New Probabilistic Methods for Observational Cosmology

未来的天文测量将产生如此海量的数据，新的分析方法变得势在必行。特别是当大量信息必须被提炼成理论见解，而个别项目本身实际上不太确定时，基于概率的方法提供了令人印象深刻的优势。该项目将生成工具包，以实施这种新的方法，从压倒性的大型数据集中提取知识。由于有可能改变宇宙学和其他面临数据淹没威胁的领域的科学研究方式，这项工作的影响怎么估计都不为过。这些方法将使用并传播与应用数学的合作，使这一不可能成为可能。新的宇宙学调查将需要使用更多的星系来测量更小的信号，这些星系是以较低的置信度单独观测的。这将需要尽可能保留信息的数据分析。这个项目将为宇宙学数据分析创造新的方法，允许使用不损失的衍生数据产品进行推断，例如星系星表、最佳拟合红移或相关函数点估计，而是更接近原始成像和光谱数据的东西。这些技术将以概率推理和应用数学技术的原理为基础。这项工作创建了三个相关的工具集。工具集1用于重建和边缘化宇宙密度场，可以是质量、星系或中性气体密度场，也可以是二维投影质量密度。工具集2用于宇宙学推断，它适当利用了关于星系和类星体红移的概率信息，改进了概率红移信息，并提供了丢失红移的信息性推算，从而为较小规模的科学问题产生了预测和工具。工具集3用于传播概率图像级别的量，如星系形状和点扩散函数，以用于大尺度结构的弱透镜研究。这将允许根据观测数据对星系形状进行有条件的先验推断，并将其用于合理的切变场和宇宙学参数的正演模拟测量。该项目的工具包将是用于宇宙学推断和大规模结构测量的第一个实用方法，可以充分和适当地、合理地使用概率输出。这将是第一次有可能同时进行星系级性质的推断或改进，以及大规模的结构和宇宙学推断。同时推断将显著减少宇宙学测量中的统计偏差，并减少星表级别数量的差异。工具包将是论文和方法，但也是开放源码基础，具有宇宙学以外的好处。这些进展将有助于制定产生和交付概率产出的标准。这项研究将通过撰写关于物理科学中的推理、数据分析和计算统计的教学论文，接触到学术界内外的人群。

Future astronomical surveys will be producing such enormous quantities of data that new analysis methods are becoming imperative. Especially when large quantities of information must be distilled into theoretical insights, and the individual items are themselves actually of less certainty, a probability-based approach offers impressive advantages. This project will generate toolkits to implement such novel approaches to the extraction of knowledge from overwhelmingly large data sets. With the potential to transform the way science is done both in cosmology and in other areas under threat of being swamped with data, the impact of this work cannot be overestimated. The methods will both use and propagate collaborations with applied mathematics that make the impossible possible.New cosmological surveys will require measurement of smaller signals using larger numbers of galaxies which are individually observed at lower confidence. This will require data analyses that are as information-preserving as possible. This project will create new methods for cosmological data analysis that permit inferences using not lossy, derived data products, such as galaxy catalogs, best-fit redshifts, or correlation function point estimates, but something much closer to the original imaging and spectroscopic data. These techniques will be informed by the principles of probabilistic inference and applied-mathematics technology. The work creates three related toolsets. Toolset 1 is for reconstruction and marginalization of cosmological density fields, which could be the mass, galaxy, or neutral-gas density field, or the two-dimensional projected mass density. Toolset 2 is for cosmological inference that makes proper use of probabilistic information about galaxy and quasar redshifts, improving probabilistic redshift information, and providing informative imputation of missing redshifts, thereby producing predictions and tools for smaller-scale scientific questions. Toolset 3 is for propagation of probabilistic image-level quantities such as galaxy shapes and the point-spread function, into weak-lensing studies of large-scale structure. This will permit inference from survey data conditional priors over galaxy shapes, and use them in a justified forward-modeling measurement of the shear field and cosmological parameters. The toolsets from this project will be the first practical methods for cosmological inference and large-scale structure measurement that can make full and proper, justified, use of probabilistic outputs. For the first time, it will be possible to perform simultaneous inference or refinement of catalog-level properties along with large-scale structure and cosmological inferences. Simultaneous inference will significantly reduce statistical biases in cosmological measurements, and also reduce variance in catalog-level quantities.The toolsets will be papers and methods but also open-source codebases, with benefits beyond cosmology. These developments will help create standards for generating and delivering probabilistic outputs. The research will reach populations inside and outside academia by producing pedagogical papers on inference, data analysis, and computational statistics in the physical sciences.