A Radar-Shaped Statistic for Testing and Visualizing Uniformity Properties in Computer Experiments

TL;DR

This paper introduces a radar-shaped statistic to evaluate and visualize the uniformity of point distributions in computer experiments across all 1D projections, enhancing the analysis of space-filling designs.

Contribution

It presents a novel radar-type statistic that assesses uniformity in all directions, providing a comprehensive visualization tool for design quality in computer experiments.

Findings

Effective visualization of uniformity defects across projections

Demonstrated on standard space-filling designs

Developed a rotation-independent global statistic

Abstract

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. In this article 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 radar type representation, allowing the uniformity defects of a design to be identified with respect to its projections onto straight lines. The advantages of this new tool are demonstrated on usual examples of space-filling designs (SFD) and a global statistic independent of the angle of rotation is studied.