Stratified sample tiling

Abstract

The paper introduces a practical method for the construction of large-scale point sets for analysis of computer models. The constructed experimental design is useful for (probabilistic) integration, construction of approximation or a screening. The essence of the presented approach is the stratification of the design domain into an orthogonal grid of substrata and a subsequent tiling with tiles of points. If optimized, such tiles experience a major reduction of the number of degrees of freedom in the optimization process. That way, optimal or near-optimal point patterns can be feasibly identified and are further utilized for construction of larger point sets, thanks to the idea of self-similarity and structured space stratification The space-filling properties of the resulting point sets may be further enhanced by various “scrambling” strategies, which may remove the undesired sample collapsibility achieved via regular tiling. The performance of the constructed point sets is compared to Quasi Monte Carlo (QMC), Randomized Quasi Monte Carlo (RQMC) sequences, which are still today considered by engineers and even scientists as choices for variance reduction of numerical integration Further, the mentioned sampling strategies are compared in the terms of robustness when integrating a multivariate function with a localized feature. It is concluded that the proposed sampling approach reaches a superior performance in numerical integration and identification of function extremes as compared to sampling methods used by practicing researchers and engineers. Additionally, the reader is supplied with the open-access, ready-to-use implementation of the presented algorithm named SampleTiler.