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.