Statistical Modeling and Computation of Extreme Values in Large Datasets

当今环境、地球和生物科学中的许多问题涉及大量的空间数据，这些数据来自远程地面传感器、卫星图像、地理信息系统和公共卫生来源等。极值分析在许多这样的应用中特别有趣。例如，严重的潮汐、热浪、暴雨和极端空气污染事件等自然危险事件可能会给我们的社会造成巨大的破坏。该项目的目标是更好地了解空间相关的极端事件，以便进行有效的量化风险管理。该项目对统计学、地球科学、环境科学、运筹学、机器学习和风险管理等多个跨学科领域产生了广泛的影响。大数据中极值分析和预测的建模和计算方法可以应用于极端气候变化研究、环境危险事件分析、保险风险评估和农业规划等广泛的实际和重要问题。直到最近，空间极值分析开始变得可行，这要归功于大空间数据的可获得性，这为准确量化极端事件的风险、更好地了解极端事件之间的联系、及时监测极端事件的频率和强度的变化以及可靠地预测未观测位置的极值提供了巨大的机会。然而，这样的大数据规模也给统计建模和计算带来了挑战。该项目的目标是将理论方法和计算方法相结合，开发新的模型以及推理和预测算法，以满足对大数据中极值的高效分析工具日益增长的需求。特别是，该项目将重点开展以下研究工作。首先，发展了一类新的非平稳极大稳定过程模型，该模型对高维空间极值具有灵活和理想的依赖结构。然后，将提出新的可扩展和可并行化的推理工具来估计所提出的非平稳最大稳定过程模型。然后，将研究分而治之的条件采样算法来预测大型空间数据上的极值，该算法为未观测位置的预测值提供点估计和不确定性度量。最后，将所开发的方法应用于解决实际问题。

Numerous problems in environmental, earth, and biological sciences nowadays involve large amounts of spatial data, obtained from remote ground sensors, satellite images, geographic information systems, and public health sources, etc. Analysis of extreme values is of particular interests in many such applications. For instance, natural hazardous events such as severe tides, heat waves, heavy rainfalls, and extreme air pollution events can cause substantial damages in our society. The goal of this project is to better understand spatially dependent extreme events for efficient quantitative risk management. The project has a broad impact on multiple interdisciplinary fields including statistics, geoscience, environmental science, operations research, machine learning, and risk management. The modeling and computational approaches for extreme value analysis and prediction in big data can be applied to a wide range of practical and important problems including extreme climate change studies, environmental hazardous event analysis, insurance risk assessments, and agriculture planning.Extreme events are rare events by definition. Until recently, analysis of spatial extreme values starts to become feasible, thanks to the availability of big spatial data, which provides great opportunities to accurately quantify the risk of extreme events, better understand the links among extreme events, promptly monitor changes in the frequency and intensity of extreme events, and reliably predict extreme values at unobserved locations. However, such big data sizes also impose challenges for statistical modeling and computation. The objective of this project is to combine theoretical methods and computational approaches to develop novel models, along with inference and prediction algorithms, to meet the increasing demand of efficient analytical tools for extreme values in big data. In particular, the project will focus on the following research thrusts. First, a new class of nonstationary max-stable process models will be developed with flexible and desirable dependence structures for high-dimensional spatial extreme values. Then new scalable and parallelizable inference tools will be proposed for the estimation of the proposed nonstationary max-stable process models. Afterwards, divide-and-conquer conditional sampling algorithms will be studied for the prediction of extremes over large spatial data, which provides both point estimations and uncertainty measures for the predicted values at unobserved locations. Finally, the developed method will be applied to solve real problems.