Stefan Sommer (University of Copenhagen)
Thursday, November 23, 2023, 11am
Conditioned diffusions in geometric statistics: Means, bridges, and shape variation along phylogenetic trees
Statistics of manifold valued data such as shapes appearing in medical imaging and morphology is traditionally formulated using geodesic distances and least-squares. In the talk, I will outline an approach to geometric statistics where geodesic distances are replaced with (-log)likelihoods of diffusion processes on the geometric spaces. This leads to new statistics and new estimation algorithms. One example is the diffusion mean, an alternative to the classical Frechet mean. I will discuss the motivation behind the diffusion mean, its construction and statistical properties. The diffusion mean is closely connected to conditioned diffusions, bridges, and I will link these to conditioned diffusion processes in morphology and phylogenetic analysis where branching processes are conditioned on the leaves of a phylogenetic tree.