Statistical Modeling and Computation of Extreme Values in Large Datasets

如今，环境、地球和生物科学中的许多问题都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。在许多这样的应用中，对极值的分析是特别重要的。例如，严重的潮汐、热浪、暴雨和极端的空气污染事件等自然灾害事件会对我们的社会造成实质性的损害。该项目的目标是更好地了解空间依赖性极端事件，以便进行有效的定量风险管理。该项目对多个跨学科领域具有广泛的影响，包括统计学、地球科学、环境科学、运筹学、机器学习和风险管理。大数据中极值分析和预测的建模和计算方法可以广泛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一系列实际和重要问题。从定义上讲，极端事件是罕见事件。直到最近，由于大空间数据的可用性，空间极值分析开始变得可行，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很大的机会。然而，如此大的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结合起来，开发新颖的模型，以及推理和预测算法，以满足对大数据极值高效分析工具日益增长的需求。具体而言，该项目将侧重于以下研究重点。首先，将开发一类新的非平稳极大稳定过程模型，该模型具有高维空间极值的灵活和理想的依赖结构。然后提出了新的可扩展和可并行的推理工具来估计所提出的非平稳最大稳定过程模型。随后，将研究分治法条件采样算法在大空间数据极值预测中的应用，该算法提供了对未观测位置预测值的点估计和不确定性度量。最后，将所开发的方法应用于实际问题的解决。

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.