面向高维贝叶斯推断的序贯多重重要性采样
Sequential multiple importance sampling for high-dimensional Bayesian inference
AI总结：
本文提出序贯多重重要性采样（SeMIS）算法，通过软截断先验作为中间提议分布连接先验与后验，在高维贝叶斯推断中实现了更优的证据估计与后验采样，并在有限元模型更新中成功定位结构损伤。
摘要：
本文提出了一种用于高维贝叶斯推断的序贯多重重要性采样（SeMIS）算法。该方法利用每个提议分布生成的所有样本来估计贝叶斯证据，同时通过重要性重采样方案获得后验样本。SeMIS的一个关键创新是使用软截断先验分布作为中间提议分布，为连接先验分布与后验分布提供了一种新途径。通过使来自高似然区域的样本能够穿越低概率区域，SeMIS增强了具有挑战性的推断问题中的模式混合能力。与子集模拟（SuS）和基于结构可靠性方法的自适应贝叶斯更新（aBUS）的对比评估表明，SeMIS在证据估计（更低的偏差和方差）和后验采样（更高的有效样本量以及更接近真实后验的近似）方面均取得了优越的性能，尤其对于多峰分布。SeMIS的有效性进一步在一个高维有限元模型更新应用中得到了验证，在该应用中它通过量化刚度损失成功定位了结构损伤。所提出的算法不仅推进了面向复杂后验分布的贝叶斯计算，而且为土木工程系统中的不确定性量化提供了一种稳健的工具，为概率结构健康监测提供了新的可能性。
英文摘要：
This paper introduces a sequential multiple importance sampling (SeMIS) algorithm for high-dimensional Bayesian inference. The method estimates Bayesian evidence using all generated samples from each proposal distribution while obtaining posterior samples through an importance-resampling scheme. A key innovation of SeMIS is the use of a softly truncated prior distribution as the intermediate proposal, providing a new way bridging prior and posterior distributions. By enabling samples from high-likelihood regions to traverse low-probability zones, SeMIS enhances mode mixing in challenging inference problems. Comparative evaluations against subset simulation (SuS) and adaptive Bayesian updating with structural reliability methods (aBUS) demonstrate that SeMIS achieves superior performance in evidence estimation (lower bias and variance) and posterior sampling (higher effective sample sizes and closer approximation to the true posterior), particularly for multimodal distributions. The efficacy of SeMIS is further validated in a high-dimensional finite element model updating application, where it successfully localizes structural damages by quantifying stiffness loss. The proposed algorithm not only advances Bayesian computation for complex posterior distributions but also provides a robust tool for uncertainty quantification in civil engineering systems, offering new possibilities for probabilistic structural health monitoring.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
