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Optimal Experimental Design with the Sigma Point method

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons86465

Schenkendorf,  R.
Process Synthesis and Process Dynamics, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons86195

Kremling,  A.
Systems Biology, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons86397

Mangold,  M.
Process Synthesis and Process Dynamics, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

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Schenkendorf, R., Kremling, A., & Mangold, M. (2009). Optimal Experimental Design with the Sigma Point method. IET Systems Biology, 3(1), 10-23. doi:10.1049/iet-syb:20080094.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-9329-1
Abstract
Using mathematical models for a quantitative description of dynamical systems requires the identification of uncertain parameters by minimising the difference between simulation and measurement. Due to the measurement noise also the estimated parameters possess an uncertainty expressed by their variances. To get highly predictive models, very precise parameters are needed. The Optimal Experimental Design (OED) as a numerical optimisation method is used to reduce the parameter uncertainty by minimising the parameter variances iteratively. A frequently applied method to define a cost function for OED is based on the inverse of the Fisher Information Matrix. The application of this traditional method has at least two shortcomings for models that are non-linear in their parameters: (i) it gives only a lower bound of the parameter variances and (ii) the bias of the estimator is neglected. Here, we show that by applying the Sigma Point method a better approximation of characteristic values of the parameter statistics can be obtained, which has a direct benefit on OED. An additional advantage of the Sigma Point method is that it can also be used to investigate the influence of the parameter uncertainties on the simulation results. The Sigma Point method is demonstrated for the example of a widely used biological model. © The Institution of Engineering and Technology 2008 [accessed May 27, 2009]