Optimum Addition of Information to Computer Experiments in View of Uniformity and Orthogonality

Abstract

Computer experiments have become ubiquitous across the engineering, physical and chemical sciences. Computer experiments are constructed to emulate the behavior of a physical system. Assume that we perform an experiment using a two-level uniform design. If, after obtaining data, we decide additional runs of the computer simulator are needed, how to add more runs after collecting our data? How to design the experiment to efficiently extract useful information from it? In this paper, we try to answer these questions by providing a new approach for constructing efficient uniform designs by adding new runs to an existing uniform design. The optimization criteria are the uniformity criteria measured by Lee, symmetric, wrap-around, centered and mixture discrepancy and the orthogonality criteria measured by the B-criterion and the O-criterion. We investigate the relationship between orthogonality and uniformity criteria in view of analytical expressions and lower bounds.