title: Likelihood based observability analysis and confidence intervals for predictions of dynamic models.
abstract: BACKGROUND
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Physics Department, University of Freiburg, Hermann Herder Straße 3, 79104 Freiburg, Germany. ckreutz@fdm.uni-freiburg.de
authors.forename: Clemens
authors.initials: C
authors.lastname: Kreutz
authors.forename: Andreas
authors.initials: A
authors.lastname: Raue
authors.forename: Jens
authors.initials: J
authors.lastname: Timmer
mesh_terms: D016013:Likelihood Functions; D020935:MAP Kinase Signaling System; D020928:Mitogen-Activated Protein Kinases / Q000378:metabolism; D008954:Models, Biological; D049490:Systems Biology / Q000379:methods*
chemical_list: D020928:Mitogen-Activated Protein Kinases