An evolutionary nested sampling algorithm for Bayesian model updating and model selection using modal measurement

Abstract

Nested sampling (NS) is a highly efficient and easily implemented sampling algorithm that has been successfully incorporated into Bayesian inference for model updating and model selection. The key step of this algorithm lies in proposing a new sample in each step that has a higher likelihood to replace the sample that has the lowest likelihood evaluated in the previous iteration. This process, also regarded as a constrained sampling step, has significant impact on the algorithm efficiency. This paper presents an evolutionary nested sampling (ENS) algorithm to promote the proposal of effective samples for Bayesian model updating and model selection by introducing evolutionary operators into standard NS. Instead of randomly drawing new samples from prior space, ENS algorithm proposes new samples from previously evaluated samples in light of their likelihood values without any evaluation of gradient. The main contribution of the presented algorithm is to greatly improve the sampling speed in the constrained sampling step by use of previous samples. The performances of the proposed ENS algorithm for model updating and model selection are examined through two numerical examples.