Spatial Regression Models for Extremes

Abstract

Meteorological data are often recorded at a number of spatial locations. This gives rise to the possibility of pooling data through a spatial model to overcome some of the limitations imposed on an extreme value analysis by a lack of information. In this paper we develop a spatial model for extremes based on a standard representation for site-wise extremal behavior, combined with a spatial latent process for parameter variation over the region. A smooth, but possibly non-linear, spatial structure is an intrinsic feature of the model, and difficulties in computation are solved using Markov chain Monte Carlo inference. A simulation study is carried out to illustrate the potential gain in efficiency achieved by the spatial model. Finally, the model is applied to data generated from a climatological model in order to characterize the hurricane climate of the Gulf and Atlantic coasts of the United States.