Group symmetric Latin hypercube designs for symmetrical global sensitivity analysis

Abstract

Symmetrical global sensitivity analysis (SGSA) is of use in studying the symmetrical structure of a model via symmetrical global sensitivity indices (SGSI). The computation of SGSI is a challenging task because the model to compute is black-box and expensive. An experimental design, called a group symmetric Latin hypercube design (GSLHD) is proposed for SGSA. It achieves maximum uniformity in univariate margins and maintains a symmetrical structure that ensures the estimability of SGSI. Based on the proposed GSLHD, SGSI can be efficiently estimated by using output values evaluated from the model. Construction methods and sampling properties of the proposed design are presented. Numerical studies on benchmark test problems demonstrate that the proposed design is effective in shrinking the estimation bias and volatility with economically feasible sample sizes.