A Model for Extremes on a Regular Spatial Lattice

• Activity Number: 400
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Dan Cooley*+ and Grant B Weller
• Companies: Colorado State University and Colorado State University
• Keywords: precipitaton ; spectral/angular measure ; tail dependence ; EM algorithm

Abstract

We propose a model which can be used to characterize extremes on a regular spatial lattice. Analogous to lattice models from spatial statistics, the proposed model creates an overall model composed from many smaller models. The spatial domain is covered by a number of small and overlapping subregions and data on these subregions is modeled with parametric multivariate extreme value models of low dimension. We show that these subregion models can be combined in such a way that the angular measure of the overall model meets the requirements of an extreme value distribution.

We aim to perform inference for the model via an EM algorithm. The algorithm assumes the data arise from the sum two pieces: a first-order piece which corresponds to the limiting angular measure, and a second-order nuisance piece. The model is designed specifically for threshold exceedance data and is used to model data, such as extreme precipitation which at any given time is likely to be extreme only in limited areas of the study region.