Uncertainty Analysis for Non-identifiable Dynamical Systems: Profile Likelihoods, Bootstrapping and More

  • Fabian Fröhlich
  • Fabian J. Theis
  • Jan Hasenauer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8859)


Dynamical systems are widely used to describe the behaviour of biological systems. When estimating parameters of dynamical systems, noise and limited availability of measurements can lead to uncertainties. These uncertainties have to be studied to understand the limitations and the predictive power of a model. Several methods for uncertainty analysis are available. In this paper we analysed and compared bootstrapping, profile likelihood, Fisher information matrix, and multi-start based approaches for uncertainty analysis. The analysis was carried out on two models which contain structurally non-identifiable parameters. We showed that bootstrapping, multi-start optimisation, and Fisher information matrix based approaches yield misleading results for parameters which are structurally non-identifiable. We provide a simple and intuitive explanation for this, using geometric arguments.


parameter estimation uncertainty analysis bootstrapping profile likelihood identifiability 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Fabian Fröhlich
    • 1
    • 2
  • Fabian J. Theis
    • 1
    • 2
  • Jan Hasenauer
    • 1
    • 2
  1. 1.Institute of Computational BiologyHelmholtz Zentrum MünchenNeuherbergGermany
  2. 2.Department of MathematicsTechnische Universität MünchenGarchingGermany

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