A Procedure for Generating Batch-Means Confidence Intervals for Simulation: Checking Independence and Normality

Batch means are sample means of subsets of consecutive subsamples from a simulation output sequence. Independent and normally distributed batch means are not only the requirement for constructing a confidence interval for the mean of the steady-state distribution of a stochastic process, but are also the prerequisite for other simulation procedures such as ranking and selection (R&S). We propose a procedure to generate approximately independent and normally distributed batch means, as determined by the von Neumman test of independence and the chi-square test of normality, and then to construct a confidence interval for the mean of a steady-state expected simulation response. It is our intention for the batch means to play the role of the independent and identically normally distributed observations that confidence intervals and the original versions of R&S procedures require. We perform an empirical study for several stochastic processes to evaluate the performance of the procedure and to investigate the problem of determining valid batch sizes.