Maximum projection designs for computer experiments

Abstract

Space-filling properties are important in designing computer experiments. The traditional maximin and minimax distance designs only consider space-filling in the full dimensional space. This can result in poor projections onto lower dimensional spaces, which is undesirable when only a few factors are active. Restricting maximin distance design to the class of Latin hypercubes can improve one-dimensional projections, but cannot guarantee good space-filling properties in larger subspaces. We propose designs that maximize space-filling properties on projections to all subsets of factors. We call our designs maximum projection designs. As a result, our design criterion can be computed at a cost no more than a design criterion that ignores projection properties.