Data Analysis on Sample Spaces with a Manifold Stratification

AOOD Program working group.

Many statistics problems deal with data naturally sampled from spaces with singularities.  For example, such is the case for shape data in three dimensions, where the sample space is a singular orbifold, or metric tree data, where the sample space is a polyhedral complex. Our goals are to understand the role of intrinsic and extrinsic geometry near singularities in asymptotics and to develop nonparametric methodologies and fast inference techniques in applications.