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    Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

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    Type
    Article
    Authors
    Cao, Jiguo
    Huang, Jianhua Z.
    Wu, Hulin
    KAUST Grant Number
    KUS-CI-016-04
    Date
    2012-01
    Permanent link to this record
    http://hdl.handle.net/10754/599154
    
    Metadata
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    Abstract
    Ordinary 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.
    Citation
    Cao 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.
    Sponsors
    Cao'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.
    Publisher
    Informa UK Limited
    Journal
    Journal of Computational and Graphical Statistics
    DOI
    10.1198/jcgs.2011.10021
    PubMed ID
    23155351
    PubMed Central ID
    PMC3496750
    ae974a485f413a2113503eed53cd6c53
    10.1198/jcgs.2011.10021
    Scopus Count
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