Batch Means for Interval Estimation in Steady-State Simulations

• One disadvantage of replication is that data must be deleted on each replication.
• One disadvantageof a single-replication is its data tend to be autocorrelated.
• The method of batch mean divides the output data from one replication into a few large batches.
• Treat the means of these batches as if they were independent. See the formula on page 463 and 464.

• The key isssue is that no commonly accepted method for choosing an accetable batch size m. This is actually one of the research areas in simulation.
  • Schmeiser found for a fixed total sample size there is little benefit from dividing it into more than k = 30 batches.
  • Although there is typically autocorrelation between batch means at all lags, the lag-1 autocorrelation $corr(\hat{Y_j},\hat{Y_{j+1}})$ is usually studied to assess the dependence between batch means.
  • The lag-1 autocorrelation between batch means can be estimated using the method described earlier. They should not be estimated from a small number of batch means, i.e. we need to have large number of batches, though the size of batches could be small.
  • If the total sample size is to be chosen sequentially (i.e. choose one for one experiment, choose another one for improvement etc.), then it is helpful to allow the batch size and number of batches to grow as the run length increases.

• Example 12.18 on page 465.