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Have we really been analyzing terminating simulations incorrectly all these years?

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Author
Sanchez, Paul J.
White, K. Preston Jr.
Date
2013
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Abstract
We all know how to estimate a confidence interval for the mean based on a random sample. The interval is centered on the sample mean, with the half-width proportional to the sample standard error. We know also that terminating simulations generate independent observations. What simulators appear to have overlooked is that independence alone is insufficient to guarantee a valid random sample—the observations must also be identically distributed. This is a good assumption if the outcome of each replication is a single observation, but it is demonstrably incorrect if the outcome is an aggregate value and the replications have differing numbers of observations. In this paper we explore the implications of this oversight when within-replication observations are independent. We then derive analytic results showing that although the impact on interval estimates can sometimes be negligible, there also are circumstances where the variance of our estimates is significantly increased. We finish with a simple example which demonstrates the potential impact for practitioners.
Description
Proceedings of the 2013 Winter Simulation Conference R. Pasupathy, S.-H. Kim, A. Tolk, R. Hill, and M. E. Kuhl, eds.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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http://hdl.handle.net/10945/43599
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