Collaborative Research: Photometric redshifts via Bayesian functional data analysis

许多测绘天空的项目都需要精确估计星系消退的速度。一种广泛使用的技术是通过仔细测量星系的颜色来得出这个数字，即红移，该方法使用了一种称为“照片zs”的分析方法。不幸的是，目前的估计方法不够精确，无法实现主要的调查科学目标。目前的天文学家和统计学家团队将提高照片Z的精度和可靠性。这项工作将为正在进行和正在开发的大型调查提供关键的使能技术，这是对天文学的一项相当大的投资。这个项目将增加这项投资的回报。这项研究需要天文学和统计学方面的创新，以及可能产生重大额外影响的新统计方法的开发。这项研究将通过暑期学校和其他特别课程，帮助培训不同的学生和博士后，学习高级统计学。从历史上看，许多这样的学员一直在从事数据科学的职业生涯。目前和即将到来的自动化数字天文测量旨在通过仔细绘制数亿个星系的分布和属性图，并测量数千颗超新星的细节，进一步推动“精确宇宙学”领域的发展。这需要使用宽带测光数据，通过被称为光度红移的技术，或简称Photo-zs，准确和精确地估计星系的红移。不幸的是，目前的估计方法不能从这些调查中获得最完整的科学回报。本项目联合天文学家和统计学家，通过使用贝叶斯函数数据分析(贝叶斯函数数据分析)对星系的光谱能量分布进行建模，来提高照片zs的精度和可靠性，这是一种强调预测建模和跨分级、多阶段发现链彻底传播信息和不确定性的方法。该项目将使用模块化的分层建模框架，并考虑到相似性和多样性，既有传统的参数化，也有新的数据驱动的参数化。由于这个框架将产生概率照片-z估计，可能存在复杂的不确定性，该团队还将研究如何以最佳方式提供此类估计并将其用于宇宙学科学。他们的算法的开源实现将在适当的时候由图形处理单元加速。这项研究将为研究生提供有价值的跨学科培训，同时通过创新地结合FDA、机器学习和高性能计算来开发新的统计方法。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Many projects mapping the sky require precise estimates of the speed at which galaxies are receding. A wide-spread technique derives this number, the redshift, from carefully measuring galaxy colors, using an analysis called "photo-zs". Unfortunately, current estimation methods are not precise enough to achieve major survey science goals. The present team of astronomers and statisticians will improve both the precision and the reliability of photo-zs. This work will provide key enabling technology for large surveys in progress and in development, which represent a considerable investment in astronomy. This project will increase the return on that investment. The research requires innovation in both astronomy and statistics and the development of new statistical methods likely to have significant additional impact. The research will help to train a diverse population of students and postdocs in advanced statistics via summer schools and other special sessions, and historically, many such trainees have gone on to pursue careers in data science.Current and forthcoming automated digital sky surveys aim to push further into "precision cosmology" territory by meticulously mapping the distribution and properties of hundreds of millions of galaxies, and measuring the details of thousands of supernovae. This requires accurate and precise estimation of the redshifts of galaxies using broad-band photometric data, by the technique known as photometric redshifts, or photo-zs for short. Unfortunately, current estimation methods do not enable the most complete science return from these surveys. The present project unites astronomers and statisticians to improve the precision as well as the reliability of photo-zs, by modeling spectral energy distributions of galaxies, using Bayesian functional data analysis (FDA), an approach that emphasizes predictive modeling and thorough propagation of information and uncertainty across hierarchical, multi-stage discovery chains. The project will use a modular, hierarchical modeling framework and account for similarity and diversity, with both conventional parameterizations, and new data-driven parameterizations. Because this framework will produce probabilistic photo-z estimates, with possibly complex uncertainties, the team will also study how optimally to provide such estimates and to use them for cosmological science. Open-source implementations of their algorithms will be accelerated by graphics processing units where appropriate. The research will provide valuable inter-disciplinary training to a graduate student, while developing new statistical methods by innovatively combining FDA, machine learning, and high-performance computing.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.