An efficient approach to implement dynamic batch means estimators in simulation output analysis

Abstract

Estimating the variance of the sample mean is a classical problem of stochastic simulation. Traditional batch means estimators require specification of the simulation run length a priori. Dynamic batch means (DBM) is a new approach to implement the traditional batch means in fixed memory by dynamically changing both batch size and number of batches without the knowledge of the simulation run length. This article further improves the DBM by considering small storage requirements and fast computation. The proposed algorithm is useful when the simulation run length is random and extremely long in simulation models.