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.

层次回归已成为统计和数据科学中普遍存在的工具。在流行病学，政治学，基因组学等领域的社会和自然科学研究人员的应用研究人员依赖于层次回归是其数据分析工具箱的基本要素。但是，在层次回归的实际和宽度使用方面仍然存在主要障碍。主要限制是计算 - 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。通过该研究项目，研究人员旨在为应用统计学家和数据科学家的社区提供一系列工具，以开放更有效的用户友好型统计建模。该项目为学生提供了研究培训机会。研究人员将专注于开发定制的计算和分析工具，用于层次建模的统计推断。用于推理的流行工具，例如MCMC和变异方法，很少利用模型中的友好分析结构，它们通常依赖于对目标密度及其梯度的许多评估。在该项目中，研究人员将探索后密度的分析和数值特性，并通过构建自定义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，以及用于部分微分方程的数值解决方案的快速算法的工具。该奖项反映了NSF的法定任务，并被认为是通过使用基金会的知识分子优点和更广泛影响的审查标准来通过评估来通过评估来支持的。