Generalized pointwise bias error bounds for response surface approximations

Abstract

This paper proposes a generalized pointwise bias error bounds estimation method for polynomial-based response surface approximations when bias errors are substantial. A relaxation parameter is introduced to account for inconsistencies between the data and the assumed true model. The method is demonstrated with a polynomial example where the model is a quadratic polynomial while the true function is assumed to be cubic polynomial. The effect of relaxation parameter is studied. It is demonstrated that when bias errors dominate, the bias error bounds characterize the actual error field better than the standard error. The bias error bound estimates also help to identify regions in the design space where the accuracy of the response surface approximations is inadequate. It is demonstrated that this information can be utilized for adaptive sampling in order to improve accuracy in such regions.