Collaborative Research: Advanced Statistical Methods and Computation for Emerging Challenges in Astrophysics and Astronomy

加州-波士顿天体统计学合作正在为天文学和天体物理学的统计推断开发基于模型的策略。他们专门设计了高度结构化的模型，以说明来源和数据生成机制中的特殊复杂性，目的是回答有关基本天文和物理过程的具体科学问题。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。他们将在涉及多尺度结构和/或多层次潜在变量和不完整数据的高度结构化模型下，使用、推广和宣传推理和高效的计算方法。这样的模型非常适合于解释天体物理学中数据生成机制的许多物理和仪器过滤器。这项合作的具体目的是开发一种混合的参数化和灵活的多尺度模型，可以与复杂的计算机模型相结合，以边缘或联合的方式描述光谱、空间和时间数据。例如，在天文学中，对来自相同观测但不同区域(图像、光谱和时间序列)的数据的分析通常是分开进行的。这简化了分析，但牺牲了信息，例如光谱如何随时间或跨图像变化。该合作提出了多体制数据的连贯方法，包括联合使用高通量空间光谱数据来分离和识别复杂的太阳特征，以及分析来自恒星日冕的光谱的系统时间变化。他们还建议将复杂的计算机模型嵌入高度结构化的模型中，这一战略允许将多个计算机模型与基于物理的参数和(或)灵活的多尺度模型结合起来，以得出综合方法，解决天文来源和仪器的复杂性。构建这种高度结构化的模型需要在复杂性和实用性之间进行微妙的权衡，并对它们进行拟合，这带来了巨大的计算挑战。这项提议包括一系列旨在生产高效定制蒙特卡罗方法的研究项目。过去十年来，天基仪器的巨大进步导致了具有前所未有能力的新一代望远镜的部署。这类仪器通常是为满足特定的科学目标而量身定做的，并正在提高天文学家可获得的数据的质量和数量。大规模的新调查正在产生大量新的星表，其中包含数兆字节的数据，包括电磁光谱的高分辨率光谱学、成像和时间序列，以及太阳大气中爆炸性动态过程的超高分辨率成像。科学家们希望得出关于天文起源的物理环境和结构、支配行星、恒星和星系的诞生和死亡的过程和规律，以及最终宇宙的结构和演化的结论。这种复杂仪器和复杂科学的结合给天文学家带来了海量数据分析和数据挖掘的挑战。加州-波士顿天体统计合作计划使用源自精心设计的天文和数学模型的原则性统计方法来应对这些挑战。随着合作开发方法和分发自由软件，它还将教育天文学社区，让他们了解复杂的统计方法的好处。预计拟议研究的根本影响将是天文学家更普遍地接受和使用适当的方法。这项合作不仅旨在开发天文学的新方法，而且计划将这些问题作为开发新的通用统计方法的跳板，特别是在信号处理、多水平建模、计算机建模和计算统计方面。合作将利用天文学中提出的统计学挑战作为新的复杂推理和计算技术的试验场，这些技术将有助于解决整个自然、社会、医学和工程科学中的复杂数据分析挑战。

The California-Boston AstroStatistics Collaboration is developing model-based strategies for statistical inference in astronomy and astrophysics. They specifically design highly structured models to account for particular complexities in the sources and data generation mechanisms with the goal of answering specific scientific questions as to the underlying astronomical and physical processes. This strategy requires state-of-the-art statistical inference, sophisticated scientific computing, and careful model-checking procedures. They will employ, extend and publicize inferential and efficient computational methods under highly-structured models that involve multi-scale structure and/or multiple levels of latent variables and incomplete data. Such models are ideally suited to account for the many physical and instrumental filters of the data generation mechanisms in astrophysics. The collaboration specifically aims to develop a mixture of parametrized and flexible multi-scale models that can be combined with complex computer-models to describe spectral, spatial, and timing data, either marginally or jointly. In astronomy, for example, the analyses of data from the same observation, but in different regimes (images, spectra, and time series) are typically conducted separately. This simplifies analysis, but sacrifices information, for example as to how a spectrum varies over time or across an image. The Collaboration proposes to develop coherent methods for multi-regime data including the joint use of high throughput spatio-spectral data to isolate and identify complex solar features and the analysis of systematic temporal variance in spectra from stellar coronae. They also propose to embed complex computer models into highly structured models, a strategy which allows the combination of multiple computer models along with physics-based parametric and/or flexible multi-scale models to derive comprehensive methods that address complexities in both the astronomical sources and the instrumentation. Building such highly structured models requires subtle tradeoffs between complexity and practicality and fitting them poses significant computational challenges. This proposal includes a suite of research projects that aim to produce efficient tailored Monte Carlo methods.Dramatic advances in space-based instrumentation over the past decade have led to the deployment of a new generation of telescopes with unprecedented capabilities. Such instruments are often tailored to meet specific scientific goals and are increasing both the quality and the quantity of data available to astronomers. Massive new surveys are resulting in enormous new catalogs containing terabytes of data, in high resolution spectrography, imaging, and time-series across the electromagnetic spectrum, and in ultra high resolution imaging of explosive dynamic processes in the solar atmosphere. Scientists wish to draw conclusions as to the physical environment and structure of astronomical source, the processes and laws which govern the birth and death of planets, stars, and galaxies, and ultimately the structure and evolution of the universe. This combination of complex instrumentation and complex science leads to massive data analytic and data-mining challenges for astronomers. The California-Boston AstroStatistics Collaboration plans to tackle these challenges using principled statistical methods derived from carefully designed astronomical and mathematical models. As the Collaboration develops methods and distributes free software, it will also educate the astronomical community as to the benefit of sophisticated statistical methods. It is expected that a fundamental impact of the proposed research will be more general acceptance and use of appropriate methods among astronomers. The Collaboration not only aims to develop new methods for astronomy but plans to use these problems as springboards in the development of new general statistical methods, especially in signal processing, multilevel modeling, computer modeling, and computational statistics. The collaboration will use the statistical challenges posed in astronomy as a testing ground for new sophisticated inferential and computational techniques that will help solve complex data analytic challenges throughout the natural, social, medical, and engineering sciences.