Statistics on Manifolds

4 credits

This is a graduate topics course covering statistics with manifold constraints. Topics include Frechet means and variances, principal geodesic analysis, directional statistics, random fields on manifolds, statistical distances between distributions, transport problems, and information geometry. Manifold constraints will be considered on simplexes, spheres, Stiefel manifold, stratified manifolds, cone of positive definite matrices, trees, compositional data, and other relevant manifolds. Prerequisites: DSC 210 and DSC 212. Restricted to students within the DSC-MS-001 and DSC-PhD-001 major.