Variance Reduction in Simulation Experiments: A Mathematical-Statistical Framework

摘要

Many of the fundamental ideas in computer simulation, and particularly techniques for efficient simulation, had their origins in the Monte Carlo estimation literature. The theory of sampling is another closely related field that predates the development of simulation. Although there has been significant research interest in variance reduction, there have been few attempts to structure and define the discipline. Variance reduction techniques (VRTs) are transformations. They transform simulation experiments into related experiments that yield better estimates of some parameters of interest, where better usually means more precise. This research identifies and defines the components from which all variance reduction techniques are built. Given a general mathematical-statistical definition of simulation experiments, these components or classes of transformations are shown to be useful, to be mutually exclusive, and to generate all possible VRTs via composition. Benefits of the research include: 1) the facility to unambiguously define new or existing VRTs, eliminating confusion that currently exists in literature, 2) the facility to decompose VRTs into combinations of transformations, making the relationships between VRTs clear, 3) the development of a theoretical foundation for analytical treatment of VRTs, and 4) the development of a setting for proposing new VRTs and research questions. In addition, increased understanding of the area should promote more and better application of variance reduction in practice.