A0540
Title: Space filling designs on Riemannian manifolds
Authors: Xiangshun Kong - Beijing Institute of Technology (China) [presenting]
Abstract: The aim is to propose a new approach to generating space-filling designs over Riemannian manifolds by using a Hilbert curve. Different from ordinary Euclidean spaces, a novel transformation is constructed to link the uniform distribution over a Riemannian manifold and that over its parameter space. With the help of this transformation, the uniformity of the design points in the sense of the Riemannian volume measure can be guaranteed by the intrinsic measure preserving the property of the Hilbert curve. It has been proved that these generated designs are not only asymptotically optimal under minimax and maximin distance criteria but also perform well in minimizing the Wasserstein distance from the target distribution and controlling estimation errors in numerical integration. Furthermore, an efficient algorithm is developed for the numerical generation of these space-filling designs. Compared with the existing methods, the advantages of the new approach are verified through numerical simulations.
