Models for Extremes on a Spatial Lattice

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。研究人员和他的同事提出并研究了一个模型，该模型可用于描述规则空间晶格上的极端情况（特别是阈值不稳定性）。 一个空间模型的阈值偏差数据需要处理的情况下，数据值超过阈值，只有在有限的地区的研究区域。 所提出的模型通过创建由许多较小模型组成的整体模型来实现这一点。 空间域被覆盖的一些小的和重叠的子区域和这些子区域上的数据建模与参数的多元极值模型的低维。 研究人员表明，这些子区域模型可以结合在这样一种方式，即整体模型的角度测量满足极值分布的要求。 从低维模型构建整体模型的想法受到了空间统计学中的格模型的启发，模型的基础是基于传统极值理论的思想。虽然极端事件很少发生，但由于其对人类和经济的重大影响，了解极端事件的性质非常重要。 最近，人们对极端情况的空间建模非常感兴趣，特别是在建模地球物理数据（如降水）的背景下。 尽管在这一领域的兴趣，仍然存在着一个极端的模型，可以描述在许多地方记录的空间数据的依赖性的需要。 该提案的目标是开发和研究记录在空间点阵上的阈值重复数据的模型。 虽然这项建议中的研究是由空间和地球物理数据驱动的，但这些方法可以用于气候科学以外的极端应用。由于缺乏高维的多元极值模型，这一领域的进展是显着的，很可能被扩展和适应。

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.