Minimum Spanning Tree: A new approach to assess the quality of the design of computer experiments

In the computer experiment setting, if the relationship between the response and inputs is unknown, then the purpose is to use designs that spread the points at which we observe the response evenly throughout the region. These designs are called Space-Filling Designs. Different measures or metrics quantify how a set of points is spread out. In this paper, we present two types of measures of uniformity: discrepancy and point-to-point measures which take into account the distances between the pairs of points. However these criteria of quantification do not permit the qualification of the distribution. Thus, we discuss a new approach to assess the quality of computer experiments. This approach is based on a graph constructed from the set of points of the experimental design. This graph, called Minimum Spanning Tree, allows us to deduce two parameters—the mean and the standard deviation of the edges length—which characterize the points distribution to be studied.