B1135
Title: Optimal design of experiments on Riemannian manifolds
Authors: Hang Li - Astrazeneca (United States) [presenting]
Abstract: The theory of optimal design of experiments has been traditionally developed in Euclidean spaces. New theoretical results and an algorithm for finding the optimal design of an experiment located on a Riemannian manifold are provided. It is shown that analogously to the results in Euclidean spaces, $D$-optimal and $G$-optimal designs are equivalent on manifolds, and we provide a lower bound for the maximum prediction variance of the response evaluated over the manifold. In addition, a converging algorithm that finds the optimal experimental design on manifold data is proposed. Numerical experiments demonstrate the importance of considering the manifold structure in a designed experiment when present, and the superiority of the proposed algorithm.
