Handling Uncertainty in Model-Based Optimal Experimental Design

Abstract

In contrast to the majority of published works in the field of model-based optimal experimental design which focused on numerical studies so as to demonstrate the validity of the OED approach or the development of new criteria or numerical approaches, this work is mainly concerned with the experimental application and practical insights gained from the adaption of an optimal design framework. The presented work is discussed based on the determination of protein ion-exchange equilibrium parameters. For this purpose, special attention is paid to the explicit modeling of all laboratory steps so as to prepare, implement, and analyze experiments in order to have a realistic definition of the numeric design problem and to formally include experimental restrictions and sources of uncertainties in the problem formulation. Moreover, whereas the effect of erroneous assumptions in the initially assumed parameter values have been covered by various authors, in this work, uncertainties are considered in a more general way including those which arise during an imprecise implementation of optimal planned experiments. To compensate for uncertainty influences, a feed-back based approach to optimal design is adopted based on the combination of the parallel and sequential design approaches. Uncertainty identification is done by solution of an augmented parameter estimation problem, where deviations in the experimental design are detected and estimated together with the parameter values. It has been shown that uncertainty influences vanish along with the iterative refinement of the experiment design variables and estimated parameter values.

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