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

对地球内部深处的遥感是具有挑战性的。由于极端的压力和温度，直接采集地球内部深处的样本是不可能的。我们对地球的了解？S深部是从一系列地表观察中拼凑而成的。在地面观测中，地震发出的地震波是探测地球深部的有效探测器，由地球表面的地震仪网络记录的成本相对较低。密集的全球地震台网带来了前所未有的海量地震数据，这为研究人员探索地球深处的S提供了机遇和挑战。关键的挑战是，使用现有的计算资源直接将统计方法应用于这种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，利用现有的计算资源，加强我们对地球深部的了解？S，调查者提出了一系列新的欠抽样框架下的统计方法。所提出的方法提供了在统一的框架内研究各种不同的统计问题的机会，例如函数估计和变量选择。研究人员将建立渐近和有限样本理论来研究所提出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的科学和工程领域都是一个巨大的挑战。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，以及建造强大的超级计算机。然而，这些解决方案的高昂成本给研究人员带来了非同寻常的预算障碍。建议的二次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利于科学和工程领域的广泛研究。它们将为本科生和研究生提供独特的教育体验，让他们参与尖端统计和跨学科研究，并在统计学、地球物理学和计算生物学这三个不同的领域激发新的研究思路。

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.