Empirical Uniform Bounds For Heteroscedastic Metamodeling

This paper proposes pointwise variance estimation-based and metamodel-based empirical uniform bounds for heteroscedastic metamodeling based on the state-of-the-art nominal uniform bound available from the literature by considering the impact of noise variance estimation. Numerical results show that the existing nominal uniform bound requires a relatively large number of design points and a high number of replications to achieve a prescribed target coverage level. On the other hand, the metamodel-based empirical bound outperforms the nominal bound and other competing bounds in terms of empirical simultaneous coverage probability and bound width, especially when the simulation budget is small. However, the pointwise variance estimation-based empirical bound is relatively conservative due to its larger width. When the budget is sufficiently large so that the impact of heteroscedasticity is low, both empirical bounds' performance approaches that of the nominal bound.