New Tools for Sparse Inference in Large-scale Multiple Comparisons

摘要提案编号：DMS - 0505423提案题目：大规模多重比较中稀疏推理的新工具机构：普渡大学提出了一项针对大规模多重比较创建新工具的研究项目。这一领域的工作主要集中在理想化的模型上，如标准高斯模型，尚未解决的是许多其他模型的潜力，这些模型更具现实性和影响力。在本提案中，研究者研究了三个方面的问题：(a)。制定大量数据——开发具有科学现实性和影响力的模型，以及数学上的简单性，以便进行仔细的研究。(b)。开发新工具——通过探索各种各样的模型，揭示新现象，开发易于实现且理论上合理的工具。(c)。细致的渐近研究——布置渐近研究的框架，仔细比较现有和新提出的推理工具，研究这些工具的最优性。该项目的动机在于，在基因组学、天文学和图像处理等科学领域产生的大量数据集导致了统计学的一个新领域：大规模同时假设检验或多重比较。这个新领域的进步将使不同科学领域的科学家能够从大量数据集中快速提取他们需要的信息，开发易于实现的工具是统计界的直接兴趣。该项目通过开发新工具和新理论，以及揭示新现象，推动了该领域的边界。该项目生产的工具在理论上听起来和实际可行，可用于解决基因组学、天文学和图像处理等领域的问题。

ABSTRACTPrincipal Investigators: Jin, Jiashun Proposal Number: DMS - 0505423Proposal Title: New Tools for Sparse Inference in Large-scale Multiple Comparisons Institution: Purdue University A research effort is proposed to create new tools for large-scale multiple comparisons. Work in this field has been concentrated on idealized models such as the standard Gaussian model, what has not been addressed is the potential of many other models which have more realism and impact. In this proposal, the investigator studies problems in three areas: (a). Formulation of massive data -- Develop models which have Scientific realism and impact, as well as mathematical simplicity such that careful study is possible. (b). Development of new tools -- By exploring a wide variety of models, expose new phenomena and develop tools which are easy-to-implement and theoretically sound. (c). Delicate asymptotic study -- Lay out framework for asymptotic study, carefully compare the existing and newly proposed inference tools, study on the optimality of such tools.The motivation of this project lies in that, massive datasets produced in scientific areas such as Genomics, astronomy, and image processing lead to a new field in statistics: large-scale simultaneous hypothesis testing or multiple comparisons. The vision is advances in this new field will enable the scientists from various scientific fields to quickly extract the information they need from massive datasets, and it is the immediate interest of the statistics community to develop easy-to-implement tools. This project pushes the boundary of the field by developing new tools and novel theories, as well as exposing new phenomena. The project produces tools which are theoretically sounding and practically feasible for solving problems in areas such as Genomics, astronomy, and image processing.