Likelihood-based Inference on Nonlinear spaces: Using Diffusion Processes on Riemannian Manifolds

When data in higher dimensions with a certain constraint on it, say a set of locations on a sphere, is encountered, some classical statistical analysis methods fail, as the data no longer assumes its values in a linear space. In this thesis we consider such datasets and aim to do likelihood-based inference on the center of the data. To model the...