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Identifiability analysis of linear ordinary differential equation systems with a single trajectory

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  • Qiu, Xing
  • Xu, Tao
  • Soltanalizadeh, Babak
  • Wu, Hulin

Abstract

Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system is unidentifiable, the estimation procedure may fail or produce erroneous and misleading results. Although several qualitative identifiability measures have been proposed, much less effort has been given to developing quantitative (continuous) scores that are robust to uncertainties in the data, especially for those cases in which the data are presented as a single trajectory beginning with one initial value. In this paper, we first derived a closed-form representation of linear ODE systems that are not identifiable based on a single trajectory. This representation helps researchers design practical systems and choose the right prior structural information in practice. Next, we proposed several quantitative scores for identifiability analysis in practice. In simulation studies, the proposed measures outperformed the main competing method significantly, especially when noise was presented in the data. We also discussed the asymptotic properties of practical identifiability for high-dimensional ODE systems and conclude that, without additional prior information, many random ODE systems are practically unidentifiable when the dimension approaches infinity.

Suggested Citation

  • Qiu, Xing & Xu, Tao & Soltanalizadeh, Babak & Wu, Hulin, 2022. "Identifiability analysis of linear ordinary differential equation systems with a single trajectory," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003344
    DOI: 10.1016/j.amc.2022.127260
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    References listed on IDEAS

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    1. Leqin Wu & Xing Qiu & Ya-xiang Yuan & Hulin Wu, 2019. "Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 657-667, April.
    2. Commenges, D. & Jolly, D. & Drylewicz, J. & Putter, H. & Thiébaut, R., 2011. "Inference in HIV dynamics models via hierarchical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 446-456, January.
    3. Marc Lavielle & Adeline Samson & Ana Karina Fermin & France Mentré, 2011. "Maximum Likelihood Estimation of Long-Term HIV Dynamic Models and Antiviral Response," Biometrics, The International Biometric Society, vol. 67(1), pages 250-259, March.
    4. Yangxin Huang & Dacheng Liu & Hulin Wu, 2006. "Hierarchical Bayesian Methods for Estimation of Parameters in a Longitudinal HIV Dynamic System," Biometrics, The International Biometric Society, vol. 62(2), pages 413-423, June.
    5. Yangxin Huang & Hulin Wu, 2006. "A Bayesian approach for estimating antiviral efficacy in HIV dynamic models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(2), pages 155-174.
    6. 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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    Cited by:

    1. Soradi-Zeid, Samaneh & Mesrizadeh, Mehdi, 2023. "On the convergence of finite integration method for system of ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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