Sequential adaptive designs in computer experiments for response surface model fit

• Authors: William Notz;Chen Quin Lam
• Venue: Sequential adaptive designs in computer experiments for response surface model fit
• Year: 2008

Computer simulations have become increasingly popular as a method for studying physical processes that are difficult to study directly. These simulations are based on complex mathematical models that are believed to accurately describe the physical process. We consider the situation where these simulations take a long time to run (several hours or days) and hence can only be conducted a limited number of times. As a result, the inputs (design) at which to run the simulations must be chosen carefully. For the purpose of fitting a response surface to the output from these simulations, a variety of designs based on a fixed number of runs have been proposed. In this thesis, we consider sequential adaptive designs as an “efficient” alternative to fixed-point designs. We propose new adaptive design criteria based on a cross validation approach and on an expected improvement criterion, the latter inspired by a criterion originally proposed for global optimization. We compare these new designs with others in the literature in an empirical study and they shown to perform well. The issue of robustness for the proposed sequential adaptive designs is also addressed in this thesis. While we find that sequential adaptive designs are potentially more effective and efficient than fixed-point designs, issues such as numerical instability do arise. We address these concerns and also propose a diagnostic tool based on cross validation prediction error to improve the performance of sequential designs. We are also interested in the design of computer experiments where there are control variables and environmental (noise) variables. We extend the implementation of the proposed sequential designs to achieve a good fit of the unknown integrated response surface (i.e., the averaged response surface taken over the distributions of the environmental variables) using output from the simulations. The goal is to find an optimal choice of the control variables while taking into account the distributions of the noise variables.