A randomized Halton algorithm in R

TL;DR

This paper introduces an R implementation of a scrambled Halton sequence generator that enables practitioners to evaluate the effectiveness of randomized quasi-Monte Carlo sampling for variance reduction in numerical integration.

Contribution

The paper presents the rhalton R function for generating scrambled Halton sequences, facilitating easy assessment of RQMC benefits across different problems.

Findings

RQMC can significantly reduce variance compared to MC

The efficiency gain varies depending on the problem

The code allows flexible extension of sample size and dimension

Abstract

Randomized quasi-Monte Carlo (RQMC) sampling can bring orders of magnitude reduction in variance compared to plain Monte Carlo (MC) sampling. The extent of the efficiency gain varies from problem to problem and can be hard to predict. This article presents an R function rhalton that produces scrambled versions of Halton sequences. On some problems it brings efficiency gains of several thousand fold. On other problems, the efficiency gain is minor. The code is designed to make it easy to determine whether a given integrand will benefit from RQMC sampling. An RQMC sample of n points in $[0,1]^d$ can be extended later to a larger n and/or d.