Confidence intervals for replicated batch means estimators

In the simulation output analysis and experiment design of simulation systems, people usually use batch means (BM) and independent replications (IR). In the former case, batching observations in one long run are chosen, and in the latter, a number of smaller runs is replicated. However, for the former one the sample data are correlated, while the latter one suffers from an initialization bias at the beginning of each run. The replicated batch means (RBM), combining IR and BM, overcomes the problems of data correlation and initialization bias, but suffers from more calculation loads. Based on the existing studies, this paper gives RBM confidence-interval estimation of the steady-state mean considering the initial bias, and then compares these three methods above.