A negative dependence framework to assess different forms of scrambling

TL;DR

This paper introduces a dependence-based framework to evaluate and compare the effectiveness of random and deterministic scrambling methods for low-discrepancy sequences like Faure and Halton, focusing on improving small sample performance.

Contribution

It proposes a new dependence framework to assess deterministic and random scrambling, guiding the choice of optimal scrambling methods for better sequence performance.

Findings

Deterministic scrambling can mitigate known defects in sequences.

Random scrambling improves sequence uniformity for small samples.

The framework helps select effective scrambling strategies.

Abstract

We use the framework of dependence to assess the benefits of scrambling randomly versus deterministically for Faure and Halton sequences. We attempt to answer the following questions: when a deterministic sequence has known defects for small sample sizes, should we address these defects by applying random scrambling or should we find a "good" deterministic scrambling yielding a sequence that can then be randomized using a less computer-intensive randomization method such as a digital shift? And in the latter case, how do we choose a deterministic scrambling and how do we assess whether it is good or not?