From Likelihood to Limit State: A Reliability-Inspired Framework for Bayesian Evidence Estimation and High-dimensional Sampling

TL;DR

This paper presents a novel Bayesian sampling method that interprets evidence as a failure probability, enabling efficient high-dimensional posterior estimation using subset simulation, with demonstrated advantages over existing algorithms.

Contribution

It introduces a reliability-inspired framework for Bayesian evidence estimation and high-dimensional sampling, leveraging subset simulation and importance resampling.

Findings

Comparable or better evidence estimation performance than state-of-the-art methods

Effective in high-dimensional parameter spaces

Applicable to practical engineering problems like finite element model updating

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 becomes difficult for high-dimensional problems, especially when multiple modes exist. This paper introduces an efficient Bayesian posterior sampling algorithm, based on a new interpretation of evidence from the perspective of structural reliability estimation. That is, the evidence can be equivalently formulated as an integration of failure probabilities, by regarding the likelihood function as a limit state function. The evidence is then evaluated with subset simulation (SuS) algorithm. 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 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 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.