This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in arbitrary dimensions. Second, we connect the proposed metric (defined in the spatial domain) to the quality metri...
Published in Kant-Studien
This paper examines Kant’s pre-Critical distinction between the capacity of an immaterial simple substance to occupy space by having a spatial location and the sphere of its activity, in contrast to the power of material compound bodies to fill space by their extension and solidity. I highlight some important features of Descartes’ metaphysical and...
In the field of sensitivity analysis, Sobol' indices are widely used to assess the importance of inputs of a model to its output. Among the methods that estimate these indices, the replication procedure is noteworthy for its efficient cost. A practical problem is how many model evaluations must be performed to guarantee a sufficient precision on th...
In the eld of sensitivity analysis, Sobol' indices are widely used to assess the importance of inputs of a model to its output. Among the methods that estimate these indices, the replication procedure is noteworthy for its efficient cost. A practical problem is how many model evaluations must be performed to guarantee a sufficient precision on the ...
Published in Statistics and Computing
When setting up a computer experiment, it has become a standard practice to select the inputs 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 ...
In this paper, the authors compare a Monte Carlo method and an optimization-based approach using genetic algorithms for sequentially generating space-filling experimental designs. It is shown that Monte Carlo methods perform better than genetic algorithms for this specific problem.
