Nested-simulation view of Sobol' index estimation yields MSE rates, optimal outer/inner budgets, and jackknife/LHS guidance for pick-freeze-style estimators.
Exploring multi-dimensional spaces: a Comparison of Latin Hypercube and Quasi Monte Carlo Sampling Techniques
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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.
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Nested Simulation Methods for Sobol' Index Estimation: Bias Correction, Budget Allocation, and Latin Hypercube Sampling
Nested-simulation view of Sobol' index estimation yields MSE rates, optimal outer/inner budgets, and jackknife/LHS guidance for pick-freeze-style estimators.