2020/08/18 by Owen, Art B. · 2 citations
#Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2008.08051
Quasi-Monte Carlo (QMC) points are a substitute for plain Monte Carlo (MC) points that greatly improve integration accuracy under mild assumptions on the problem. Because QMC can give errors that are o(1/n) as n→∞, changing even one point can change the estimate by an amount much larger than the error would have been and worsen the convergence rate. As a result, certain practices that fit quite naturally and intuitively with MC points are very detrimental to QMC performance. These include thinning, burn-in, and taking sample sizes such as powers of 10, other than the ones for which the QMC points were designed. This article looks at the effects of a common practice in which one skips the first point of a Sobol' sequence. The retained points ordinarily fail to be a digital net and when scrambling is applied, skipping over the first point can increase the numerical error by a factor proportional to √(n) where n is the number of function evaluations used.