Variance Reduction via Simultaneous Importance Sampling and Control Variates Techniques Using Vegas

TL;DR

This paper introduces a combined variance reduction method for Monte Carlo integration using importance sampling and control variates, implemented in a Python wrapper for Vegas, demonstrating improved accuracy on benchmark problems.

Contribution

It presents a novel approach that simultaneously applies importance sampling and control variates, enhancing Monte Carlo integration accuracy.

Findings

Improved accuracy in Monte Carlo integration benchmarks

Effective implementation in Vegas via CoVVVR

Demonstrated benefits of combined variance reduction techniques

Abstract

Monte Carlo (MC) integration is an important calculational technique in the physical sciences. Practical considerations require that the calculations are performed as accurately as possible for a given set of computational resources. To improve the accuracy of MC integration, a number of useful variance reduction algorithms have been developed, including importance sampling and control variates. In this work, we demonstrate how these two methods can be applied simultaneously, thus combining their benefits. We provide a python wrapper, named CoVVVR, which implements our approach in the Vegas program. The improvements are quantified with several benchmark examples from the literature.