2022/09/26 by Jasper Marijn Everink, Yiqiu Dong, Everink, Jasper Marijn +3 · 1 citation
Computer Science · #62F15 #65C05 #90C25 #Bayesian Methods and Mixture Models #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Geochemistry and Geologic Mapping #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2209.12481
openalex publication_date 2022/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a constrained prior such that the posterior assigns positive probability to the boundary of the constraint set. We show that by projecting posterior mass onto the constraint set, we obtain a new posterior with a rich probabilistic structure on the boundary of that set. If the original posterior is a Gaussian, then such a projection can be done efficiently. We apply the method to Bayesian linear inverse problems, in which case samples can be obtained by repeatedly solving constrained least squares problems, similar to a MAP estimate, but with perturbations in the data. When combined into a Bayesian hierarchical model and the constraint set is a polyhedral cone, we can derive a Gibbs sampler to efficiently sample from the hierarchical model. To show the effect of projecting the posterior, we applied the method to deblurring and computed tomography examples.