Exploring multi-dimensional spaces: a Comparison of Latin Hypercube and Quasi Monte Carlo Sampling Techniques

TL;DR

This paper compares Monte Carlo, Latin Hypercube, and Quasi Monte Carlo sampling methods across various test problems, finding Quasi Monte Carlo with Sobol sequences generally offers superior efficiency, especially for unknown function types.

Contribution

It provides a comparative analysis of sampling techniques, highlighting the robustness of Quasi Monte Carlo with Sobol sequences for diverse integration tasks.

Findings

Quasi Monte Carlo outperforms Monte Carlo and Latin Hypercube in most cases.

Latin Hypercube can be more efficient for certain functions and small sample sizes.

Quasi Monte Carlo is the most reliable method for unknown function types.

Abstract

Three sampling methods are compared for efficiency on a number of test problems of various complexity for which analytic quadratures are available. The methods compared are Monte Carlo with pseudo-random numbers, Latin Hypercube Sampling, and Quasi Monte Carlo with sampling based on Sobol sequences. Generally results show superior performance of the Quasi Monte Carlo approach based on Sobol sequences in line with theoretical predictions. Latin Hypercube Sampling can be more efficient than both Monte Carlo method and Quasi Monte Carlo method but the latter inequality holds for a reduced set of function typology and at small number of sampled points. In conclusion Quasi Monte Carlo method would appear the safest bet when integrating functions of unknown typology.