Confidence Interval of Bayesian Network and Global Sensitivity Analysis

2017 ◽  
Author(s):  
Sangjune Bae ◽  
Nam Ho Kim ◽  
Chanyoung Park
Keyword(s):  
Sensitivity Analysis ◽  
Confidence Interval ◽  
Bayesian Network ◽  
Global Sensitivity Analysis ◽  
Global Sensitivity

Confidence Interval of Bayesian Network and Global Sensitivity Analysis

AIAA Journal ◽  
2017 ◽  
Vol 55 (11) ◽  
pp. 3916-3924 ◽  
Author(s):  
Sangjune Bae ◽  
Nam H. Kim ◽  
Chanyoung Park ◽  
Zaeill Kim
Keyword(s):  
Sensitivity Analysis ◽  
Confidence Interval ◽  
Bayesian Network ◽  
Global Sensitivity Analysis ◽  
Global Sensitivity

Global Sensitivity Analysis for a Bayesian Network

2016 ◽  
Author(s):  
Chenzhao Li ◽  
Sankaran Mahadevan
Keyword(s):  
Sensitivity Analysis ◽  
Bayesian Network ◽  
Prior Distribution ◽  
Global Sensitivity Analysis ◽  
Auxiliary Variable ◽  
Uncertainty Reduction ◽  
Sensitivity Index ◽  
Global Sensitivity ◽  
First Order ◽  
Deterministic Function

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.

Management of Sampling Uncertainty Using Conservative Estimate of Probability in Bayesian Network

2017 ◽  
Author(s):  
Sangjune Bae ◽  
Nam H. Kim ◽  
Seung-gyo Jang
Keyword(s):  
Sensitivity Analysis ◽  
Bayesian Network ◽  
Global Sensitivity Analysis ◽  
Epistemic Uncertainty ◽  
Probability Of Failure ◽  
System Level ◽  
Conservative Estimate ◽  
Component Level ◽  
Global Sensitivity ◽  
Design Changes

Since the safety of a system is often assessed by the probability of failure, it is crucial to calculate the probability accurately in order to achieve the target safety. Despite such importance, calculating the precise probability is not a trivial task due to the inherent aleatory variability and epistemic uncertainty. Therefore the safety is assessed by a conservative estimate of the probability rather than using a single value of the probability. In general, there are two ways to achieve the target probability: Shifting the probability or reducing the uncertainty. In this paper, among various sources of epistemic uncertainty, the uncertainty quantification error from sampling is considered to calculate the conservative estimate of a system probability of failure. To quantify and shape the epistemic uncertainty, Bayesian network is utilized for constituting the relationship between the system probability and component probabilities, while global sensitivity analysis is employed to connect the variance in the probabilities in system level with that in the component level. Based on this, local sensitivity of the conservative estimate with respect to a design change in a component is derived and approximated for a simple numerical calculation using Bayesian network and global sensitivity analysis. This is to show how a design can meet the probabilistic criteria considering propagated uncertainty when the design changes.

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