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首页> 外文期刊>ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B. Mechanical Engineering >Sensitivity Analysis of a Bayesian Network
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Sensitivity Analysis of a Bayesian Network

机译：贝叶斯网络的敏感性分析

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摘要

In a Bayesian network (BN), how a node of interest is affected by the observation at another node is a main concern, especially in backward inference. This challenge necessitates the proposed global sensitivity analysis (GSA) for BN, which calculates the Sobol’ sensitivity index to quantify the contribution of an observation node toward the uncertainty of the node of interest. In backward inference, a low sensitivity index indicates that the observation cannot reduce the uncertainty of the node of interest, so that a more appropriate observation node providing higher sensitivity index should be measured. This GSA for BN confronts two challenges. First, the computation of the Sobol’ index requires a deterministic function while the BN is a stochastic model. This paper uses an auxiliary variable method to convert the path between two nodes in the BN to a deterministic function, thus making the Sobol’ index computation feasible. Second, the computation of the Sobol’ index can be expensive, especially if the model inputs are correlated, which is common in a BN. This paper uses an efficient algorithm proposed by the authors to directly estimate the Sobol’ index from input–output samples of the prior distribution of the BN, thus making the proposed GSA for BN computationally affordable. This paper also extends this algorithm so that the uncertainty reduction of the node of interest at given observation value can be estimated. This estimate purely uses the prior distribution samples, thus providing quantitative guidance for effective observation and updating.
机译：在贝叶斯网络（BN）中，感兴趣的节点如何受到另一个节点的观察的影响是主要问题，特别是在后向推理中。该挑战需要为BN提供所提出的全局敏感性分析（GSA），其计算Sobol'敏感性指数，以量化观察节点对感兴趣节点的不确定性的贡献。在后向推理中，低灵敏度指数表明观察不能降低感兴趣的节点的不确定性，从而应测量提供更高灵敏度指数的更合适的观察节点。这个GN的GN面对两个挑战。首先，Sobol“索引的计算需要确定性函数，而BN是随机模型。本文使用辅助变量方法将BN中的两个节点之间的路径转换为确定性函数，从而使Sobol的索引计算可行。其次，Sobol“索引的计算可能是昂贵的，特别是如果模型输入相关，则在BN中常见。本文采用作者提出的高效算法直接从BN的先前分配的输入 - 输出样本中直接估计Sobol'指数，从而使所提出的GSA用于计算地计算得起的BN。本文还扩展了该算法，使得可以估计在给定观察值时感兴趣的节点的不确定性降低。这种估计纯粹使用了现有的分发样本，从而提供了有效观察和更新的定量指导。

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