Delineating parameter unidentifiabilities in complex models

Dhruva V. Raman, James Anderson, and Antonis Papachristodoulou
Phys. Rev. E 95, 032314 – Published 13 March 2017

Abstract

Scientists use mathematical modeling as a tool for understanding and predicting the properties of complex physical systems. In highly parametrized models there often exist relationships between parameters over which model predictions are identical, or nearly identical. These are known as structural or practical unidentifiabilities, respectively. They are hard to diagnose and make reliable parameter estimation from data impossible. They furthermore imply the existence of an underlying model simplification. We describe a scalable method for detecting unidentifiabilities, as well as the functional relations defining them, for generic models. This allows for model simplification, and appreciation of which parameters (or functions thereof) cannot be estimated from data. Our algorithm can identify features such as redundant mechanisms and fast time-scale subsystems, as well as the regimes in parameter space over which such approximations are valid. We base our algorithm on a quantification of regional parametric sensitivity that we call ‘multiscale sloppiness’. Traditionally, the link between parametric sensitivity and the conditioning of the parameter estimation problem is made locally, through the Fisher information matrix. This is valid in the regime of infinitesimal measurement uncertainty. We demonstrate the duality between multiscale sloppiness and the geometry of confidence regions surrounding parameter estimates made where measurement uncertainty is non-negligible. Further theoretical relationships are provided linking multiscale sloppiness to the likelihood-ratio test. From this, we show that a local sensitivity analysis (as typically done) is insufficient for determining the reliability of parameter estimation, even with simple (non)linear systems. Our algorithm can provide a tractable alternative. We finally apply our methods to a large-scale, benchmark systems biology model of necrosis factor (NF)-κB, uncovering unidentifiabilities.

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  • Received 15 June 2016
  • Revised 22 October 2016

DOI:https://doi.org/10.1103/PhysRevE.95.032314

©2017 American Physical Society

Physics Subject Headings (PhySH)

NetworksPhysics of Living SystemsNonlinear DynamicsInterdisciplinary Physics

Authors & Affiliations

Dhruva V. Raman*, James Anderson, and Antonis Papachristodoulou

  • Department of Engineering Science, University of Oxford, 17 Parks Road, OX1 3PJ Oxford, United Kingdom

  • *dhruva.raman@eng.cam.ac.uk

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Issue

Vol. 95, Iss. 3 — March 2017

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