Advances in Bayesian Model Selection under Misspecification

Model selection, selecting one or more statistical models from a collection of candidate models in a data-driven way, is a fundamental problem in statistics with widespread applications in multiple disciplines of science, engineering, and finance, among others. Bayesian methods have been immensely popular as a default tool for model selection because of their intrinsic penalty for model complexity and their ability to seamlessly integrate into high-dimensional settings where the number of candidate models can far exceed the size of the available data. Through this project, the investigator will develop new methodological tools with accompanying theory for robust Bayesian model selection with applications to dependent data settings commonly encountered in practice. These are closely related to machine learning and artificial intelligence. Research findings will be shared through publications and presentations in leading venues.  Additionally, open-source software for the implementation of the methods developed will be made publicly available. The investigator is also committed to strengthening the project's educational impact by mentoring students and developing specialized graduate and undergraduate courses at the institution. This project will provide a rigorous theoretical foundation for Bayesian model selection under misspecification, coupled with scalable computational tools tailored for high-dimensional applications. Bayesian methods are inherently model-based and, hence, susceptible to model misspecification. Since generative models are understood to provide only an approximate description of reality, the impact of departures from the modeling assumptions is an important point of consideration, especially in modern complex applications where computational feasibility is also a guiding factor in dictating model choice. This project will systematically study the impact of model misspecification on Bayesian model selection performance and develop robust, efficient methods that continue to perform well even when some modeling assumptions are violated. Applications will span variable selection, graph selection, and structure learning problems, including settings with non-Gaussian or dependent data where current theory and methodology are comparatively underdeveloped. 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. NSF Award ID: 2610612 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Anirban Bhattacharya | Institution: Texas A&M University, COLLEGE STATION, TX | Award Amount: $268,210 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2610612 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2610612.html