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

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.