Bayesian improved cross entropy method with categorical mixture models for network reliability assessment
提出贝叶斯改进交叉熵方法BiCE-CM，用分类混合模型捕捉网络组件依赖，通过加权最大后验估计缓解过拟合，并用广义EM算法选择混合成分数，在静态网络稀有事件估计中比标准方法更高效准确。
We employ the Bayesian improved cross entropy (BiCE) method for rare event estimation in static networks and choose the categorical mixture (CM) as the parametric family to capture the dependence among network components. The proposed method is termed BiCE-CM. At each iteration of BiCE-CM, the mixture parameters are updated through the weighted maximum a posteriori (MAP) estimate, which mitigates the overfitting issue of the standard improved cross entropy (iCE) method through a novel balanced prior, and we propose a generalized version of the expectation–maximization (EM) algorithm to approximate this weighted MAP estimate. The resulting importance sampling distribution is proved to be unbiased. For choosing a proper number of components K in the mixture, we compute the Bayesian information criterion (BIC) of each candidate K as a by-product of the generalized EM algorithm. The performance of the proposed method is investigated through a simple illustration, a benchmark study, and a practical application. In all these numerical examples, the BiCE-CM method results in an efficient and accurate estimator that significantly outperforms the standard iCE method and the BiCE method with the independent categorical distribution.