ATD: Collaborative Research: A Geostatistical Framework for Spatiotemporal Extremes

ATD：协作研究：时空极值的地统计框架

• 批准号: 2220529
• 负责人: Guofeng Cao
• 金额: $ 15万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2220529&HistoricalAwards=false
• 关键词: ATD; Collaborative; Research; Geostatistical; Framework

Extreme weather events such as heat waves, drought, and intense precipitation can cause drastic losses and disruptions to the U.S. economy and natural systems. There is abundant evidence that the frequency and magnitude of such extremes are increasing, making it critical to better understand the spatiotemporal distributions of the extreme events and to develop efficient statistical tools to model the spatiotemporal trends and the associated uncertainties. In this research the investigators will develop a systematic, statistical approach to study certain new and challenging directions in extremes of random fields with applications in statistics, geography, geographic information science (GIScience) and climate sciences. Random fields are playing increasingly important roles in statistics and geosciences, due to their extensive applications as spatiotemporal models, where many problems involve dependent data at spatial and temporal locations.The project will also provide research training to students. Specifically, the investigators will develop methods to obtain the exact probability distributions of peak heights for smooth Gaussian and related non-Gaussian random fields such as chi-squared, t and F fields. For the nonstationary case, since the peak height distribution varies at different locations, a new concept on regional peak height distribution will be investigated. The investigators will also study the spatial distribution of peaks, which characterizes the probability to observe peaks in certain domains. This will provide valuable methods to estimate and predict the chances of extreme events in specific regions. The developed peak height distributions will be employed in multiple testing of local maxima (particularly in computing p-values) for detecting peaks for signals embedding in nonstationary Gaussian noises or non-Gaussian noises. Moreover, the investigators will extend the proposed methods for structural change detections of linear models by investigating the links between change points and peaks. The project developments will be evaluated in domain applications with national priority: characterizing and modeling of extreme heat events and land surface changes. This proposed research will integrate interdisciplinary tools from probability, statistics, geometry and GIScience to develop desired theoretical results and statistical methods, and will create synergy with related disciplines such as climate sciences, environmental sciences and social sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

热浪，干旱和巨大的降水等极端天气事件会造成巨大的损失和破坏美国经济和自然系统。有大量证据表明，这种极端的频率和幅度正在增加，这对于更好地了解极端事件的时空分布至关重要，并开发有效的统计工具来模拟时空趋势和相关的不确定性。在这项研究中，研究人员将开发一种系统的，统计的方法，以研究在统计，地理，地理信息科学（Giscience）和气候科学中应用的随机领域的某些新的和具有挑战性的方向。由于它们作为时空模型的广泛应用，随机领域在统计和地球科学中扮演着越来越重要的角色，其中许多问题涉及时空和时间位置的依赖数据。该项目还将为学生提供研究培训。具体而言，研究人员将开发方法，以获取光滑高斯和相关的非高斯随机场（例如卡方，T和F场）的峰高的确切概率分布。对于非平稳情况，由于峰高分布在不同位置有所不同，因此将研究一个有关区域峰高分布的新概念。研究者还将研究峰的空间分布，这表征了观察某些域中峰的概率。这将提供有价值的方法来估计和预测特定地区极端事件的机会。开发的峰高分布将用于对局部最大值的多次测试（尤其是在计算p值中），以检测嵌入非平稳性高斯噪音或非高斯噪音的信号。此外，研究人员将通过研究变化点与峰之间的联系来扩展线性模型结构变化检测的建议方法。该项目的开发将在具有国家优先级的领域应用中进行评估：表征和建模极端热事件和陆地表面变化。这项拟议的研究将从概率，统计，几何学和司法机构中整合跨学科工具，以发展理论的结果和统计方法，并将与诸如气候科学，环境科学和社会科学等相关学科造成协同作用。这一奖项反映了NSF的法定任务，并通过评估范围来反映出范围的范围。