Methodology article

BMC Systems Biology

, 6:120

Open Access This content is freely available online to anyone, anywhere at any time.

Likelihood based observability analysis and confidence intervals for predictions of dynamic models

  • Clemens KreutzAffiliated withPhysics Department, University of FreiburgFreiburg Centre for Biosystems Analysis (ZBSA), University of Freiburg Email author 
  • , Andreas RaueAffiliated withPhysics Department, University of FreiburgInstitute of Bioinformatics and Systems Biology, Helmholtz Zentrum München
  • , Jens TimmerAffiliated withPhysics Department, University of FreiburgFreiburg Centre for Biosystems Analysis (ZBSA), University of FreiburgFreiburg Institute for Advanced Studies (FRIAS), University of FreiburgFreiburg Initiative in Systems Biology (FRISYS), University of FreiburgBIOSS Centre for Biological Signalling Studies, University of FreiburgDepartment of Clinical and Experimental Medicine, Universitetssjukhuset



Predicting a system’s behavior based on a mathematical model is a primary task in Systems Biology. If the model parameters are estimated from experimental data, the parameter uncertainty has to be translated into confidence intervals for model predictions. For dynamic models of biochemical networks, the nonlinearity in combination with the large number of parameters hampers the calculation of prediction confidence intervals and renders classical approaches as hardly feasible.


In this article reliable confidence intervals are calculated based on the prediction profile likelihood. Such prediction confidence intervals of the dynamic states can be utilized for a data-based observability analysis. The method is also applicable if there are non-identifiable parameters yielding to some insufficiently specified model predictions that can be interpreted as non-observability. Moreover, a validation profile likelihood is introduced that should be applied when noisy validation experiments are to be interpreted.


The presented methodology allows the propagation of uncertainty from experimental to model predictions. Although presented in the context of ordinary differential equations, the concept is general and also applicable to other types of models. Matlab code which can be used as a template to implement the method is provided at http://​www.​fdmold.​uni-freiburg.​de/​∼ckreutz/​PPL.


Confidence intervals Identifiability Likelihood Parameter estimation Prediction Profile likelihood Optimal experimental design Ordinary differential equations Signal transduction Statistical inference Uncertainty