ATD: Collaborative Research: A Geostatistical Framework for Spatiotemporal Extremes

热浪、干旱和强降水等极端天气事件可能会对美国经济和自然系统造成严重损失和破坏。有大量证据表明，这种极端事件的频率和规模都在增加，因此必须更好地了解极端事件的时空分布情况，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极端随机场中的某些新的和具有挑战性的方向。随机场在统计学和地球科学中发挥着越来越重要的作用，因为它们作为时空模型的广泛应用，其中许多问题涉及时空位置上的相关数据。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来获得平滑高斯和相关非高斯随机场（如卡方，t和F场）峰高的精确概率分布。对于非平稳情况，由于峰高分布在不同的位置不同，一个新的概念，区域峰高分布将进行调查。研究人员还将研究峰的空间分布，其表征在某些域中观察到峰的概率。这将为估计和预测特定地区发生极端事件的可能性提供有价值的方法。所开发的峰高分布将用于局部最大值的多重测试（特别是在计算p值时），用于检测嵌入非平稳高斯噪声或非高斯噪声中的信号的峰。此外，研究人员将通过研究变化点和峰值之间的联系来扩展线性模型结构变化检测的方法。项目开发将在国家优先领域的应用中进行评估：极端热事件和地表变化的表征和建模。该研究将整合概率、统计、几何和地理信息科学等跨学科工具，以开发所需的理论结果和统计方法，并将与气候科学、环境科学和社会科学等相关学科产生协同效应。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.