Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations
KAUST Grant NumberKUS-CI-016-04
MetadataShow full item record
AbstractOrdinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
CitationCao J, Huang JZ, Wu H (2012) Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations. Journal of Computational and Graphical Statistics 21: 42–56. Available: http://dx.doi.org/10.1198/jcgs.2011.10021.
SponsorsCao's work was supported by a discovery grant from the Natural Science and Engineering Research Council of Canada (NSERC). Huang's research was partly supported by NCI (CA57030), NSF (DMS-0907170), and by Award No. KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). Wu's work was partially supported by grants from NIH/NIAID.
PublisherInforma UK Limited
PubMed Central IDPMC3496750
CollectionsPublications Acknowledging KAUST Support
- Inference in dynamic systems using B-splines and quasilinearized ODE penalties.
- Authors: Frasso G, Jaeger J, Lambert P
- Issue date: 2016 May
- Robust estimation for ordinary differential equation models.
- Authors: Cao J, Wang L, Xu J
- Issue date: 2011 Dec
- Estimating a predator-prey dynamical model with the parameter cascades method.
- Authors: Cao J, Fussmann GF, Ramsay JO
- Issue date: 2008 Sep
- Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.
- Authors: Wu H, Xue H, Kumar A
- Issue date: 2012 Jun
- Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.
- Authors: Hasegawa C, Duffull SB
- Issue date: 2018 Feb