Statistical Theory for Astrophysical Problems

天体物理问题的统计理论

• 批准号: 0806009
• 负责人: Christopher Genovese
• 金额: $ 18.96万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0806009&HistoricalAwards=false
• 关键词: Statistical; Theory; Astrophysical; Problems

Nonparametric inference has become an essential tool for studying the cosmos.This project consists of two intertwined components: (a) development of new theoretical tools and nonparametric methodologies that are inspired by problems in astrophysics but apply more broadly, and (b) application of these tools to two important astrophysical problems, which will frame the need for and guide the development of new statistical theory. Specifically, the investigators will focus on inference for the dark energy equation of state and on identifying filamentary structures from point process data such as that produced by galaxy surveys. The first problem gives rise to a challenging nonlinear inverse problem and demands a nonparametric approach, given what little is known about the dark energy equation of state. The investigators will develop new theory for nonlinear inverse problems that allow for accurate estimates and sharp confidence statements about the unknown function. These techniques will then be applied to Type Ia supernova data, possibly combined with other data sources, to make inferences about dark energy. The second problem gives rise to challenging spatial and inference problems. Current theory in the statistical literature applies to a single filament only, and techniques in the astronomical literature are not supported by theory. The investigators on this project will close that gap, developing theory for defining, identifying, and making inferences about the filamentary structures. The investigators will test this technique and apply it to galaxy survey data.One of the most important problems in cosmology is understanding dark energy.The relationship between observable quantities and dark energy produces a challenging nonlinear inverse problem. With very little strong a priori information about the nature of dark energy, parametric approaches to the problem are limited and suboptimal. And with the promise of much larger data sets in the near future, there will be need and opportunity to extract fine-scale features of the dark energy equation of state. The investigators will develop new theory of inference for such problems, with a focus on estimation under shape constraints, sharp hypothesis testing, and accurate confidence sets. The goal is a substantial improvement in accuracy over the current best techniques. In particular, the investigators will focus on the problem of understanding dark energy and on identifying filamentary structures in distribution of matter. The former is one of the central problems in modern cosmology and demands state of the art statistical techniques to get the most from the data. The investigators will develop new statistical theory and methodologies that substantially improve the precision with which features of dark energy can be estimated from supernova data and other data sources. The latter problem is central to understanding the distribution of matter in the universe. Current statistical theory only applies to a limited version of the problem, and current astronomical methodologies do not have strong theoretical support. The investigators will close that gap and develop a method and corresponding theory that can handle realistic versions of the problem and give optimal or near-optimal performance.

非参数推理已经成为研究宇宙的重要工具。这个项目由两个相互交织的部分组成：(A)受天体物理学问题的启发而开发新的理论工具和非参数方法，但应用更广泛；(B)将这些工具应用于两个重要的天体物理问题，这将框架需要和指导新统计理论的发展。具体地说，研究人员将专注于推断暗能量状态方程，并从点过程数据(如星系调查产生的数据)中识别丝状结构。第一个问题提出了一个具有挑战性的非线性逆问题，并且需要一种非参数方法，因为人们对暗能量状态方程知之甚少。研究人员将为非线性逆问题开发新的理论，允许对未知函数进行准确的估计和尖锐的置信度声明。然后，这些技术将被应用于Ia型超新星数据，可能与其他数据来源相结合，以做出关于暗能量的推断。第二个问题引发了具有挑战性的空间和推理问题。目前统计文献中的理论只适用于单丝，而天文文献中的技术没有理论支持。这个项目的研究人员将缩小这一差距，开发出定义、识别和推断丝状结构的理论。研究人员将测试这项技术，并将其应用于星系调查数据。宇宙学中最重要的问题之一是理解暗能量。可观测量和暗能量之间的关系产生了一个具有挑战性的非线性逆问题。由于几乎没有关于暗能量本质的强大先验信息，解决这个问题的参数方法是有限的和次优的。随着在不久的将来出现更大的数据集，人们将有必要也有机会提取暗能量状态方程的精细特征。研究人员将为这类问题开发新的推理理论，重点放在形状约束下的估计、尖锐的假设检验和准确的置信度集。目标是在目前最好的技术基础上大幅提高精确度。特别是，研究人员将专注于理解暗能量和识别物质分布中的丝状结构的问题。前者是现代宇宙学的核心问题之一，需要最先进的统计技术来最大限度地从数据中获得信息。研究人员将开发新的统计理论和方法，大幅提高从超新星数据和其他数据源估计暗能量特征的精度。后一个问题是理解物质在宇宙中分布的核心。目前的统计理论只适用于有限版本的问题，而目前的天文方法没有强有力的理论支持。调查人员将缩小这一差距，并开发出一种方法和相应的理论，可以处理问题的现实版本，并提供最优或接近最优的性能。