Multiplex Sampling

Abstract

The problem of estimating desired characteristics of a response $X$, where $X = h(y)$ and $y$ is a vector random variable with statistically independent components from known distributions, may be handled by standard Monte Carlo techniques. We are interested in the generalization where several distributions are of interest, one at a time, for each component of $y$ and the desired characteristics of $X$ must be estimated for each combination of component distributions. A relatively small number of observations, compared to the total number required if each combination were posed as a separate Monte Carlo problem, may be used instead by sampling from a fictitious distribution, calculating an estimate by appropriately weighting the observations, and then reusing the sample. These techniques are standard; the contribution here is to find the fictitious distribution which is best for the characteristics desired, the distributions of interest, and allied considerations. Various concepts of the meaning for "best" are examined in the paper. Finally, a quantitative evaluation is made under restricted conditions.