Collaborative Research: Photometric redshifts via Bayesian functional data analysis

许多绘制天空的项目都需要精确估计星系后退的速度。一种广泛使用的技术通过仔细测量星系的颜色，使用一种叫做“photo-zs”的分析方法，得出了这个数字，即红移。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。目前由天文学家和统计学家组成的团队将提高照片的精度和可靠性。这项工作将为正在进行和发展中的大型调查提供关键的使能技术，这代表了天文学的相当大的投资。这个项目将增加投资的回报。这项研究需要在天文学和统计学方面进行创新，并开发可能产生重大额外影响的新统计方法。这项研究将通过暑期学校和其他特别课程，帮助培养各种各样的高级统计学学生和博士后，从历史上看，许多这样的受训者后来都在数据科学领域从事职业。当前和即将到来的自动化数字天空调查旨在通过精心绘制数亿个星系的分布和性质，以及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。这需要使用宽带光度数据，通过光度红移（简称photo-zs）技术，对星系的红移进行准确而精确的估计。不幸的是，目前的估计方法无法从这些调查中获得最完整的科学回报。目前的项目将天文学家和统计学家联合起来，通过使用贝叶斯函数数据分析（FDA）对星系的光谱能量分布进行建模，提高photozs的精度和可靠性。贝叶斯函数数据分析（FDA）是一种强调预测建模和跨层次、多阶段发现链的信息和不确定性的彻底传播的方法。该项目将使用模块化、分层建模框架，并考虑相似性和多样性，包括传统参数化和新的数据驱动参数化。因为这个框架将产生概率的photo-z估计，可能有复杂的不确定性，研究小组还将研究如何最佳地提供这种估计，并将其用于宇宙科学。他们的算法的开源实现将在适当的地方由图形处理单元加速。该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开发新的统计方法。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.