Stochastic Process Methods for Statistical Analysis on Manifolds

The project will focus on the study of probability measures on finite and infinite dimensional manifolds with a view towards statistical inference for shape, curve and image data. Rigorous development of statistical tools for analysis of such data requires an improved understanding of the construction of probability measures and behaviour of random variables on non-linear spaces. Employing stochastic processes as a tool to study the interplay between probability and geometry, the project will address some fundamental issues that arise in the development of statistical theory and methodology for non-Euclidean data analysis. The outcomes of this project will have a direct bearing on efficient representation and analysis of high-resolution imaging data in biomedical studies.