Comparison of independent and stratified sampling schemes in problems of global optimization

Abstract

Let X be a compact subset of R ^d and {x_l,…,xⁿ} be a sample of random points in X. It is well—known that any properly organized stratified sampling procedure is superior to the independent sampling with respect to the variance of Monte Carlo estimates of integrals of functions in L ₂ (X). We prove similar results for some perfomance characteristics important in global optimization. We also demonstrate that the stratified sample with the maximum stratification is optimum, in a suitable sense.