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Gaussian Influence Diagrams

Author

Listed:
  • Ross D. Shachter

    (Department of Engineering-Economic Systems, Stanford University, Stanford, California 94305)

  • C. Robert Kenley

    (Tiburon Systems, Inc., 2085 Hamilton Avenue, San Jose, California 95125)

Abstract

An influence diagram is a network representation of probabilistic inference and decision analysis models. The nodes correspond to variables that can be either constants, uncertain quantities, decisions, or objectives. The arcs reveal probabilistic dependence of the uncertain quantities and information available at the time of the decisions. The influence diagram focuses attention on relationships among the variables. As a result, it is increasingly popular for eliciting and communicating the structure of a decision or probabilistic model. This paper develops the framework for assessment and analysis of linear-quadratic-Gaussian models within the influence diagram representation. The "Gaussian influence diagram" exploits conditional independence in a model to simplify elicitation of parameters for the multivariate normal distribution. It is straightforward to assess and maintain a positive (semi-)definite covariance matrix. Problems of inference and decision making can be analyzed using simple transformations to the assessed model, and these procedures have attractive numerical properties. Algorithms are also provided to translate between the Gaussian influence diagram and covariance matrix representations for the normal distribution.

Suggested Citation

  • Ross D. Shachter & C. Robert Kenley, 1989. "Gaussian Influence Diagrams," Management Science, INFORMS, vol. 35(5), pages 527-550, May.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:5:p:527-550
    DOI: 10.1287/mnsc.35.5.527
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    Cited by:

    1. Hanea, A.M. & Kurowicka, D. & Cooke, R.M. & Ababei, D.A., 2010. "Mining and visualising ordinal data with non-parametric continuous BBNs," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 668-687, March.
    2. David J. Bryg, 1995. "Continuous Trees and NEVADA Simulation," Medical Decision Making, , vol. 15(4), pages 318-332, October.
    3. Andersson, Steen A. & Perlman, Michael D., 1998. "Normal Linear Regression Models With Recursive Graphical Markov Structure," Journal of Multivariate Analysis, Elsevier, vol. 66(2), pages 133-187, August.
    4. Gómez-Villegas, M.A. & Main, P. & Navarro, H. & Susi, R., 2014. "Sensitivity to hyperprior parameters in Gaussian Bayesian networks," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 214-225.
    5. Pan, Yue & Ou, Shenwei & Zhang, Limao & Zhang, Wenjing & Wu, Xianguo & Li, Heng, 2019. "Modeling risks in dependent systems: A Copula-Bayesian approach," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 416-431.
    6. Hanea, Anca & Morales Napoles, Oswaldo & Ababei, Dan, 2015. "Non-parametric Bayesian networks: Improving theory and reviewing applications," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 265-284.
    7. Cobb, Barry R. & Shenoy, Prakash P., 2008. "Decision making with hybrid influence diagrams using mixtures of truncated exponentials," European Journal of Operational Research, Elsevier, vol. 186(1), pages 261-275, April.
    8. Bielza, Concha & Gómez, Manuel & Shenoy, Prakash P., 2011. "A review of representation issues and modeling challenges with influence diagrams," Omega, Elsevier, vol. 39(3), pages 227-241, June.
    9. Abdul Salam & Marco Grzegorczyk, 2023. "Model averaging for sparse seemingly unrelated regression using Bayesian networks among the errors," Computational Statistics, Springer, vol. 38(2), pages 779-808, June.
    10. Yao Liu & Shuai Wang & Can Zhou & Xiaofei Wang, 2024. "Propagation Computation for Mixed Bayesian Networks Using Minimal Strong Triangulation," Mathematics, MDPI, vol. 12(13), pages 1-13, June.
    11. Agogino, Alice & Chao, Susan & Goebel, Kai & Alag, Satnam & Cammon, Bradly & Wang, Jiangxin, 1998. "Intelligent Diagnosis Based On Validated And Fused Data For Relilability And Safety Enhancement Of Automated Vehicles In An IVHS," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt1mw2v298, Institute of Transportation Studies, UC Berkeley.
    12. Borgonovo, Emanuele & Tonoli, Fabio, 2014. "Decision-network polynomials and the sensitivity of decision-support models," European Journal of Operational Research, Elsevier, vol. 239(2), pages 490-503.
    13. repec:jss:jstsof:35:i07 is not listed on IDEAS
    14. Gómez-Villegas, Miguel A. & Maín, Paloma & Susi, Rosario, 2008. "Extreme inaccuracies in Gaussian Bayesian networks," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1929-1940, October.
    15. Christopher Raphael, 2003. "Bayesian Networks with Degenerate Gaussian Distributions," Methodology and Computing in Applied Probability, Springer, vol. 5(2), pages 235-263, June.
    16. John M. Charnes & Prakash P. Shenoy, 2004. "Multistage Monte Carlo Method for Solving Influence Diagrams Using Local Computation," Management Science, INFORMS, vol. 50(3), pages 405-418, March.
    17. Yijing Li & Prakash P. Shenoy, 2012. "A Framework for Solving Hybrid Influence Diagrams Containing Deterministic Conditional Distributions," Decision Analysis, INFORMS, vol. 9(1), pages 55-75, March.
    18. Castillo, Enrique & Menéndez, José María & Sánchez-Cambronero, Santos, 2008. "Predicting traffic flow using Bayesian networks," Transportation Research Part B: Methodological, Elsevier, vol. 42(5), pages 482-509, June.
    19. Finn Jensen & Thomas Nielsen, 2013. "Probabilistic decision graphs for optimization under uncertainty," Annals of Operations Research, Springer, vol. 204(1), pages 223-248, April.
    20. Barry R. Cobb, 2007. "Influence Diagrams with Continuous Decision Variables and Non-Gaussian Uncertainties," Decision Analysis, INFORMS, vol. 4(3), pages 136-155, September.
    21. Concha Bielza & Peter Müller & David Ríos Insua, 1999. "Decision Analysis by Augmented Probability Simulation," Management Science, INFORMS, vol. 45(7), pages 995-1007, July.
    22. Zohar, Ron & Geiger, Dan, 2007. "Estimation of flows in flow networks," European Journal of Operational Research, Elsevier, vol. 176(2), pages 691-706, January.
    23. Castillo, Enrique & Gutiérrez, José Manuel & Hadi, Ali S., 1998. "Modeling Probabilistic Networks of Discrete and Continuous Variables," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 48-65, January.

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