层次贝叶斯反问题：高维统计观点

IF 6.1 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2025-08-07 DOI:10.1137/24m1629328

Daniel Sanz-Alonso, Nathan Waniorek

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引用次数: 0

摘要

SIAM评论，第67卷，第3期，第543-575页，2025年8月。摘要。本文利用高维统计技术分析了层次贝叶斯反问题。我们的分析利用了层次贝叶斯正则化器的一个性质，我们称之为近似可分解性，以获得最大后验估计所获得的重构误差的非渐近界。新理论解释了利用稀疏性、群稀疏性和未知参数的稀疏表示的层次贝叶斯模型如何在高维设置中实现准确的重建。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint

SIAM Review, Volume 67, Issue 3, Page 543-575, August 2025.
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 nonasymptotic 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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来源期刊

SIAM Review 数学-应用数学

CiteScore

16.90

自引率

0.00%

发文量

期刊介绍： Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter. Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.