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.

Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

“…However, each mentioned technique can be used for both classes of problems. 5 For the scaled sensitivity matrix ߙܵ ሚ the maximum collinearity index should be also scaled as ߛ ௫ ߙ ⁄ such that ߳ ఊ ሺߙܵ ሚ ሻ ൌ ߙ߳ ఊ and ߳ሺߙܵ ሚ ሻ ൌ ݉ܽ‫ݔ‬൛߳ , ߙ߳ ఊ ൟ 6 In linear estimation one recommended column equilibration is to scale the columns of ܵ ሚ to unit length (Belsley, 1991) The procedure in Fig. 2 consists as follows:…”

Model-Based Design of Experiments in the Presence of Continuous Measurement Systems

“…16,17 Uncertainty on the design variables can also be considered in the design formulation to take into account possible deviations from planned conditions during experiment execution. 18 The dynamic information matrix is usually expressed by a discrete dynamic form of the Fisher information matrix as proposed by Zullo 10 …”

A statistical perspective on oxygen diffusion and surface exchange experiments: Sensitivity analysis, parameter estimation and robust optimal experimental design

“…While the exact value of the parameters may not be known well a priori, relevant publications may indicate them with some uncertainty [41]. In particular, one can use this information in a robust OED [42].…”