Confidence Interval Estimation of the Mean of Stationary Stochastic Processes: a Comparison of Batch Means and Weighted Batch Means Approach (TECHNICAL NOTE)

Abstract

Suppose that we have one run of n observations of a stochastic process by means of computer simulation and would like to construct a condifence interval for the steady-state mean of the process. Seeking for independent observations, so that the classical statistical methods could be applied, we can divide the n observations into k batches of length m (n= k.m) or alternatively, transform the correlated batch means vector into an independent vector. These methods are known as (ordinary) batch means and weighted batch means, respectively. In this paper, using the probability of coverage and the half length of a confidence interval as criteria for comparison, we empirically show that weighted batch means is superior to ordinary batch means, and that it is less sensitive to batch sizes and total number of observations.