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A Parameter-Free Model Comparison Test Using Differential Algebra

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  • Heather A. Harrington
  • Kenneth L. Ho
  • Nicolette Meshkat

Abstract

We present a method for rejecting competing models from noisy time-course data that does not rely on parameter inference. First we characterize ordinary differential equation models in only measurable variables using differential-algebra elimination. This procedure gives input-output equations, which serve as invariants for time series data. We develop a model comparison test using linear algebra and statistics to reject incorrect models from their invariants. This algorithm exploits the dynamic properties that are encoded in the structure of the model equations without recourse to parameter values, and, in this sense, the approach is parameter-free. We demonstrate this method by discriminating between different models from mathematical biology.

Suggested Citation

  • Heather A. Harrington & Kenneth L. Ho & Nicolette Meshkat, 2019. "A Parameter-Free Model Comparison Test Using Differential Algebra," Complexity, Hindawi, vol. 2019, pages 1-15, February.
    • Handle: RePEc:hin:complx:6041981
    DOI: 10.1155/2019/6041981
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    References listed on IDEAS

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    1. Peter S. Swain & Keiran Stevenson & Allen Leary & Luis F. Montano-Gutierrez & Ivan B.N. Clark & Jackie Vogel & Teuta Pilizota, 2016. "Inferring time derivatives including cell growth rates using Gaussian processes," Nature Communications, Nature, vol. 7(1), pages 1-8, December.
    2. Godfrey, Keith R. & Chapman, Michael J., 1990. "Identifiability and indistinguishability of linear compartmental models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(3), pages 273-295.
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