Likelihood-based observability analysis and confidence intervals for model predictions

Clemens Kreutz (February 22, 2012)

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Abstract

Dynamic models of biochemical networks contain unknown parameters like the reaction rates and the initial concentrations of the compounds. The large number of parameters as well as their nonlinear impact on the model responses hampers the determination of confidence regions for parameter estimates. At the same time, classical approaches translating the uncertainty of the parameters into confidence intervals for model predictions are hardly feasible.

We present the so-called prediction profile likelihood which is utilized to generate reliable confidence intervals for model predictions. The prediction confidence intervals of the dynamic states are exploited for a data-based observability analysis. Moreover, a validation profile likelihood is introduced that can be applied when noisy validation experiments are judged.

The presented approaches are also applicable if there are non-identifiable parameters. Such ambiguities yield insufficiently specified model predictions that can be interpreted as nonobservability. The properties and applicability the approach are demonstrated by two examples, a small but instructive ODE model, and a model for the MAP kinase signal transduction pathway.

Work done in collaboration with A. Raue and J. Timmer. This project has been funded by the BMBF grants VirtualLiver 0315766 and FRISYS 0313921.