Statistics in the Space of Metric Trees

Data generated in such areas as evolutionary biology and medical imaging is often non-Euclidean in nature, and thus not easily analyzed using standard statistical techniques for Euclidean space.  One approach to this problem is to consider the data as being sampled from some geometric, stratified space.  For example, the space of metric trees is a polyhedral complex with non-positive curvature.  In this case, geodesics (shortest paths) are unique, and the Frechet (intrinsic) mean is well-defined and computable.  We investigate properties of the Frechet mean in tree space, including non-Euclidean "sticky" behaviour, and applications to some biological problems, such as constructing species trees from gene trees and comparing the topology of blood vessels in the brain.