Exploratory designs for computational experiments

Abstract Recent work by Johnson et al. (J. Statist. Plann. Inference 26 (1990) 131–148) establishes equivalence of the maximin distance design criterion and an entropy criterion motivated by function prediction in a Bayesian setting. The latter criterion has been used by Currin et al. (J. Amer. Statist. Assoc. 86 (1991) 953–963) to design experiments for which the motivating application is approximation of a complex deterministic computer model. Because computer experiments often have a large number of controlled variables (inputs), maximin designs of moderate size are often concentrated in the corners of the cuboidal design region, i.e. each input is represented at only two levels. Here we will examine some maximin distance designs constructed within the class of Latin hypercube arrangements. The goal of this is to find designs which offer a compromise between the entropy/maximin criterion, and good projective properties in each dimension (as guaranteed by Latin hypercubes). A simulated annealing search algorithm is presented for constructing these designs, and patterns apparent in the optimal designs are discussed.