12:30–1:30 pm Searle 240A
CAM & Stats Student Seminar
Tuesday, January 23, 2024, at 12:30 PM, in Searle 240A (location change this quarter), 5735 South Ellis Avenue
Nathan Waniorek, Committee on Computational and Applied Mathematics (CCAM), The University of Chicago
"Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint"
Abstract
In this talk we will analyze hierarchical Bayesian inverse problems using techniques from high dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings.