Beyond space-filling: An illustrative case

When collecting spatial data, it has become a standard practice to position the measurement points spread out uniformly across the available space. These so-called space-filling designs are now ubiquitous in corresponding publications and conferences. The statistical folklore is that such designs have superior properties when it comes to prediction and estimation of response functions. In this presentation we want to review the circumstances under which this superiority holds, provide some new arguments and clarify the motives to go beyond space-filling. We will accompany these findings with a simple two-dimensional example with seven observations.