TECHNIQUES for EFFICIENT MONTE CARLO SIMULATION

Many Monte Carlo simulation problems lend themselves readily to the application of variance reduction techniques. These techniques can result in great improvements in simulation efficiency. This document describes the basic concepts of variance reduction (Part I), and a methodology for application of variance reduction techniques is presented in Part II. Appendices include the basic analytical expressions for application of variance reduction schemes as well as an abstracted bibliography. The techniques considered here include importance sampling, Russian roulette and splitting, systematic sampling, stratified sampling, expected values, statistical estimation, correlated sampling, history reanalysis, control variates, antithetic variates, regression, sequential sampling, adjoint formulation, transformations, orthonormal and conditional Monte Carlo. Emphasis has been placed on presentation of the material for application by the general user. This has been accomplished by presenting a step by step procedure for selection and application of the appropriate technique (s) for a given problem.