Sliced Latin Hypercube Designs

Abstract This article proposes a method for constructing a new type of space-filling design, called a sliced Latin hypercube design, intended for running computer experiments. Such a design is a special Latin hypercube design that can be partitioned into slices of smaller Latin hypercube designs. It is desirable to use the constructed designs for collective evaluations of computer models and ensembles of multiple computer models. The proposed construction method is easy to implement, capable of accommodating any number of factors, and flexible in run size. Examples are given to illustrate the method. Sampling properties of the constructed designs are examined. Numerical illustration is provided to corroborate the derived theoretical results. KEY WORDS: Computer experimentDesign of experimentsEnsembles of computer modelsNumerical integrationSpace-filling design Acknowledgments The author thanks the Editor, the Associate Editor, and three referees for their helpful comments, which have led to improvements in the article. The author also thanks Youngdeok Hwang for assistance in computing and Xu He for useful comments. This work is supported by NSF Grant DMS 1055214.