Abstract
Bounds on response surface approximation errors as a result of model inadequacy (bias error) are presented, and a design of experiments minimizing the maximal bias error is proposed. The bias-error bounds are considered as a tool to identify locations in the design space where the accuracy of the approximation fitted on a given design of experiments might be poor. Two approaches to characterize the bias error assume that the functional form of the true model is known and seek, at each point in design space, worst-case bounds on the absolute error. The first approach is implemented before data generation. This data-independent error bound can easily be implemented in a search for a design of experiments that minimize the bias error bound as it requires very little computation. The second approach is to be used posterior to the data generation and provides tightened error bound consistent with the data. This data-dependent error bound requires the solution of two linear-programming problems at each point. The data-independent error bound for design of experiments of two-variable examples is demonstrated. Randomly generated polynomials in two variables are then used to validate the data-dependent bias-error bound distribution. Although the two approaches are used in conjunction in the given examples, the data-independent error bound design of experiment is not a prerequisite for the application of the data-dependent error bounds in search for the high bias-error regions.
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