Nonparametrical Statistical Methods for Astrophysical and Cosmological Data

AST-0434343基因最近的技术进步使天文学家和宇宙学家能够收集前所未有的质量和数量的数据。这些庞大的数据集可以揭示比以往任何时候都更加复杂和微妙的影响，但它们也需要新的统计方法。该项目由两个相互交织的部分组成：(A)开发新的非参数统计方法，解决天体物理和宇宙学数据分析中反复出现的问题；(B)应用新方法帮助回答重大的天体物理和宇宙学问题。具体地说，这项研究将通过在非参数回归中构建统一的置信集来改进对宇宙微波背景谱的推断，通过开发非参数变量误差问题的新方法来表征局部环境对星系演化的影响，通过为双截断数据产生准确的密度估计器来从星等有限的星系调查中估计物质密度。该研究为博士后研究员和研究生提供跨学科培训，并加强数学和物理科学之间的交叉学科基础设施。

AST-0434343GenoveseRecent technological advances have enabled astronomers and cosmologists to collect data of unprecedented quality and quantity. These large data sets can reveal more complex and subtle effects than ever before, but they also demand new statistical approaches. This project consists of two intertwined components: (a) development of new nonparametric statistical methods that address recurrent problems in the analysis of astrophysical and cosmological data and (b) application of the new methods to help answer significant astrophysical and cosmological questions. Specifically, this research will improve inference for the Cosmic Microwave Background spectrum by constructing uniform confidence sets in nonparametric regression, characterize the influence of local environment on galaxy evolution by developing new methods for nonparametric errors-in-variables problems, and estimate the matter density from magnitude limited galaxy surveys by producing accurate density estimators for doubly truncated data.The research provides interdisciplinary training for postdoctoral fellows and graduate students, and strengthens an interdisciplinary infrastructure between the mathematical and physical sciences.