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Bayesian networks (BNs) have become increasingly popular in recent years due to their wide-ranging applications in modeling uncertain knowledge. An essential problem about discrete BNs is learning conditional probability table (CPT) parameters. If training data are sparse, purely data-driven methods often fail to learn accurate parameters. Then, expert judgments can be introduced to overcome this challenge. Parameter constraints deduced from expert judgments can cause parameter estimates to be consistent with domain knowledge. In addition, Dirichlet priors contain information that helps improve learning accuracy. This paper proposes a constrained Bayesian estimation approach to learn CPTs by incorporating constraints and Dirichlet priors. First, a posterior distribution of BN parameters is developed over a restricted parameter space based on training data and Dirichlet priors. Then, the expectation of the posterior distribution is taken as a parameter estimation. As it is difficult to directly compute the expectation for a continuous distribution with an irregular feasible domain, we apply the Monte Carlo method to approximate it. In the experiments on learning standard BNs, the proposed method outperforms competing methods. It suggests that the proposed method can facilitate solving real-world problems. Additionally, a case study of Wine data demonstrates that the proposed method achieves the highest classification accuracy.

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Initiating explosive device is the key component of weapon system. Its safety performance is directly related to the normal play of weapons, which is determined by design and implemented by production. There is a high demanding for the safety performance of initiating explosive device both in domestic and abroad. Research on the safety response rule of initiating explosive device has important actual significance. In this paper, using logistic sensitivity distribution function model to evaluate the safety response rule of initiating explosive device. Based on VC + + programming, design an analysis software of safety response rule which could draw the responsivity curves to obtain the safety response rule of initiating explosive device. Through the verification of the actual experiment data, evaluation result of the analysis software is effective and in line with the experimental data.