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

对地球内部深处的遥感具有挑战性。由于极端的压力和温度，直接对地球深处进行取样是不可能的。我们对地球的认识？因此，从一系列的表面观测中拼凑出了地球的深层内部。在地表观测中，地震发出的地震波是对地球的有效探测。在地球的内部深处，相对便宜地被地球表面的地震仪网络记录下来。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。s深的内部。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这种超大样本地震数据是禁止的。以促进地球物理发现，可以提高我们对地球的了解？的深层内部利用现有的计算资源，调查员提出了一个新的统计方法下的子抽样框架。所提出的方法提供了一个机会，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。研究人员将建立渐近和有限样本理论来研究所提出的方法的近似精度和一致性。如何分析超大样本数据几乎在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，例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带来了巨大的预算障碍。拟议的二次抽样方法提供了替代方法来克服这一挑战。该理论的建立将有利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，参与尖端的统计和跨学科研究，并激发三个不同领域的新研究方向：统计学，物理学和计算生物学。

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.