Decomposition of Some Well-Known Variance Reduction Techniques. Revision.

Proliferation of techniques and lack of unifying structure has hindered both study and application of variance reduction. The authors recently developed unifying structure, presented in detail elsewhere, is a taxonomy that views each variance reduction technique VRT as a transformation from one experiment to another. The taxonomy is exhaustive in that any VRT can be expressed as a composition of elemental transformations from six classes. This paper illustrates this taxonomy by using the notation, terminology, and concepts of the taxonomy to discuss seven VRTs. The objective is to use the readers knowledge of these well-known techniques to provide an introduction and overview of the taxonomy. Key words Common Random Numbers, Conditional Expectations, Control Variates, Importance Sampling, Monte Carlo Method, Stratified sampling, Simulation. Author