A Radial Scanning Statistic for Selecting Space-filling Designs in Computer Experiments

In the study of computer codes, filling space as uniformly as possible is important to describe the complexity of the investigated phenomenon. However, this property is not conserved by reducing the dimension. Some numeric experiment designs are conceived in this sense as Latin hypercubes or orthogonal arrays, but they consider only the projections onto the axes or the coordinate planes. We introduce a statistic which allows studying the good distribution of points according to all 1-dimensional projections. By angularly scanning the domain, we obtain a useful graphical representation. The advantages of this new tool are demonstrated on usual space-filling designs. Graphical, decisional and dimensionality issues are discussed.