We show how to apply Sobol's method of global sensitivity analysis to measure the influence exerted by a set of nodes' evidence on a quantity of interest expressed by a Bayesian network. Our method exploits the network structure so as to transform the problem of Sobol index estimation into that of marginalization inference. This way, we can efficiently compute indices for networks where brute-force or Monte Carlo based estimators for variance-based sensitivity analysis would require millions of costly samples. Moreover, our method gives exact results when exact inference is used, and also supports the case of correlated inputs. The proposed algorithm is inspired by the field of tensor networks, and generalizes earlier tensor sensitivity techniques from the acyclic to the cyclic case. We demonstrate the method on three medium to large Bayesian networks that cover the areas of project risk management and reliability engineering.

翻译：我们展示了如何应用Sobol的全球敏感性分析方法来测量一组节点证据对巴伊西亚网络表示的兴趣所施加的影响。 我们的方法利用网络结构将Sobol指数估算问题转化为边缘化推论。 这样,我们可以有效地计算出Brute-force或Monte Carlo基于基于差异的估算器进行基于差异的敏感性分析需要数百万个基于成本的样本的网络的指数。 此外,我们的方法在使用精确的推论时提供了准确的结果,也支持了相关投入的情况。 拟议的算法受强尔网络的启发,并概括了早期从环流学到周期学案例的高温敏感技术。 我们展示了三个中大巴伊斯网络覆盖项目风险管理和可靠性工程领域的方法。