Collaborative Research: Highly Principled Data Science for Multi-Domain Astronomical Measurements and Analysis

在人类探索的每一个可以想象的领域，特别是在天文学和天体物理学等高度依赖观测的领域，大量的数据资源正在上线。为了从这些数据中提取最多的信息，科学家和统计学家需要通过使用科学证明、统计原则和计算效率高的方法来进行高度原则的数据科学。该项目概述了实现这一目标的计划，同时解决了天文数据中涉及空间、时间和能源的四个具体挑战。提出的研究具有天文学中更可靠的统计方法和新的一般统计推断和计算方法的双重影响。除了提供方法和免费软件外，研究人员还计划通过研讨会和会议会议向天文学界宣传有原则的统计方法的好处。提出的研究的一个基本影响是天文学家更普遍地接受和使用有原则的方法。科学现象的有效建模、科学驱动的分类和聚类以及统计计算的一般方法也可以帮助解决整个自然科学、社会科学、医学和工程科学的复杂数据挑战。天基和地面仪器的惊人进步不断提高了天文学家可用数据的质量和数量。观测是在电磁波谱上进行的，并汇编成高分辨率但异构的光谱仪，成像和时间序列数据的巨大目录。该研究旨在利用这种多域天文测量来更好地了解天文单个源、星团乃至整个宇宙的物理环境、结构和演化。有四个主要项目。(1) pi将开发方法来解决仪器校准问题，这是天体物理学中的一个基本挑战，通过将科学动机的统计模型拟合到多个仪器观测到的多个天体的数据中。(2) pi提出了一种统计和计算效率高的算法来检测在天文学各个领域普遍存在的具有深远意义的幂律分布的边界。(3) pi将通过事后分析将用于检测点源的图像处理算法扩展到复杂的扩展多尺度结构，从而提高了计算效率。(4)针对结构复杂的天文图像，pi提出探索区分重叠点源的图像分割方法；该算法实现了通量守恒特性，这对于给出现有方法所缺乏的有物理意义的估计至关重要。这些项目在开发有效的统计方法、设计快速计算算法以及平衡复杂性和实用性之间的微妙权衡方面都涉及重大挑战。凭借其广泛而成功的记录，pi将通过在涉及多尺度结构和/或多层潜在变量的高度结构化模型下开发推理和有效的计算方法来解决这些挑战。拟议研究的中心主题是在其四个项目中的每个项目中整合和追求三个理想：科学论证，统计原理和计算效率。这三个目标推动了专门设计的方法的发展，这些方法利用了计算效率和统计原则数据驱动技术，明确地结合了对天文来源的科学理解。这确保了统计分析提高了科学家回答有关潜在天文和物理过程的具体问题的能力。这一策略需要最先进的统计推断、复杂的科学计算和仔细的模型检查程序，所有这些都是该研究小组工作的标志。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。

Massive data resources are coming online in every conceivable area of human exploration, and particularly in fields that are heavily observation-based such as astronomy and astrophysics. To extract the most information from these data, scientists and statisticians need to conduct highly principled data science, by using methods that are scientifically justified, statistically principled, and computationally efficient. This project outlines plans to achieve this goal while addressing four specific challenges in astronomical data involving space, time and energy. The proposed research has the dual impact of more reliable statistical methods in astronomy and of new general statistical inference and computational methods. In addition to providing methods and free software, the investigators also plan to communicate to the astronomical community the benefit of principled statistical methods through workshops and sessions at conferences. A fundamental impact of the proposed research is the more general acceptance and use of principled methods among astronomers. The general methods for efficient modeling of scientific phenomena, science-driven classification and clustering, and for statistical computing, can also help to solve complex data challenges throughout the natural, social, medical, and engineering sciences.Striking advances in both space-based and terrestrial instrumentation continuously increase the quality and quantity of data available to astronomers. Observations are made across the electromagnetic spectrum and compiled into enormous catalogs of high-resolution, but heterogeneous spectrograph, imaging, and time series data. The proposed research aims to use such multi-domain astronomical measurements to better understand the physical environment, structure, and evolution of astronomical individual sources, clusters, and ultimately of the entire universe. There are four major projects. (1) The PIs will develop methodology to solve the instrument calibration problem, which is a fundamental challenge in astrophysics, by fitting scientifically motivated statistical models to data from multiple astronomical objects observed by multiple instruments. (2) The PIs propose a statistically and computationally efficient algorithm to detect the boundaries of a power law distribution prevalent in various areas of astronomy and of far-reaching importance. (3) The PIs will extend image-processing algorithms designed for detecting point sources to complex extended multi-scale structures via a post-hoc analysis, which makes the computation efficient. (4) With astronomical images exhibiting complex structure, the PIs propose to explore image segmentation methods to distinguish overlapping point sources; the algorithm achieves the flux-conserving property, which is crucial for giving physically meaningful estimates that existing methods lack. These projects all involve significant challenges in developing efficient statistical methods, designing fast computational algorithms, and balancing subtle trade-offs between complexity and practicality. With their extensive and successful track record, the PIs will address these challenges by developing inferential and efficient computational methods under highly-structured models that involve multi-scale structure and/or multiple levels of latent variables. The central theme of the proposed research is the integration and pursuit of three desiderata in each of its four projects: scientific justification, statistical principles, and computational efficiency. This triple-goal advances the development of specifically designed methods that leverage computationally efficient and statistically principled data-driven techniques which explicitly incorporate scientific understanding of the astronomical sources. This ensures that the statistical analyses enhance the scientists' ability to answer specific questions about the underlying astronomical and physical processes. This strategy requires state-of-the-art statistical inference, sophisticated scientific computing, and careful model-checking procedures, all of which have been the hallmark of the work by this team of investigators.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.