Why the Straightforward Method of Antithetic Variates Is So Disappointing in Practice

摘要

The effect of stochastic variables on systems simulation models (e.g., time between failures of a machine in a job shop) is discussed. Examples where the response consists of a number that is the direct result of passing a single random number through a sequence of monotonic transformations (the simulation model) are analyzed. Results show that the success of the straightforward application of the antithetic method depends on how well the initial pairwise symmetry of antithetic uniform random variables survives the concatenation of transformations that constitute a simulation model. Even in simple examples results are less than hoped for. In realistic simulation models straightforward application of the antithetic method cannot guarantee an appreciable reduction of the variance of the estimate of the mean response. Whether a reduction can be achieved at all has to be determined experimentally in each individual case.