General sliced Latin hypercube designs

Abstract

We propose a method for construcing general sliced Latin hypercube design, intended for computer experiments. A general sliced Latin hypercube design has multiple layers, at each of which there are multiple Latin hypercube designs that can be sliced into smaller Latin hypercube designs at the next layer. The proposed method is easy to implement, capable of accommodating any number of factors and exible in run size. Such designs include ordinary Latin hypercube design and sliced Latin hypercube design as special cases. A special case of general sliced Latin hypercube design with two layers, called doubly sliced Latin hypercube design, is studied in detail, including its sampling properties. The more exible structure of doubly sliced Latin hypercube design than sliced Latin hypercube design allows more exible batch size for both collective evaluation of dierent computer models and batch sequential evaluation of a single computer model. Numerical examples are provided to show the advantage of the former over the latter.