DMS-EPSRC Collaborative Research: Advancing Statistical Foundations and Frontiers for and from Emerging Astronomical Data Challenges

统计理论和方法在科学发现和进步中发挥着根本作用，包括在现代天文学中，在现代天文学中，收集的数据规模越来越大，种类和复杂性也越来越多。新技术和仪器产生了各种各样的新兴数据类型和数据分析挑战，这反过来又需要和激发更多创新的统计方法和理论。本研究以推进统计基础和前沿为双重目标，以天文学问题为动力，为天文学挑战提供有原则的数据分析解决方案。加州-哈佛天文统计合作中心（CHASC）国际中心在完成这两项任务方面有着广泛的记录。这项研究利用了CHASC的业绩记录，在几个新项目中取得了进展。例如，将复杂的天体物理模型与用高科技仪器收集的复杂数据相匹配，通常需要进行一系列的统计分析。有几个项目的重点是发展新的统计方法，以适当地解释错误，并在这种分析序列中继续进行不确定性。额外的工作将集中于发展新的统计估计程序的理论特性，以解决与太阳耀斑和x射线观测相关的数据分析挑战。其他项目涉及从二维甚至四维数据中快速自动探测天文物体，如星系。pi将在这些项目的背景下发展统计理论和方法，建立统计基础，推动统计前沿的广泛影响，将远远超出天体统计。PIs计划提供有效的方法和算法，以应对天文学中出现的挑战，并希望在天文学研究人员中推广这种有原则的数据分析方法。它通过CHASC GitHub软件库提供的免费软件将使所提出的方法和算法的分发和影响成为可能。这些项目反映了三大主题：(1)探索对天文学有直接影响的基本统计理论，包括利用最大乘积间距的轴向特性获得置信区域的一般方法，然后将其应用于评估太阳耀斑的幂律，以及对天体物理学中流行的C-stat使用的统计原则修正；(2)评估多阶段统计分析中模型和先验分布的不规范，当重新进行贝叶斯分析不切实际时，对后验图进行后处理以纠正先验建模的缺陷；(3)复杂模型断点识别，包括天文边界快速识别算法和空间、光谱、时间联合模型断点识别算法。主题1更多的是理论驱动，而主题2和3更多的是方法和计算驱动。他们共同形成了一套丰富的案例研究，用于开发天文学问题的统计方法，从新的理论基础到创新的建模策略和高效的计算技术。因此，这项研究将影响统计学和天文学领域：激发统计学家的更多兴趣和新问题，并解决天文学中长期存在的问题。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。

Statistical theory and methods play a fundamental role in scientific discovery and advancement, including in modern astronomy, where data are collected on increasingly massive scales and with more varieties and complexity. New technology and instrumentation are spawning a diverse array of emerging data types and data analytic challenges, which in turn require and inspire ever more innovative statistical methods and theories. This research is guided by the dual aims of advancing statistical foundations and frontiers, motivated by astronomical problems and providing principled data analytic solutions to challenges in astronomy. The CHASC (California-Harvard Astrostatistics Collaboration) International Center has an extensive track record in accomplishing both tasks. This research leverages CHASC’s track record to make progress in several new projects. Fitting sophisticated astrophysical models to complex data that were collected with high-tech instruments, for example, often involves a sequence of statistical analyses. Several projects center on developing new statistical methods that properly account for errors and carry uncertainty forward within such sequences of analyses. Additional work will focus on developing theoretical properties of novel statistical estimation procedures to address data-analytic challenges associated with solar flares and X-ray observations. Other projects involve fast and automatic detection of astronomical objects such as galaxies from 2D or even 4D data. The PIs will develop statistical theory and methods in the context of these projects, building statistical foundations and pushing the frontiers of statistics forward for broad impact that will extend well beyond astrostatistics. The PIs plan to offer effective methods and algorithms for tackling emerging challenges in astronomy, with the aspiration of promoting such principled data-analytic methods among researchers in astronomy. Its provision of free software via the CHASC GitHub Software Library will enable the distribution and impact of the proposed methods and algorithms. The projects reflect three broad themes: (1) Exploring fundamental statistical theory with immediate impact in astronomy, including a general approach for obtaining confidence regions by leveraging the pivot-property of maximal product spacing, which is then applied to assess the power law of solar flares, and a statistically principled correction to the use of the popular C-stat in astrophysics; (2) Assessing the misspecification of models and prior distributions in multi-stage statistical analyses, and post processing posterior draws to correct for defects in prior modeling when redoing a Bayesian analysis is impractical; and (3) Identifying breakpoints in complex models, which includes a fast algorithm for identifying astronomical boundaries and identifying breakpoints in joint spatial, spectral, temporal models. Theme 1 is more theory driven, while Themes 2 and 3 are more methods and computation driven. Together they form a rich suite of case studies for developing statistical methods for astronomical problems, ranging from new theoretical foundations to innovative modeling strategies and to efficient computational techniques. Consequently, the research will impact both the fields of statistics and astronomy: spurring more interest and new problems for statisticians and resolving long standing problems in astronomy.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.