Title: Discrete copulas for weather forecasting: Theoretical and practical aspects
Authors: Elisa Perrone - Eindhoven University of Technology (Netherlands) [presenting]
Liam Solus - KTH Royal Institute of Technology (Sweden)
Caroline Uhler - Massachusetts Institute of Technology (United States)
Abstract: Discrete copulas are fascinating geometric objects of great importance for empirical modeling in the applied sciences. We analyze mathematical and practical features of discrete copulas, i.e., restrictions of copula functions to non-square grid domains. In particular, we (1) highlight fundamental connections between copulas and discrete geometry, and (2) discuss their application to weather forecasting problems. First, we present a geometric approach to describe families of discrete copulas through the properties of their associated polytopes. Specifically, we inquire into the geometric attributes of these polytopes such as bounding hyperplanes, vertices, and volume. Then, we discuss the role of discrete copulas in empirical postprocessing methods of numerical weather ensemble forecasts by presenting a case study on weather data of the Austrian region.