Controlling Correlations in Latin Hypercube Samples

Monte Carlo integration is competitive for high-dimensional integrands. Latin hypercube sampling is a stratification technique that reduces the variance of the integral. Previous work has shown that the additive part of the integrand is integrated with error Op (n −1/2) under Latin hypercube sampling with n integrand evaluations. A bilinear part of the integrand is more accurately estimated if the sample correlations among input variables are negligible. Other authors have proposed an algorithm for controlling these correlations. We show that their method reduces the correlations by roughly a factor of 3 for 10 ≤ n ≤ 500. We propose a method that, based on simulations, appears to produce correlations of order Op (n −3/2). An analysis of the algorithm indicates that it cannot be expected to do better than n −3/2.