Since Monte Carlo simulation is a sampling procedure, results obtained from the procedure inevitably involve sampling errors, which decrease as the sample size increases. Increasing the sample size to achieve a higher precision generally means an increase in computer time for generating random variates and data processing. Variance-reduction techniques aim at obtaining high accuracy for the Monte Carlo simulation results without having to substantially increase the sample size. Hence variance-reduction techniques enhance the statistical efficiency of the Monte Carlo simulation. When applied properly, variance-reduction techniques sometimes can make the difference between an impossible, expensive, simulation study and a feasible, useful one.
Variance-reduction techniques attempt to reduce the error associated with the Monte Carlo simulation results by using known information about the problem at hand. Naturally, such an objective cannot be attained if the analyst is completely ignorant about the problem. On the other extreme, the error is zero if the analyst has complete knowledge about the problem. Rubinstein (1981) stated that “variance reduction cannot be obtained from nothing; it is merely a way of not wasting information.” Therefore, for a problem that is not known at the initial stage of the study, pilot simulations can be performed for the purpose of gaining useful insight into the problem. The insight, then, can be incorporated later into the variance-reduction techniques for a more efficient
simulation study. Therefore, most of the variance-reduction techniques require additional effort on the part of analysts.
