Definition
The Batch Method (or Batch Means) is a statistical technique used in nonterminating simulations to obtain independent samples from a single, very long simulation run. It involves dividing the steady-state portion of the run into several contiguous “batches.”
Why It Matters
It ensures that the data from computer simulations is statistically valid and not just a fluke of starting conditions. This rigorous approach allows us to trust virtual tests for high-stakes decisions in finance and engineering.
Core Concepts
- Problem of Autocorrelation: Successive observations in a simulation are often correlated (e.g., if one customer waits a long time, the next one likely will too). This violates the “independence” requirement for standard statistical tests.
- The Solution: By making each batch sufficiently long, the correlation between the mean of one batch and the next becomes negligible.
- Batch Means: The average MOP is calculated for each batch. These “batch means” are then treated as independent data points for calculating confidence intervals or performing t-tests.
- Comparison to Replication:
- Replication: Multiple short runs; each starts with a warm-up.
- Batching: One long run; only one warm-up discarded. More efficient for reaching steady state.