Optimal Design of Experiments on Riemannian Manifolds

The theory of optimal design experiments has been traditionally developed on an Euclidean space. In this paper, new theoretical results and algorithm for finding the experiment located a Riemannian manifold are provided. It is shown that analogously to in spaces, D-optimal G-optimal designs equivalent manifolds, we provide lower bound maximum prediction variance response evaluated over manifold. addition, converging finds experimental data proposed. Numerical demonstrate importance considering structure designed when present, superiority proposed algorithm.