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GLOBAL SENSITIVITY ANALYSIS FOR A BAYESIAN NETWORK

机译:贝叶斯网络的全局敏感性分析

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In a Bayesian network, how a node of interest is affected by the observation of another node is of interest in both forward propagation and backward inference. The proposed global sensitivity analysis (GSA) for Bayesian network aims to calculate the Sobol' sensitivity index of a node with respect to the node of interest. The desired GSA for Bayesian network confronts two challenges. First, the computation of the Sobol' index requires a deterministic function while the Bayesian network is a stochastic model. Second, the computation of the Sobol' index can be expensive, especially if the model inputs are correlated, which is common in a Bayesian network.To solve the first challenge, this paper uses the auxiliary variable method to convert the path between two nodes in the Bayesian network to a deterministic function, thus making the Sobol' index computation feasible in a Bayesian network. To solve the second challenge, this paper proposes an efficient algorithm to directly estimate the first-order Sobol' index from Monte Carlo samples of the prior distribution of the Bayesian network, so that the proposed GSA for Bayesian network is computationally affordable. Before the updating, the proposed algorithm can predict the uncertainty reduction of the node of interest purely using the prior distribution samples, thus providing quantitative guidance for effective observation and updating.
机译:在贝叶斯网络中,如何通过对另一个节点的观察来影响感兴趣的节点对前向传播和后向推断感兴趣。贝叶斯网络的拟议全局敏感性分析(GSA)旨在计算关于感兴趣的节点的节点的索波尔'敏感性指标。贝叶斯网络所需的GSA面对两个挑战。首先,Sobol'索引的计算需要确定性函数,而贝叶斯网络是随机模型。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,这在贝叶斯网络中很常见。要解决第一个挑战,本文使用辅助变量方法转换两个节点之间的路径贝叶斯网络到一个确定性函数,从而使Sobol'指数计算在贝叶斯网络中可行。为了解决第二个挑战,本文提出了一种高效的算法,直接估计来自贝叶斯网络的先前分配的Monte Carlo样本的一阶Sobol'指数,从而计算贝叶斯网络的提议GSA是计算的。在更新之前,所提出的算法可以纯粹使用先前分布样本来预测利息节点的不确定性降低,从而为有效观察和更新提供定量指导。

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