Scalable Bayesian regression: Analytical and numerical tools for efficient Bayesian analysis in the large data regime

可扩展贝叶斯回归：在大数据领域进行高效贝叶斯分析的分析和数值工具

• 批准号: 2311354
• 负责人: Andrew Gelman
• 金额: $ 29.99万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2311354&HistoricalAwards=false
• 关键词: Scalable; Bayesian; regression; Analytical; numerical

Hierarchical regression has become a ubiquitous tool in statistics and data science. Applied researchers across the social and natural sciences, in fields such as epidemiology, political science, genomics, and many more, rely on hierarchical regression as an essential element of their data analysis toolbox. However, there are still major obstacles in practical and widespread use of hierarchical regression. The primary limitation is computational—learning from complex models with large amounts of data can require extensive compute time. With this research project, the investigators aim to supply the communities of applied statisticians and data scientists with a range of tools that open up more efficient user-friendly statistical modeling. This project provides research training opportunities for students.The investigators will focus on the development of customized computational and analytical tools for statistical inference for hierarchical modeling. Popular tools for inference such as MCMC and variational methods rarely take advantage of friendly analytical structure in the model and they typically rely on many evaluations of the target density and its gradient. In this project, the investigators will exploit the analytical and numerical properties of the posterior density and capitalize on the oftentimes extensive friendly structure of models by building customized methods. This will involve the use of modern numerical linear algebra, approximation theory, and the tools of fast algorithms for the numerical solution of partial differential equations.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.

分层回归已经成为统计学和数据科学中无处不在的工具。社会科学和自然科学领域的应用研究人员，如流行病学，政治学，基因组学等领域，依赖分层回归作为其数据分析工具箱的基本要素。然而，分层回归的实际和广泛使用仍然存在重大障碍。主要的限制是计算-从具有大量数据的复杂模型中学习可能需要大量的计算时间。通过这个研究项目，研究人员的目标是为应用统计学家和数据科学家提供一系列工具，以开发更有效的用户友好型统计建模。本计画为学生提供研究训练的机会，研究人员将专注于发展客制化的计算与分析工具，以进行阶层式模型的统计推论。流行的推理工具，如MCMC和变分方法很少利用模型中友好的分析结构，它们通常依赖于对目标密度及其梯度的许多评估。在这个项目中，研究人员将利用后验密度的分析和数值特性，并通过构建定制方法来利用模型的广泛友好结构。这将涉及使用现代数值线性代数，近似理论，和偏微分方程的数值解的快速算法的工具。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。