REFINED LATINIZED STRATIFIED SAMPLING: A ROBUST SEQUENTIAL SAMPLE SIZE EXTENSION METHODOLOGY FOR HIGH-DIMENSIONAL LATIN HYPERCUBE AND STRATIFIED DESIGNS

摘要

A robust sequential sampling method, refined latinized stratified sampling, for simulation-based uncertainty quantification and reliability analysis is proposed. The method combines the benefits of the two leading approaches, hierarchical Latin hypercube sampling (HLHS) and refined stratified sampling, to produce a method that significantly reduces the variance of statistical estimators for very high-dimensional problems. The method works by hierarchically creating sample designs that are both Latin and stratified. The intermediate sample designs are then produced using the refined stratified sampling method. This causes statistical estimates to converge at rates that are equal to or better than HLHS while affording maximal flexibility in sample size extension (one-at-a-time or n-at-a-time sampling are possible) that does not exist in HLHS-which grows the sample size exponentially. The properties of the method are highlighted for several very high-dimensional problems, demonstrating the method has the distinct benefit of rapid convergence for transformations of all kinds.