Subset Simulation for High-dimensional and Multi-modal Bayesian Inference

Abstract: 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.