Discussion of 'Space-filling designs for computer experiments: A review'

摘要

Space-fillingness has become a new noun with already more than 500 hits on Google. In his excellent review, Professor Joseph makes a clear case, why this is rightfully so and why the notion has become ubiquitous in computer simulation experiments. The main idea of the new approach proposed by the author is to use a weighted version of the reciprocal distance criterion, which, in a special case, corresponds to minimizing the sum of reciprocals of the volumes of the cubes formed by all pairs of points. The resulting MaxPro criterion seems to be very good to force space-filling properties in all dimensions and, importantly, motivates tempting modifications.