CAREER: Subsampling Methods in Statistical Modeling of Ultra-Large Sample Geophysics

对地球深处进行遥感是一项挑战。由于极端的压力和温度，对地球深处的直接采样是不可能的。我们对地球的了解？因此，从一系列的地表观测结果中拼凑出了月球的深层内部。在地面观测中，地震发出的地震波是对地球的有效探测。这些地震是由地球表面的地震仪网络相对便宜地记录下来的。密集的全球地震仪网络带来了前所未有的地震数据量，为研究人员探索地球提供了机遇和挑战。内心深处。关键的挑战是，使用当前的计算资源直接将统计方法应用于超大样本地震数据是令人望而却步的。为了促进地球物理的发现，从而增进我们对地球的了解？利用现有的计算资源，研究者在子抽样框架下提出了一系列新的统计方法。所提出的方法提供了一个机会来研究各种不同的统计问题，如函数估计和变量选择，在一个统一的框架。研究者将建立渐近和有限样本理论来研究所提出的方法的逼近精度和一致性。如何分析超大样本数据在几乎所有科学和工程领域都是一个重大挑战。科学家和工程师开发了各种解决方案来解决这个问题，比如开发云计算来聚合广泛的计算资源和构建强大的超级计算机。然而，这些解决方案的高成本给研究人员造成了巨大的预算障碍。提出的子抽样方法提供了克服这一挑战的替代方法。即将建立的理论将有益于科学和工程领域的广泛研究。他们将为本科生和研究生提供独特的教育体验，让他们参与前沿的统计和跨学科研究，并在统计学、地球物理学和计算生物学这三个不同领域激发新的研究方向。

Remote sensing of the Earth's deep interior is challenging. Direct sampling of the Earth's deep interior is impossible due to the extreme pressures and temperatures. Our knowledge of the Earth?s deep interior is thus pieced together from a range of surface observations. Among surface observations, seismic waves emitted by earthquakes are effective probes of the Earth?s deep interior and are relatively inexpensively recorded by networks of seismographs at the Earth's surface. Unprecedented volumes of seismic data brought by dense global seismograph networks offer researchers both opportunities and challenges to explore the Earth?s deep interior. The key challenge is that directly applying statistical methods to this ultra-large sample seismic data using current computing resources is prohibitive. To facilitate geophysical discoveries that can enhance our understanding of the Earth?s deep interior using current computing resources, the investigator proposes a family of novel statistical methods under a subsampling framework. The proposed methods provide an opportunity to study various distinct statistical problems, such as function estimation and variable selection, in a unified framework. The investigator will establish asymptotic and finite sample theory to investigate the approximation accuracy and consistency of the proposed methods.How to analyze ultra-large sample data creates a significant challenge in almost all fields of science and engineering. Scientists and engineers develop various solutions to tackle the problem, such as developing cloud computing for aggregating a wide range of computing resources and building powerful supercomputers. However, the high cost of these solutions creates an extraordinary budget barrier for researchers. The proposed subsampling methods provide alternative methods to surmount this challenge. The theory to be established will benefit a wide spectrum of research in science and engineering. They will offer a unique educational experience for both undergraduate and graduate students to participate in cutting-edge statistical and interdisciplinary research and inspire new lines of researches in three distinct fields: statistics, geophysics, and computational biology.