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arXiv · 2401.03074

Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint

Daniel Sanz-Alonso·Nathan Waniorek
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Abstract

This paper analyzes 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.

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Daniel Sanz-Alonso, Nathan Waniorek. 2024-01-05. Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint. https://arxiv.org/abs/2401.03074

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