Nested symmetrical Latin hypercube designs

Symmetrical global sensitivity analysis (SGSA) can aid practitioners in reducing the model complexity by identifying symmetries within the model. In this paper, we propose a nested symmetrical Latin hypercube design (NSLHD) for implementing SGSA in a sequential manner. By combining the strengths of the nested Latin hypercube design and symmetrical design, the proposed design allows for the implementation of SGSA without the need to pre-determine the sample size of the experiment. We develop a random sampling procedure and an efficient sequential optimization algorithm to construct flexible NSLHDs in terms of runs and factors. Sampling properties of the constructed designs are studied. Numerical examples are given to demonstrate the effectiveness of the NSLHD for designing sequential sensitivity analysis.