Batching methods in simulation output analysis: what we know and what we don't

As an advanced tutorial, we discuss batching methods for determining point-estimator precision for steady-state simulation experiments. We emphasize batching methods in which each batch provides a point estimator analogous to that of the experiment, but we mention other methods that use batches, especially the more-general idea of standardized time series. Despite the preponderance of literature on confidence-interval estimation for the mean using adjacent nonoverlapping batches, we focus on estimating the point estimator's standard error and consider both general point estimators and general batching relationships. Literature on multivariate batching exists, but we focus on the univariate problem. We consider the initial-transient problem only in passing. Specific issues include form of the point estimator, definition of the batch statistics, form of the batch-statistics estimator, optimal batch size (including various definitions of optimal) and determining batch size. This paper is a short summary of the issues, with a fairly complete bibliography.