改进贝叶斯共轭梯度法的不确定性校准，提升可信度。
Randomised Postiterations for Calibrated BayesCG
- 引入随机后迭代策略优化后验校准
- 理论证明后验误差分布更可靠
- 适合需要精准不确定量化场景
贝叶斯共轭梯度法（BayesCG）可为线性系统提供概率解，但存在校准不足问题，限制了其在不确定性量化中的应用。近期通过后迭代构建先验的方法虽改善了计算性能，却未能解决校准缺陷。本文提出一种新型随机化后迭代策略，在保持良好收敛性的同时显著提升贝叶斯后验的校准能力。理论分析给出了校准改进的保证，并基于后验误差分布结果验证。数值实验在合成数据与反问题场景中均表明，该方法有效增强了不确定性量化效果，提升了计算流程中不确定性的传播可靠性。
原文摘要 · Abstract (English)
The Bayesian conjugate gradient method offers probabilistic solutions to linear systems but suffers from poor calibration, limiting its utility in uncertainty quantification tasks. Recent approaches leveraging postiterations to construct priors have improved computational properties but failed to correct calibration issues. In this work, we propose a novel randomised postiteration strategy that enhances the calibration of the BayesCG posterior while preserving its favourable convergence characteristics. We present theoretical guarantees for the improved calibration, supported by results on the distribution of posterior errors. Numerical experiments demonstrate the efficacy of the method in both synthetic and inverse problem settings, showing enhanced uncertainty quantification and better propagation of uncertainties through computational pipelines.
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