A Mathematically Rigorous Way To Analyze Statistics from Simulations

Research fills gap in probabilistic simulation modeling and analysis

Apr 30, 2020
As Featured In 
Operations Research

New research from Maryland Smith’s Michael C. Fu offers a rigorous way to analyze statistics generated from simulation models.

The new result fills a gap in probabilistic simulation modeling and analysis. Fu, the Smith Chair of Management Science in the Decision, Operations and Information Technologies department at the University of Maryland’s Robert H. Smith School of Business, worked with four co-authors, two at Stanford University and two in China at Fudan University and Peking University.

In a research note published in the journal Operations Research, the researchers provide a mathematical proof establishing that an important form of statistical estimator generated from simulation models follows a central limit theorem, a key property in statistics. This important result forms the basis for the construction of confidence intervals, which quantify the accuracy of statistical estimators of system performance based on Monte Carlo-based simulations. These statistics are used to understand the impact of risk and uncertainty in simulation models arising in finance, manufacturing, transportation, and supply chain management.

“Such estimators arise in a number of different simulation-based computational settings,” write the researchers. "Our results apply to quantiles, conditional value-at-risk, quantile sensitivities, and other computational contexts as well.” The paper describes their theoretical results and provides applications that illustrate their theory.

Read more:Technical Note — Central Limit Theorems for Estimated Functions at Estimated Points,” is featured in Operations Research.

About the Author(s)

Michael Fu

Michael Fu has a joint appointment with the Institute for Systems Research and an affiliate appointment with the Department of Electrical and Computer Engineering, both in the A. James Clark School of Engineering. He was named a Distinguished Scholar-Teacher at the University of Maryland for 2004-2005. His research interests include simulation modeling and analysis, operations management, applied probability and queueing theory, with application to manufacturing and finance. He received an SB in mathematics and SB/SM in electrical engineering & computer science from MIT in 1985 and a PhD in applied mathematics from Harvard University in 1989.

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