Collaborative Research: New MCMC-Enabled Bayesian Methods for Complex Data and Computer Models Applied in Astronomy

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。加利福尼亚-波士顿天文统计合作正在开发一种新的基于模型的统计推断策略，将计算机模型嵌入到多层次模型中，明确说明天文来源和新高科技望远镜固有的数据生成机制的复杂性。必须充分利用由此产生的高度结构化的模型，以了解基本的天文和物理过程。这种策略需要最先进的科学计算，先进的统计推断方法和仔细的模型检查程序。该协作组织有使用这些方法解决天文学中突出的数据分析问题的记录。此外，PI（货车戴克，孟和余）在开发合作将扩展，使用和宣传的方法方面具有丰富的研究经验：在涉及多层次潜变量和不完整数据的高度结构化模型下的推理和有效的计算方法。这种模型非常适合于解释高能天体物理学中数据生成机制的许多物理和仪器过滤器。这五位天文学家（Chiang，Connors，Kashyap，Kelly和Siemiginowska）都拥有高能和/或光学天文学仪器和科学方面的专业知识，并且都与统计学家合作，努力开发适当的方法来解决科学问题。该合作的具体目标是开发一种参数化和灵活的多尺度模型的混合物，这些模型可以与复杂的计算机模型相结合，以描述光谱，空间和时序数据，无论是边缘还是联合。这些模型是在一个完全贝叶斯框架中开发的，该框架使我们能够结合外部信息，提供一致的不确定性估计，并校准拟议的基础物理模型的统计比较。这些方法要求协作组开发新的复杂的统计计算技术，用于对复杂的、往往是多模态的后验分布进行蒙特卡罗探索。新发射的或即将发射的天基望远镜是针对与具体科学目标有关的数据收集挑战而设计的。这些仪器提供了大量的新调查，产生了包含TB数据的新目录，高分辨率光谱和电磁频谱成像，以及太阳大气中动态和爆炸过程的令人难以置信的详细电影。一系列新仪器正在帮助科学家们在我们对物理宇宙的理解方面取得令人印象深刻的进步，但同时也为研究所产生数据的科学家们带来了大量的数据分析挑战。仪器的复杂性，天文学来源的复杂性，以及科学问题的复杂性导致了许多微妙的推理问题，需要复杂的统计工具。例如，数据部分缺失，受到不同的测量误差的影响，并且被不相关的伪影污染。科学家们希望得出的结论，如物理环境和结构的来源，过程和法律的诞生和死亡的行星，恒星和星系，并最终结构和演变的宇宙。复杂的基于天体物理学的计算机模型与复杂的数学模型一起使用沿着，以预测从天文来源和来源群体观察到的数据。加州-波士顿天文统计合作旨在通过建立使用最先进的统计，天文和计算机模型分析复杂数据的框架来解决天体物理学中产生的突出统计问题。在这样做的合作将不仅开发新的方法，天文学，但也将使用这些问题作为一个跳板，在新的一般统计方法的发展，特别是在信号处理，多级建模，计算机建模和计算统计。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The California-Boston AstroStatistics Collaboration is developing a new model-based strategy for statistical inference that embeds computer models into multilevel models that explicitly account for complexities of both astronomical sources and the data generation mechanisms inherent in new high-tech telescopes. The resulting highly structured models must be fully utilized in order to learn about the underlying astronomical and physical processes. This strategy requires state-of-the-art scientific computation, advanced methods for statistical inference, and careful model checking procedures. The Collaboration has a track record using these methods to solve outstanding data-analytic problems in astronomy. In addition, the PIs (van Dyk, Meng, and Yu) have substantial research experience in developing the methods that the Collaboration will extend, employ, and publicize: inferential and efficient computational methods under highly-structured models that involve 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 mechanism in high-energy astrophysics. The five astronomers (Chiang, Connors, Kashyap, Kelly, and Siemiginowska) all have expertise on the instrumentation and science of high-energy and/or optical astronomy, and, all have collaborated with statisticians in efforts to develop appropriate methods to address scientific questions. 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. The models are developed in a fully Bayesian framework that allows us to incorporate external information, provide coherent estimates of uncertainty, and calibrate statistical comparisons of proposed underlying physical models. These methods require the Collaboration to develop new sophisticated statistical computing techniques for Monte Carlo exploration of complex and often multi-modal posterior distributions.In recent years, technological advances have dramatically increased the quality and quantity of data available to astronomers. Newly launched or soon-to-be launched space-based telescopes are tailored to data-collection challenges associated with specific scientific goals. These instruments provide massive new surveys resulting in new catalogs containing terabytes of data, high resolution spectrography and imaging across the electromagnetic spectrum, and incredibly detailed movies of dynamic and explosive processes in the solar atmosphere. The spectrum of new instruments is helping scientists make impressive strides in our understanding of the physical universe, but at the same time generating massive data analysis challenges for scientists who study the resulting data. The complexity of the instruments, the complexity of the astronomical sources, and the complexity of the scientific questions leads to many subtle inference problem that require sophisticated statistical tools. For example, data are partially missing, are subject to varying measurement errors, and are contaminated with irrelevant artifacts. Scientists wish to draw conclusions as to the physical environment and structure of the 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. Sophisticated astrophysics-based computer-models are used along with complex mathematical models to predict the data observed from astronomical sources and populations of sources. The California-Boston AstroStatistics Collaboration aims to tackle outstanding statistical problems generated in astrophysics by establishing frameworks for the analysis of complex data using state-of-the-art statistical, astronomical, and computer models. In so doing the Collaboration will not only develop new methods for astronomy but will also use these problems as a spring board in the development of new general statistical methods, especially in signal processing, multilevel modeling, computer modeling, and computational statistics.