Traditionally, the sensitivity analysis of a Bayesian network studies the
impact of individually modifying the entries of its conditional probability
tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a
comprehensive account of each inputs' relevance, since simultaneous
perturbations in two or more parameters often entail higher-order effects that
cannot be captured by an OAT analysis. We propose to conduct global
variance-based sensitivity analysis instead, whereby $n$ parameters are viewed
as uncertain at once and their importance is assessed jointly. Our method works
by encoding the uncertainties as $n$ additional variables of the network. To
prevent the curse of dimensionality while adding these dimensions, we use
low-rank tensor decomposition to break down the new potentials into smaller
factors. Last, we apply the method of Sobol to the resulting network to obtain
$n$ global sensitivity indices. Using a benchmark array of both expert-elicited
and learned Bayesian networks, we demonstrate that the Sobol indices can
significantly differ from the OAT indices, thus revealing the true influence of
uncertain parameters and their interactions.

传统上，贝叶斯网络的敏感性分析研究了以逐个修改其条件概率表的方式对其影响，我们提出进行全局基于方差的敏感性分析，使用低秩张量分解来降低维度，并通过 Sobol 法得出全局敏感性指标，从而展示不确定参数及其交互作用的真实影响。