Newcomb-Benford's law as a fast ersatz of discrepancy measures

TL;DR

This paper introduces a novel, computationally efficient method based on Newcomb-Benford's law to evaluate the quality of random samples, serving as a fast alternative to traditional discrepancy measures in high-dimensional design of experiments.

Contribution

The paper proposes a new discrepancy measure using Newcomb-Benford's law, significantly reducing computational cost while maintaining comparable assessment quality.

Findings

The new metric provides similar information to classical discrepancy measures.

It offers a substantial reduction in computational time.

The method is effective for high-dimensional sampling assessment.

Abstract

Thanks to the increasing availability in computing power, high-dimensional engineering problems seem to be at reach. But the curse of dimensionality will always prevent us to try out extensively all the hypotheses. There is a vast literature on efficient methods to construct a Design of Experiments (DoE) such as low discrepancy sequences and optimized designs. Classically, the performance of these methods is assessed using a discrepancy metric. Having a fast discrepancy measure is of prime importance if ones want to optimize a design. This work proposes a new methodology to assess the quality of a random sampling by using a flavor of Newcomb-Benford's law. The performance of the new metric is compared to classical discrepancy measures and showed to offer similar information at a fraction of the computational cost of traditional discrepancy measures.