Optimal Experiment Design for Model Discrimination using the Sigma Point Method

Abstract

Abstract Bioprocesses can be controlled and optimised by dynamic process models. However, often different models are available for describing the dynamics in a similar way. In order to discriminate efficiently among rival models, optimal experiment design for model discrimination (OED-MD) has been developed. In this work the OED-MD method proposed by Schwaab et al. (2008) will be used for discriminating among dynamic models of microbial growth rate as a function of temperature. In this model discrimination procedurethe variance-covariance matrix of the parameters is needed, which is traditionally approximated by the inverse of the Fisher information matrix using the Cramer-Rao lower bound. For models nonlinear in the parameters, this can be a severe underestimation of the actual parameter uncertainty. A more accurate estimation of the variance-covariance matrix of the parameters can be obtained by using the so-called sigma point method ( Schenkendorf et al., 2009 ). The main contribution of this paper is that the sigma point method is used for accurately computing the variance- covariance matrix of the parameters. This matrix is subsequently employed in the procedure for discriminating between two possible models of microbial growth rate as a function of temperature. In addition, the sigma point method is compared with the classic Fisher information matrix approach on the level of discriminating potential.