2022/11/17 by Jianpeng Chan, Chan, Jianpeng, Iason Papaioannou +3 · 1 citation
Decision Sciences · Environmental Science · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #Hydrology and Drought Analysis #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.2211.09542
openalex publication_date 2022/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a modification of the improved cross entropy (iCE) method to enhance its performance for network reliability assessment. The iCE method performs a transition from the nominal density to the optimal importance sampling (IS) density via a parametric distribution model whose cross entropy with the optimal IS is minimized. The efficiency and accuracy of the iCE method are largely influenced by the choice of the parametric model. In the context of reliability of systems with independent multi-state components, the obvious choice of the parametric family is the categorical distribution. When updating this distribution model with standard iCE, the probability assigned to a certain category often converges to 0 due to lack of occurrence of samples from this category during the adaptive sampling process, resulting in a poor IS estima tor with a strong negative bias. To circumvent this issue, we propose an algorithm termed Bayesian improved cross entropy method (BiCE). Thereby, the posterior predictive distribution is employed to update the parametric model instead of the weighted maximum likelihood estimation approach employed in the original iCE method. A set of numerical examples illustrate the efficiency and accuracy of the proposed method.