[+] Author and Article Information
Chenzhao Li

Vanderbilt University, 2301 Vanderbilt Place PMB 351826, Nashville, TN 37235

Sankaran Mahadevan

Vanderbilt University, 2301 Vanderbilt Place PMB 351826, Nashville, TN 37235

1Corresponding author.

ASME doi:10.1115/1.4037454 History: Received August 31, 2016; Revised January 27, 2017


In a Bayesian network, 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 for Bayesian network, which calculates the Sobol' sensitivity index to quantify the contribution of an observation node towards 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 Bayesian network confronts two challenges. First, the computation of the Sobol' index requires a deterministic function while the Bayesian network is a stochastic model. This paper uses an 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. Second, the computation of the Sobol' index can be expensive, especially if the model inputs are correlated, which is common in a Bayesian network. 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 Bayesian network, thus making the proposed GSA for Bayesian network 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.

Copyright (c) 2017 by ASME
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