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Research Papers

Sensitivity Analysis of a Bayesian Network

[+] Author and Article Information
Chenzhao Li

Department of Civil
and Environmental Engineering,
Vanderbilt University,
2301 Vanderbilt Place PMB 351826,
Nashville, TN 37235
e-mail: chenzhao.li@vandebilt.edu

Sankaran Mahadevan

Department of Civil
and Environmental Engineering,
Vanderbilt University,
2301 Vanderbilt Place PMB 351826,
Nashville, TN 37235
e-mail: sankaran.mahadevan@vandebilt.edu

1Corresponding author.

Manuscript received August 31, 2016; final manuscript received January 27, 2017; published online September 7, 2017. Assoc. Editor: Yan Wang.

ASME J. Risk Uncertainty Part B 4(1), 011003 (Sep 07, 2017) (10 pages) Paper No: RISK-16-1112; doi: 10.1115/1.4037454 History: Received August 31, 2016; Revised January 27, 2017

In a Bayesian network (BN), 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 (GSA) for BN, which calculates the Sobol’ sensitivity index to quantify the contribution of an observation node toward 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 BN confronts two challenges. First, the computation of the Sobol’ index requires a deterministic function while the BN is a stochastic model. This paper uses an auxiliary variable method to convert the path between two nodes in the BN 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 BN. 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 BN, thus making the proposed GSA for BN 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.

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Figures

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Fig. 1

Possible Bayesian inference results: (a) desired inference and (b) undesired inference

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Fig. 2

Auxiliary variable for a CPD

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Fig. 3

Auxiliary variable for a BN

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Fig. 4

Deterministic function for the path X1→XN

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Fig. 6

Equally probable interval

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Fig. 7

Steps to realize the proposed algorithm

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Fig. 8

Beam with mass–spring–damper

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Fig. 10

Posterior distributions at observation value of A3=4500

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Fig. 11

Dynamic BN of example 2

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Fig. 12

Observations, example 2

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Fig. 13

Posterior distribution of state variables

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Fig. 14

VRR of the state variables

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