Title: Distance-to-set priors for Bayesian constraint modeling
Authors: Jason Xu - Duke University (United States) [presenting]
Abstract: Distance-to-set penalties provide a flexible way to incorporate a broad range of constraints for tasks cast as an optimization problem, especially as they apply to majorization-minimization (MM) algorithms. However, their use in statistical modeling is largely limited, and few results are available pertaining to inference after obtaining a point estimate. We consider a class of distance-to-set priors to facilitate constrained Bayesian inference. We draw connections between the existing MM and optimization approaches and Bayesian constraint relaxation, and we show that this class of priors has desirable theoretical properties for constrained Bayesian inference. Moreover, we elucidate why distance-to-set priors are particularly amenable to gradient-based sampling algorithms and can succeed in sampling the posterior in situations in which one is limited in the ability to relax the constraints. Finally, we demonstrate our results in various simulated and real-world settings.