Sequentially Refined Latin Hypercube Designs: Reusing Every Point

The use of iteratively enlarged Latin hypercube designs for running computer experiments has recently gained popularity in practice. This approach conducts an initial experiment with a computer code using a Latin hypercube design and then runs a follow-up experiment with additional runs elaborately chosen so that the combined design set for the two experiments forms a larger Latin hypercube design. This augmenting process can be repeated multiple stages, where in each stage the augmented design set is guaranteed to be a Latin hypercube design. We provide a theoretical framework to put this approach on a firm footing. Numerical examples are given to corroborate the derived theoretical results. Supplementary materials for this article are available online.