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Using Ranked Nodes to Model Qualitative Judgments in Bayesian Networks
October 2007 (vol. 19 no. 10)
pp. 1420-1432
Although Bayesian Nets (BNs) are increasingly being used to solve real world risk problems, their use is still constrained by the difficulty of constructing the node probability tables (NPTs). A key challenge is to construct relevant NPTs using the minimal amount of expert elicitation, recognising that it is rarely cost-effective to elicit complete sets of probability values. We describe a simple approach to defining NPTs for a large class of commonly occurring nodes (called ranked nodes). The approach is based on the doubly truncated Normal distribution with a central tendency that is invariably a type of weighted function of the parent nodes. In extensive real-world case studies we have found that this approach is sufficient for generating the NPTs of a very large class of nodes. We describe one such case study for validation purposes. The approach has been fully automated in a commercial tool, called AgenaRisk, and is thus accessible to all types of domain experts. We believe this work represents a useful contribution to BN research and technology since its application makes the difference between being able to build realistic BN models and not.

[1] AgenaRisk Software, Agena Ltd., www.agenarisk.com, 2007.
[2] F. Cozman and E. Krotkov, “Truncated Gaussians as Tolerance Sets,” Technical Report CMU-RI-TRI, Robotics Inst., Carnegie Mellon Univ., 1997.
[3] F.J. Díez, “Parameter Adjustment in Bayes Networks: The Generalized Noisy or-Gate,” Proc. Ninth Ann. Conf. Uncertainty in Artificial Intelligence (UAI '93), D. Heckerman and A.Mamdani, eds., pp. 99-105, 1993.
[4] M.K. Druzdzel and L.C. van der Gaag, “Elicitation of Probabilities for Belief Networks: Combining Qualitative and Quantitative Information,” Proc 11th Ann. Conf. Uncertainty in Artificial Intelligence (UAI '95), pp. 141-148, Aug. 1995.
[5] M.K. Druzdzel and L.C. van der Gaag, “Building Probabilistic Networks: Where Do the Numbers Come From,” IEEE Trans. Knowledge and Data Eng., vol. 12, no. 4, pp. 481-486, July/Aug. 2000.
[6] N.E. Fenton, P. Krause, and M. Neil, “Software Measurement: Uncertainty and Causal Modeling,” IEEE Software, vol. 10, no. 4, pp. 116-122, 2002.
[7] N.E. Fenton, W. Marsh, M. Neil, P. Cates, S. Forey, and M. Tailor, “Making Resource Decisions for Software Projects,” Proc. 26th Int'l Conf. Software Eng. (ICSE '04), pp. 397-406, May 2004.
[8] N.E. Fenton, M. Neil, P. Hearty, D. Marquez, W. Marsh, P. Krause, and R. Mishra, “Predicting Software Defects in Varying Development Lifecycles Using Bayesian Nets,” Information and Software Technology, vol. 49, no. 1, pp. 32-43, 2007.
[9] D. Heckerman, A. Mamdani, and M. Wellman, “Real-World Applications of Bayesian Networks,” Comm. ACM, vol. 38, no. 3, pp. 25-26, 1995.
[10] K. Huang and M. Henrion, “Efficient Search-Based Inference for Noisy-OR Belief Networks,” Proc. 12th Ann. Conf. Uncertainty in Artificial Intelligence (UAI '96), pp. 325-331, 1996.
[11] Hugin Software, Hugin A/S, www.hugin.com, 2007.
[12] D. Kahneman, P. Slovic, and A. Tversky, Judgment under Uncertainty: Heuristics and Biases. Cambridge Univ. Press, 1982.
[13] D. Koller and A. Pfeffer, “Object-Oriented Bayesian Networks,” Proc. 13th Ann. Conf. Uncertainty in Artificial Intelligence (UAI '97), pp. 302-313, Aug. 1997.
[14] K. Laskey, “Sensitivity Analysis for Probability Assessments in Bayesian Networks,” IEEE Trans. Systems, Man, and Cybernetics, vol. 25, no. 6, pp. 901-909, June 1995.
[15] K.B. Laskey and S. Mahoney, “Network Fragments: Representing Knowledge for Constructing Probabilistic Model Networks,” Proc. 13th Ann. Conf. Uncertainty in Artificial Intelligence (UAI '98), 1998.
[16] K.B. Laskey and S.M. Mahoney, “Network Engineering for Agile Belief Network Models,” IEEE Trans. Knowledge and Data Eng., vol. 12, no. 4, pp. 487-498, July/Aug. 2000.
[17] B. Littlewood, L. Strigini, D. Wright, N.E. Fenton, and M. Neil, “Bayesian Belief Networks for Safety Assessment of Computer-Based Systems,” System Performance Evaluation Methodologies and Applications, pp. 349-364, 2000.
[18] S. Mahoney and K. Laskey, “Network Engineering for Complex Belief Networks,” Proc. 12th Ann. Conf. Uncertainty in Artificial Intelligence (UAI '96), pp. 389-396, 1996.
[19] P.S. Maybeck, Stochastic Models, Estimation and Control, vol. 1. Academic Press, 1979.
[20] S. Monti and G. Carenini, “Dealing with the Expert Inconsistency in Probability Elicitation,” IEEE Trans. Knowledge and Data Eng., vol. 12, no. 4, pp. 499-508, July/Aug. 2000.
[21] M. Neil, N.E. Fenton, and L. Nielsen, “Building Large-Scale Bayesian Networks,” The Knowledge Eng. Rev., vol. 15, no. 3, pp.257-284, 2000.
[22] M. Neil, N.E. Fenton, S. Forey, and R. Harris, “Using Bayesian Belief Networks to Predict the Reliability of Military Vehicles,” IEE Computing and Control Eng. J., vol. 12, no. 1, pp. 11-20, 2001.
[23] M. Neil, B. Malcolm, and R. Shaw, “Modelling an Air Traffic Control Environment Using Bayesian Belief Networks,” Proc. 21st Int'l System Safety Conf., Aug. 2003.
[24] M. Neil, P. Krause, and N. Fenton, Software Quality Prediction Using Bayesian Networks in Software Engineering with Computational Intelligence. Kluwer Int'l Series in Eng. and Computer Science, vol.731, 2003.
[25] M. Neil, N.E. Fenton, and M. Tailor, “Using Bayesian Networks to Model Expected and Unexpected Operational Losses,” Risk Analysis: An Int'l J., vol. 25, no. 4, pp. 963-972, 2005.
[26] J. Pearl, “Graphical Models, Causality, and Intervention,” Statistical Science, vol. 8, no. 3, pp. 266-273, 1993.
[27] S. Renooij, “Probability Elicitation for Belief Networks: Issues to Consider,” The Knowledge Eng. Rev., vol. 16, no. 3, pp. 255-269, 2000.
[28] M. Takikawa and B. D'Ambrosio, “Multiplicative Factorization of Noisy-Max,” Proc. 15th Ann. Conf. Uncertainty in Artificial Intelligence (UAI '99), 1999.
[29] L.C. van der Gaag, S. Renooij, C.L.M. Witteveen, B.M.P. Aleman, and B.G. Taal, “Probabilities for a Probabilistic Network: A Case-Study in Oesophageal Carcinoma,” Technical Report UU-CS-2001-01, Univ. of Utrecht, Jan. 2001.
[30] L.C. van der Gaag, S. Renooija, C.L.M. Wittemana, B.M.P. Alemanb, and B.G. Taal, “Probabilities for a Probabilistic Network: A Case Study in Oesophageal Cancer,” Artificial Intelligence in Medicine, vol. 25, no. 2, pp. 123-148, 2002.
[31] M.P. Wellman, “Fundamental Concepts of Qualitative Probabilistic Networks,” Artificial Intelligence, vol. 44, no. 3, pp. 257-303, 1990.
[32] A. Zagorecki and M. Druzdzel, “An Empirical Study of Probability Elicitation under Noisy-OR Assumption,” Proc. 17th Int'l Florida Artificial Intelligence Research Soc. Conf. (FLAIRS '04), pp. 880-885, 2004.

Index Terms:
Bayesian networks, node probability tables, ranked nodes, probability elicitation, risk analysis
Citation:
Norman E. Fenton, Martin Neil, Jose Galan Caballero, "Using Ranked Nodes to Model Qualitative Judgments in Bayesian Networks," IEEE Transactions on Knowledge and Data Engineering, vol. 19, no. 10, pp. 1420-1432, Oct. 2007, doi:10.1109/TKDE.2007.1073
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