On batch means in the simulation and statistics communities

Batching is a well known technique for estimating the variance of point estimators computed from simulation experiments. The batch statistic variance estimator is simply the (appropriately scaled) sample variance of the estimator computed on subsets of data. The simulation and statistics communities seem to be largely unaware of each other's results in this area. Some empirical and theoretical results from the simulation and statistics literature will be discussed and compared. In particular, we discuss the important issue of selecting batch size and present a new data based method for determining it. The basic idea is to empirically estimate the optimal batch size for a smaller simulation length, and then extrapolate using knowledge of the optimal order of magnitude of batch length for the original simulation length. We provide a small simulation showing the effectiveness of the proposed method.