Statistics for manifold-valued data

Multivariate data with complicated constraints such as manifold-valued data is frequently encountered in the physical, biological and medical sciences, however it is difficult to define tractable statistical models and estimate their parameters due to the curvature and nonlinear geometry of the sample space. This project aims to develop and then implement a new suite of fully flexible, interpretable and tractable models for manifold-valued data, along with robust and accurate estimation techniques for their parameters. The outcomes of the project are of direct mathematical interest as well as having significant interest to science and business disciplines where manifold-valued data is commonly observed.