Dependence in Spatial and Multivariate Extremes

• Activity Number: 101
• Type: Roundtables
• Date/Time: Monday, August 10, 2015 : 7:00 AM to 8:15 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Dan Cooley*
• Companies: Colorado State University
• Keywords: rainfall ; pollution ; tail dependence

Abstract

Multivariate and spatial extreme behavior is of increasing interest in the environmental sciences; for example, one may wish to assess the probability of high levels of multiple air pollutants occurring simultaneously or the probability of flooding resulting in extreme rainfall at many locations. To estimate risk associated with events that are extreme in multiple components or at multiple locations requires modeling dependence in the tail of the joint distribution. This discussion will focus on existing models for multivariate and spatial extremes. A good statistical model is both useful for application and based in probability theory. Finding models for tail dependence that balance these two aims is a current challenge in extreme value theory. Topics to be discussed are the spectral representation for multivariate extremes and modeling in the asymptotically dependent and asymptotically independent cases. In spatial extremes, we will discuss current models and their strengths and limitations. We also will discuss challenges for inference with multivariate and spatial extremes models the realistic dimensionality limitations.