Di. 13.08.2019, Oberseminar Stochastik
Thema: Extremal Behaviour of Spatially Aggregated Data with an Application to Downscaling. Referent: Dr. Marco Oesting, (Uni Siegen), Dienstag, 13.08.2019, Zeit: 10:Uhr, Raum: EN-C201
Extremal Behaviour of Spatially Aggregated Data with an Application to Downscaling.
Diensstag, den 13. August 2019,
um 10:00 Uhr, im Raum ENC-D 201,
Referent: Dr. Marco Oesting, (Uni Siegen)
Abstract:Spatial extreme value theory and, especially, max-stable processes are widely applied tools to assess risks in environmental science. Inference methods for these models typically rely on station measurements at various sites within the region of interest. In many applications, however, gridded data that might be interpreted as spatial aggregates are available. Understanding the link from these gridded data to point measurements is an important area of research in environmental sciences called downscaling.
In this talk, we focus on the tail behaviour of aggregated data which may differ from the behaviour of point measurements. For a large class of aggregating functionals, we introduce a coefficient that quantifies this difference as a function of the extremal dependence. We also obtain the joint extremal dependence for multiple aggregation functionals applied to the same process. The results provide a theoretical link between the extremal distribution of the aggregated data and the corresponding underlying process, which we exploit to develop a method for statistical downscaling. We apply our framework to downscale daily temperature maxima in the south of France from a gridded data set. This is joint work with Sebastian Engelke and Raphaël de Fondeville.