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R package for statistical inference in dynamical systems using kernel based gradient matching: KGode

Author

Listed:
  • Mu Niu

    (University of Glasgow)

  • Joe Wandy

    (University of Glasgow)

  • Rónán Daly

    (University of Glasgow)

  • Simon Rogers

    (University of Glasgow)

  • Dirk Husmeier

    (University of Glasgow)

Abstract

Many processes in science and engineering can be described by dynamical systems based on nonlinear ordinary differential equations (ODEs). Often ODE parameters are unknown and not directly measurable. Since nonlinear ODEs typically have no closed form solution, standard iterative inference procedures require a computationally expensive numerical integration of the ODEs every time the parameters are adapted, which in practice restricts statistical inference to rather small systems. To overcome this computational bottleneck, approximate methods based on gradient matching have recently gained much attention. The idea is to circumvent the numerical integration step by using a surrogate cost function that quantifies the discrepancy between the derivatives obtained from a smooth interpolant to the data and the derivatives predicted by the ODEs. The present article describes the software implementation of a recent method that is based on the framework of reproducing kernel Hilbert spaces. We provide an overview of the methods available, illustrate them on a series of widely used benchmark problems, and discuss the accuracy–efficiency trade-off of various regularization methods.

Suggested Citation

  • Mu Niu & Joe Wandy & Rónán Daly & Simon Rogers & Dirk Husmeier, 2021. "R package for statistical inference in dynamical systems using kernel based gradient matching: KGode," Computational Statistics, Springer, vol. 36(1), pages 715-747, March.
  • Handle: RePEc:spr:compst:v:36:y:2021:i:1:d:10.1007_s00180-020-01014-x
    DOI: 10.1007/s00180-020-01014-x
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    References listed on IDEAS

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    1. Liang, Hua & Wu, Hulin, 2008. "Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1570-1583.
    2. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
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    1. Kim-Hung Pho & Ngoc-Hien Nguyen & Huu-Nhan Huynh & Wing-Keung Wong, 2021. "A Detailed Guide on How to Use Statistical Software R for Text Mining," Advances in Decision Sciences, Asia University, Taiwan, vol. 25(3), pages 92-110, September.

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