Generalized Latin Hypercube Design for Computer Experiments

Space filling designs, which satisfy a uniformity property, are widely used in computer experiments. In the present paper the performance of non-uniform experimental designs which locate more points in a neighborhood of the boundary of the design space is investigated. These designs are obtained by a quantile transformation of the one-dimensional projections of commonly used space filling designs. This transformation is motivated by logarithmic potential theory, which yields the arc-sine measure as equilibrium distribution. Alternative distance measures yield to Beta distributions, which put more weight in the interior of the design space. The methodology is illustrated for maximin Latin hypercube designs in several examples. In particular it is demonstrated that in many cases the new designs yield a smaller integrated mean square error for prediction. Moreover, the new designs yield to substantially better performance with respect to the entropy criterion.