Adaptive Quasi-Monte Carlo Integration Based on MISER and VEGAS

Abstract

Quasi-Monte Carlo (QMC) routines are one of the most common tech-niques for solving integration problems in high dimensions. However, their efficiency degrades if the variation of the integrand is concentrated in small areas of the inte-gration domain. Adaptive algorithms cope with this situation by adjusting the flow of computation based on previous integrand evaluations. We explore ways to modify the Monte Carlo based adaptive algorithms MISER and VEGAS such that low-discrepancy point sets are used instead of random sam-ples. Experimental results show that the proposed algorithms outperform plain QMC as well as the original adaptive integration routine for certain classes of test cases.