Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it is difficult to infer high-dimensional problems, especially when multiple modes exist. This paper introduces an efficient Bayesian posterior sampling algorithm that draws inspiration from subset simulation (SuS). It is based on a new interpretation of evidence from the perspective of structural reliability estimation, regarding the likelihood function as a limit state function. The posterior samples can be obtained following the principle of importance resampling as a postprocessing procedure. The estimation variance is derived to quantify the inherent uncertainty associated with the SuS estimator of evidence. The effective sample size is introduced to measure the quality of the posterior sampling. Three benchmark examples are first considered to illustrate the performance of the proposed algorithm by comparing it with two state-of-art algorithms. It is then used for the finite element (FE) model updating, showing its applicability in practical engineering problems. The proposed SuS algorithm exhibits comparable or even better performance in evidence estimation and posterior sampling, compared to the aBUS and MULTINEST algorithms, especially when the dimension of unknown parameters is high. In the application of the proposed algorithm for FE model updating, satisfactory results are obtained when the configuration (number and location) of sensory system is proper, underscoring the importance of adequate sensor placement around critical degrees of freedom.

翻译：贝叶斯分析在给定数据和模型条件下估计未知参数分布方面具有关键作用。由于维度灾难，高维问题的推断尤为困难，当存在多模态时更是如此。本文提出一种高效的贝叶斯后验采样算法，其灵感来源于子集模拟（SuS）。该算法基于从结构可靠性估计视角对证据的新解释，将似然函数视为极限状态函数。后验样本可通过重要性重采样原则作为后处理步骤获得。推导了估计方差以量化SuS证据估计器固有的不确定性。引入有效样本量来衡量后验采样的质量。首先通过三个基准算例，与两种先进算法比较以说明所提算法的性能。随后将其应用于有限元（FE）模型修正，展示其在实际工程问题中的适用性。与aBUS和MULTINEST算法相比，所提出的SuS算法在证据估计和后验采样方面表现出相当甚至更优的性能，特别是在未知参数维度较高时。在有限元模型修正的应用中，当传感系统配置（数量与位置）适当时可获得满意结果，这凸显了在关键自由度周围合理布置传感器的重要性。