A Mathematically Rigorous Way To Analyze Statistics from Simulations

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.