Design for Computer Experiments: Comparing and Generating Designs in Kriging Models

Abstract

The selection of design points is mandatory when the goal is to study how the observed response varies upon changing the set of input variables. In physical experimentation, the researcher is asked to investigate a number of issues to gain valuable inferences. Design of experiments (D.o.E.) is a helpful tool for achieving this goal. Unfortunately, designing a computer experiment (CE), used as a surrogate for the physical one, differs in several aspects from designing a physical experiment. As suggested by the pioneers of CEs, the output can be predict by assuming Gaussian responses and that covariance depends parametrically on the distance between the locations, according to the Kriging model. Latin hypercube (LH) training sets are used in most cases. In this chapter, we discuss the influence of LHs on the prediction error of the conditional expectation step of the Kriging model using examples. Our suggestion is to perform these preliminary tests in order to assess which class of LH seems to fit the specific application.