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

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 and Latin Hypercube Sampling and the Quasi Monte Carlo method 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. There are also some types of functions for which Latin Hypercube Sampling can be more efficient than the Monte Carlo method. For the same functions types it can be more efficient than the Quasi Monte Carlo method at small number of sampled points.JRC.DDG.01-Econometrics and applied statistic