This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The investigator and his colleagues propose and study a model which can be used to characterize extremes (specifically threshold exceedances) on a regular spatial lattice. A spatial model for threshold exceedance data needs to handle situations where data values exceed the threshold only in limited areas of the study region. The proposed model accomplishes this by creating an overall model composed of 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. The investigators 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. The idea of constructing an overall model from models of lower dimension is inspired by lattice models from spatial statistics, and the model's foundation is based on ideas from traditional extreme value theory.
Although they occur infrequently, understanding the nature of extreme events is important because of their significant human and economic impact. Recently, there has been much interest in spatial modeling of extremes, particularly in the context of modeling geophysical data such as precipitation. Despite the interest in this area, there still exists a need for extremes models which can describe the dependence in spatial data which are recorded at many locations. The goal of this proposal is to develop and study a model for threshold exceedance data that is recorded on a spatial lattice. While the research in this proposal is motivated by spatial, geophysical data, the methodologies could be utilized in extremes applications well beyond climate science. Because multivariate extremes models for high dimensions are lacking, advancements in this area are significant and are likely to be extended and adapted.
