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Open Access Methodology article

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

Clemens Kreutz12*, Andreas Raue17 and Jens Timmer123456

Author Affiliations

1 Physics Department, University of Freiburg, Hermann Herder Straße 3, 79104 Freiburg, Germany

2 Freiburg Centre for Biosystems Analysis (ZBSA), University of Freiburg, Habsburgerstraße 49, 79104 Freiburg, Germany

3 Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Albertstraße 19, 79104 Freiburg, Germany

4 Freiburg Initiative in Systems Biology (FRISYS), University of Freiburg, Schaenzlestraße 1, 79104 Freiburg, Germany

5 BIOSS Centre for Biological Signalling Studies, University of Freiburg, Schaenzlestraße 18, 79104 Freiburg

6 Department of Clinical and Experimental Medicine, Universitetssjukhuset, 58183 Linköping, Sweden

7 Institute of Bioinformatics and Systems Biology, Helmholtz Zentrum München, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany

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BMC Systems Biology 2012, 6:120  doi:10.1186/1752-0509-6-120

Published: 5 September 2012



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∼ckreutz/PPL webcite.

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