STOCHASTICS SEMINAR SERIES -- Replicated Batch Means for Steady-State Simulations
Batch means and multiple independent replications are two of the most popular output analysis methods for steady-state simulations. In this study, we consider a new, hybrid output analysis method called replicated batch means, in which a small number of independent replications are conducted and the observations that are collected from these replications are further grouped into batches. We show that the confidence intervals constructed by the replicated batch means method are valid for large batch sizes. Moreover, we derive expressions for the expected values and variances of the steady-state mean and variance estimators for stationary processes and large sample sizes. Using these asymptotic expressions, we compare the replicated batch means method with the standard batch means and multiple independent replications methods. We also study the behavior of our replicated batch means method for non-stationary processes and finite sample sizes using numerical experiments. We use several different initialization methods, some of which are first addressed in this study, to select the initial states of each replication. Our numerical results show that for some of the initialization methods under consideration, the replicated batch means method appears to consistently provide better coverages of confidence intervals than the standard batch means and independent replications methods, sometimes even by a large margin.