A farewell to the use of antithetic variates in Monte Carlo simulation

Abstract

Antithetic variates (AV) is one the oldest and most popular variance reduction techniques (VRTs), commonly using complementary random numbers. The AV variance reduction is generally justified by the negative correlation it produces in paired simulation estimates. A new and simpler interpretation of the AV role is presented, showing AV as solely a procedure for input sample means compensation, without any further contribution from the complementary idea. The proposed interpretation is based on the descriptive sampling framework, viewing input samples as composed of a set of values and their sequencing. Simulation experiments and third-party results give support to this interpretation. However, when newer simulation sampling methods, like Latin Hypercube Sampling, Descriptive Sampling, Moment Matching and Quasi-Monte Carlo are adopted, all of them based on a controlled selection of the input sample values, AV turns irrelevant. Other VRTs are also affected by the ideas presented here.