Abstract: Based on the work of Wang and Fang (1990a,b), this paper extends the definition of discrepancy of a set of points with respect to a distribution. To construct multivariate uniform designs, two transformations, discrepancy-preserving transformation and density-preserving transformation, and a method of separating variables are introduced. Also, for some special domains useful in statistics, some related transformations are given. In particular, as an application of the method of separating variables, we give an approach of constructing a uniform design in the Stiefel manifold and outline its applications in projection pursuit methods.
Key words and phrases: Computer experiment, Latin hypercube, number-theoretic method, projection pursuit, Stiefel manifold, uniform design.