Mathematical models of "real world" systems are typically too large and complex to solve using analytical methods, and so one must use simulation. Because a simulation is basically a random experiment, it is essential to analyze the resulting output using statistical techniques. Often, this entails estimating the estimator's variance, bias, or mean-squared error, and one desires simulation methods that result in estimators for which these measures of quality are as small as possible. The goal of this project is to develop new methods to improve the quality of simulation estimators by extracting or utilizing more information from the simulation than is done in the standard approaches. The method is related to the Rao-Blackwell theorem of statistics.
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