Interactive analysis of simulation output by the method of batch means

An interactive FORTRAN subroutine is presented for use with ongoing simulations to determine and collect the sample size needed to estimate the mean of a process with a specified level of statistical precision. The subroutine can be used with simulation models written in a variety of languages, e.g., FORTRAN, GASP, GPSS, SIMSCRIPT. The subroutine partitions a sequence of observations on the random variable of interest into a series of consecutive batches, finding those batch sizes whose batch means are independent. The classical iid method is then applied to build a confidence interval on the mean. Under interactive user control, the subroutine then goes back to the simulation model as often as may be necessary to extend sample size to the point that the confidence interval satisfies the user's needs.

This paper complements an earlier paper presenting software for interactive autoregressive analysis of simulation output [1]. The present paper reports on the use of both techniques to analyze data produced by data models for which analytic results are known. The method of batch means is not successful in identifying the batch size for which the batch means are known to be independent in one of these data sets. This raises serious questions about the procedure used to test for independence of batch means, and points out the need for further research in this area.