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

Understand

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.