We employ the Bayesian improved cross entropy (BiCE) method for rare event estimation in static networks and choose the categorical mixture as the parametric family to capture the dependence among network components. At each iteration of the BiCE method, 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 method results in an efficient and accurate estimator that significantly outperforms the standard iCE method and the BiCE method with the independent categorical distribution.

翻译：本文采用贝叶斯改进交叉熵（BiCE）方法对静态网络中的稀有事件进行估计，并选取分类混合分布作为参数族以捕捉网络组件间的依赖关系。在BiCE方法的每次迭代中，通过加权最大后验（MAP）估计更新混合参数，该估计利用一种新颖的平衡先验缓解了标准改进交叉熵（iCE）方法的过拟合问题，我们提出了广义期望最大化（EM）算法来逼近此加权MAP估计。由此得到的重要性抽样分布被证明是无偏的。为选取混合分布中合适的组分数量$K$，我们通过广义EM算法的副产品计算各候选$K$的贝叶斯信息准则（BIC）。通过简单算例、基准研究及实际应用对所提方法的性能进行了验证。在所有数值实验中，BiCE方法生成的估计量兼具高效性与准确性，其表现显著优于标准iCE方法及采用独立分类分布的BiCE方法。