Computational experience with the batch means method

Abstract

This article discusses implementation issues for the LBATCH and ABATCH batch means procedures of Fishman and Yarberry (1997). Theses procedures dynamically increase the batch size and the number of contiguous batches based on the outcome of a hypothesis test for independence among the batch means. We show that both procedures require O(n) time and O(log2 n) space, where n is the desired sample size. Although like complexities are known for static fixed batch size algorithms, the dynamic setting of the LBATCH and ABATCH rules offers an important additional advantage not present in the static approach. As the analysis evolves with increasing sample path length, it allows a user to assess how well the estimated variance of the sample mean stabilizes. This assessment is essential to gauge the quality of the confidence interval for the sample mean. The LABATCH implementation (described in Fishman 1996 and Fishman and Yarberry 1997) of the LBATCH and ABATCH rules is the only computer package that automatically generates the data for this assessment.