Spatial Hierarchical Models for Extremes: Modeling Both Climate and Weather Effects

This paper and talk will discuss the applied aspects of joint work with Mathieu Ribatet, Department of Mathematics, Université Montpellier II, and Anthony Davison, Institute of Mathematics, École Polytechnique Fédérale de Lausanne. The complete paper Ribatet et al. [2010] is under review. Weather data are characterized by two types of spatial effects: climate effects that occur on a regional scale and weather effects that occur on a local scale. In terms of a statistical model, one can view climate effects as how the marginal distribution varies by location and the weather effects as characterizing the joint behavior. We extend recent work in spatial hierarchical models for extremes by employing a max-stable random process at the data level of the hierarchy, thereby accounting for the weather spatial effects which had often been ignored. Because the known max-stable process models can be written in closed form only for the bivariate case, we employ composite likelihood methods to implement them in our hierarchical model. Appropriate uncertainty estimates are obtained via an information sandwich approach. 1 Motivation: Climate and Weather Effects in Extreme Data Geophysical data are spatial, thus to model extreme geophysical data, one must account for its spatial behavior. This is difficult, as the data arise from a combination of both climate and weather effects. For discussion purposes, we think of climate as the distribution from which weather events are drawn. Since climate varies with location, climate spatial effects are how the marginal behavior of extremes vary over a study region. Weather spatial effects are how a particular weather event affects multiple locations. 1 Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin (Session IPS097) p.1475