The Level-Based Stratified Sampling Plan

Abstract

If the probability distribution of the input variables to a system described by a computer code is known, the distribution function of the output variable can be obtained by computer simulations. With a complicated program, each simulation can take very long time. It thus is necessary to choose the combinations of the input parameters carefully to get as much information as possible with a small number of computer runs. Different methods (true random sampling, stratified sampling, Latin hypercube sampling, and updated Latin hypercube sampling) for choosing the input parameters are described in the literature. As a criteria for a good sampling plan, unbiased estimates and low mean squared error are used. By computer experiments, it has been shown that the sampling plans based on Latin hypercubes often have the smallest variance of the estimated output variable. In this article it is shown that a stratified sampling plan with strata defined by the surfaces in the sampling space where the output variable is constant has the lowest variance among all unbiased sampling plans. Unfortunately, it is possible to construct the sampling plan only if the solution is already available. However, an approximate sampling plan can be constructed if an approximate solution is known. In an application, it is shown how the results from a finite element method (FEM) model with a coarse element structure can be used to construct a sampling plan to be used with a FEM model with a finer element structure.