SAMPLE POINT UNIFORMITY USING DISCREPANCY MEASURES

摘要

Approximately uniform distributions of sample points are useful in certain problems in engineering and mathematics, notably optimization and uncertainty. For example, weight-controlled Monte Carlo simulation (MCS) ideally has samples approximately uniformly distributed throughout the sample space, and response surface methodologies benefit from an even distribution of sample points over input/output spaces. This paper advances the concept of discrepancy sensitivity, a linear approximation for the contribution of a sample to uniformity, quantifying the level of "new" information provided. Several examples are given of its use in choosing sample points for response surface characterization.