Inference Based on Pairwise Distance/Dissimilarity Measures

随着现代信息技术的发展，天文学、生物学、气候学等科学领域收集了大量具有复杂结构的数据集。在本项目中，研究人员计划探索数据采样分布与分布相关算子的谱之间的关系，并为分析基于成对距离/相异度量的常用光谱技术奠定理论基础。在理论分析的基础上，提出了一类新的统计推理工具，用于稳健估计、降维、聚类和数据汇总。将设计在计算上有效的算法，并分发其软件实现。除了统计方法的理论发展外，拟议的推断工具还将应用于利用卫星数据和气候模型输出进行的气候变化研究。这项拟议的研究是由现实世界的科学问题推动的，这些问题需要从海量数据集进行统计推断。该方法旨在从具有复杂结构的海量数据集中提取有用的信息和知识。该项目将开发的新算法不仅有可能帮助地球科学家和气候模型师分析气候记录和校准气候模型，而且还可以为范围广泛的学科的研究人员提供科学调查的统计工具。

With developments in modern information technology, massive datasets with complicated structures have been collected in many scientific fields such as astronomy, biology, climatology, etc. In this project, the investigator plans to explore the connections between the data sampling distribution and spectrum of the distribution dependent operators and to develop a theoretical foundation for analyzing commonly used spectral techniques based on pairwise distance/dissimilarity measures. Based on the theoretical analysis, a new class of statistical inference tools will be proposed for robust estimation, dimension reduction, clustering and data summarization. Computationally effective algorithms will be designed and their software implementations will be disseminated. Besides theoretical development in statistical methodology, the proposed inference tools will be applied to climate change studies using satellite data and climate model outputs. The proposed research is motivated by real world scientific problems that require statistical inference from massive datasets. The proposed method is designed to extract useful information and knowledge from those massive datasets with complicated structures. The novel algorithms to be developed in this project have the potential to not only help geoscientists and climate modelers in analyzing climate records and calibrating climate models, but also provide statistical tools for scientific investigations for researchers in a wide spectrum of disciplines.