Statistical models for space filling designs and optimalities of uniform designs

Computer experiments are very useful for exploring complicated physical phenomena in various research fields of science and engineering. Construction of computer experiments is a crucial step during the planning of experiments. There are many space filling designs for computer experiments. The uniformity and low-discrepancy sets have played an important role in the construction of designs for computer experiments. To understand the reasons why space filling designs have good performance in computer experiments, in this paper, we compare several statistical models from different statistical points of view. The overall sample mean model has been employed in the development of the Latin hypercube sampling and uniform design. However, this model considers only the overall mean of the response and is far not enough for the need in practice. In this paper, we systematically studies some alternative approaches to the uniform design, such as nonparametric regression model, goodness-of-fit, robustness against model specification and decision theory. These approaches show that the uniform design is an optimal one from several aspects. Furthermore, these approaches illustrate the advantages and potential applications of the uniform design.