An Implementation of the Batch Means Method

This article introduces the LBATCH and ABATCH rules for applying the batch means method to analyze output of Monte Carlo and, in particular, discrete-event simulation experiments. Sufficient conditions are given for these rules to produce strongly consistent estimators of the variance of the sample mean and asymptotically valid confidence intervals for the mean. The article studies the performance of these rules and two others suggested in the literature, comparing confidence interval coverage rates and mean half-lengths. The article also gives detailed algorithms for implementing the rules in O(t) time with O(log₂ t) space. FORTRAN, C, and SIMSCRIPT II.5 implementations of the procedures are available by anonymous file transfer protocol.