Applied variance reduction - some concepts and examples

Given virtually infinite computational speed and resources - in terms of both people and machines - we would all carefully structure deterministic methods. The absence of such capabilities is what motivates Monte Carlo simulation; it should not, however, cause us to abandon systemic approaches. Unfortunately, in most applications of Monte Carlo simulation, the judicious selection of sampling techniques is ignored, often at great expense. In addressing this point, the “benchmark” solution to an apparently simple (but delusive) problem provides a method of gauging the merits of some basic sampling tactics. Parallel synchronous techniques substantially reduce the sample size needed to compare alternatives on a relative basis but do little for absolute measures. On the other hand, perfecting the distribution of a short-term sequence of psuedorandom numbers can meaningfully improve the rate of convergence of estimates of the mean. These techniques can also contribute to the efficiency of large simulation models and find utility in (strict) Monte Carlo applications.