Bayesian improved cross entropy method for network reliability assessment

We identify the zero count problem (or overfitting) of cross-entropy-based methods in the context of network reliability assessment, and propose a consistent Bayesian estimator that mitigates this issue. Thereby, we derive the posterior predictive distribution of importance sampling distribution parameters that replaces the weighted maximum likelihood estimation employed in the standard cross entropy optimization. For rare event estimation, we embed the Bayesian estimator into the improved cross entropy (iCE) method and provide theoretical insights into the adaptive selection of intermediate target distributions in the iCE. The modified version of the iCE, termed the Bayesian iCE (BiCE), is proved to be unbiased. By contrast, even with higher computational cost, the standard iCE method is often significantly biased when solving network reliability problems. Our numerical investigations indicate that a uniform prior in the proposed BiCE method performs suboptimally, and an informative symmetric Dirichlet prior is suggested.