Nonparametric Smoothing of Directional and Axial Data

Explore nonparametric smoothing techniques for directional and axial data in this 43-minute seminar lecture by Professor Lutz Duembgen from Universität Bern. Delve into specialized statistical methods designed to handle data that exists on circular or spherical manifolds, where traditional smoothing approaches may not be appropriate. Learn about the unique challenges posed by directional data, such as wind directions, geological orientations, or protein conformations, and axial data where opposite directions are considered equivalent. Discover how nonparametric smoothing methods can be adapted to respect the geometric constraints of these data types while maintaining statistical rigor. Examine practical applications and theoretical foundations of these techniques, including kernel smoothing methods adapted for circular and spherical geometries. Gain insights into the mathematical frameworks that enable effective density estimation and regression for data that wraps around or exists on curved manifolds. This presentation is part of the "Representing, calibrating & leveraging prediction uncertainty from statistics to machine learning" event at the Isaac Newton Institute for Mathematical Sciences.