A New Multistage Procedure for Systematic Variance Reduction in Monte Carlo

A common technique in Monte Carlo applications is to introduce into the simulation one or more parameter values whose purpose is to lower the variance in the estimated quantity without affecting its mean. Good parameter choices may sometimes be guessed or found by using physical insight, but to date, no way has been described systematically to find parameter choices which minimize the variance. This paper develops a multistage technique for accomplishing this optimization. The technique is based on obtaining very efficient estimates of the relative parametric dependence of the variance by averaging random variables over a small number of samples chosen with fixed, but arbitrary, parameter values. The utility of the method is illustrated by applying it to the optimization of the exponential transform, a variance-reducing technique which is often used in shielding calculations.