Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification

TL;DR

This paper introduces Refined Stratified Sampling (RSS), an adaptive method for uncertainty quantification that improves variance reduction over traditional stratified sampling and Latin hypercube sampling, with potential for high-dimensional problems.

Contribution

The paper proposes RSS, an adaptive stratified sampling approach that enhances variance reduction and flexibility in uncertainty quantification compared to existing methods.

Findings

RSS reduces variance more effectively than traditional stratified sampling.

RSS offers comparable or better variance reduction than Latin hypercube sampling.

The method demonstrates improved convergence in low-dimensional UQ problems.

Abstract

A general adaptive approach rooted in stratified sampling (SS) is proposed for sample-based uncertainty quantification (UQ). To motivate its use in this context the space-filling, orthogonality, and projective properties of SS are compared with simple random sampling and Latin hypercube sampling (LHS). SS is demonstrated to provide attractive properties for certain classes of problems. The proposed approach, Refined Stratified Sampling (RSS), capitalizes on these properties through an adaptive process that adds samples sequentially by dividing the existing subspaces of a stratified design. RSS is proven to reduce variance compared to traditional stratified sample extension methods while providing comparable or enhanced variance reduction when compared to sample size extension methods for LHS - which do not afford the same degree of flexibility to facilitate a truly adaptive UQ process. An initial investigation of optimal stratification is presented and motivates the potential for major advances in variance reduction through optimally designed RSS. Potential paths for extension of the method to high dimension are discussed. Two examples are provided. The first involves UQ for a low dimensional function where convergence is evaluated analytically. The second presents a study to asses the response variability of a floating structure to an underwater shock.