Higher-Order Coverage Error Analysis for Batching and Sectioning

While batching and sectioning have been widely used in simulation, it is open regarding their higher-order coverage behaviors and whether one is better than the other in this regard. We develop techniques to obtain higher-order coverage errors for sectioning and batching. We theoretically argue that none of batching or sectioning is uniformly better than the other in terms of coverage, but sectioning usually has a smaller coverage error when the number of batches is large. We also support our theoretical findings via numerical experiments.