck process, random parameters, stochastic differential equations
in
Scandinavian Journal of Statistics
volume
37
issue
1
pages
67 - 90
publisher
Wiley-Blackwell
external identifiers
  • scopus:77949528435
ISSN
1467-9469
DOI
10.1111/j.1467-9469.2009.00665.x
language
English
LU publication?
no
id
311eb276-442a-4a27-8ecd-6d0a9d0a1958 (old id 4215982)
date added to LUP
2014-01-13 13:10:58
date last changed
2018-05-29 12:18:02
@article{311eb276-442a-4a27-8ecd-6d0a9d0a1958,
  abstract     = {Stochastic differential equations have been shown useful in describing random continuous time processes. Biomedical experiments often imply repeated measurements on a series of experimental units and differences between units can be represented by incorporating random effects into the model. When both system noise and random effects are considered, stochastic differential mixed-effects models ensue. This class of models enables the simultaneous representation of randomness in the dynamics of the phenomena being considered and variability between experimental units, thus providing a powerful modelling tool with immediate applications in biomedicine and pharmacokinetic/pharmacodynamic studies. In most cases the likelihood function is not available, and thus maximum likelihood estimation of the unknown parameters is not possible. Here we propose a computationally fast approximated maximum likelihood procedure for the estimation of the non-random parameters and the random effects. The method is evaluated on simulations from some famous diffusion processes and on real data sets},
  author       = {Picchini, Umberto and De Gaetano, Andrea and Ditlevsen, Susanne},
  issn         = {1467-9469},
  keyword      = {biomedical applications,Brownian motion with drift,CIR process,closed-form transition density expansion,Gaussian quadrature,geometric Brownian motion,maximum likelihood estimation,Ornstein–Uhlenbeck process,random parameters,stochastic differential equations},
  language     = {eng},
  number       = {1},
  pages        = {67--90},
  publisher    = {Wiley-Blackwell},
  series       = {Scandinavian Journal of Statistics},
  title        = {Stochastic differential mixed-effects models},
  url          = {http://dx.doi.org/10.1111/j.1467-9469.2009.00665.x},
  volume       = {37},
  year         = {2010},
}