Robust Design Optimization With Quadratic Loss Derived From Gaussian Process Models

Gaussian process models, which include the class of linear models, are widely employed for modeling responses as a function of control or noise factors. Using these models, the average loss at control factor settings can be estimated and compared. However, robust design optimization is often performed based on the expected quadratic loss computed as if the posterior mean were the true response function. This can give very misleading results. We propose an expected quadratic loss criterion derived by taking expectation with respect to the noise factors and the posterior predictive process. Approximate but highly accurate credible intervals for the average quadratic loss are constructed via the numerical inversion of the Lugannani–Rice saddlepoint approximation. The accuracy of the Lugannani–Rice intervals is compared with intervals constructed via moment-matching techniques on real data. This article has supplementary materials that are available online.