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Probabilistic Inference and Influence Diagrams

Author

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  • Ross D. Shachter

    (Stanford University, Stanford, California)

Abstract

An influence diagram is a network representation for probabilistic and decision analysis models. The nodes correspond to variables which can be constants, uncertain quantities, decisions, or objectives. The arcs reveal the probabilistic dependence of the uncertain quantities and the information available at the time of the decisions. The detailed data about the variables are stored within the nodes, so the diagram graph is compact and focuses attention on the relationships among the variables. Influence diagrams are effective communication tools and recent developments also allow them to be used for analysis. We develop algorithms to address questions of inference within a probabilistic model represented as an influence diagram. We use the conditional independence implied by the diagram's structure to determine the information needed to solve a given problem. When there is enough information we can solve it, exploiting that conditional independence. These same results are applied to problems of decision analysis. This methodology allows the construction of computer tools to maintain and evaluate complex models.

Suggested Citation

  • Ross D. Shachter, 1988. "Probabilistic Inference and Influence Diagrams," Operations Research, INFORMS, vol. 36(4), pages 589-604, August.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:4:p:589-604
    DOI: 10.1287/opre.36.4.589
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    Cited by:

    1. Concha Bielza & Prakash P. Shenoy, 1999. "A Comparison of Graphical Techniques for Asymmetric Decision Problems," Management Science, INFORMS, vol. 45(11), pages 1552-1569, November.
    2. Logan, Douglas M., 1990. "5.4. Decision analysis in engineering-economic modeling," Energy, Elsevier, vol. 15(7), pages 677-696.
    3. Regan, Peter J. & Holtzman, Samuel, 1995. "R&D Decision Advisor: An interactive approach to normative decision system model construction," European Journal of Operational Research, Elsevier, vol. 84(1), pages 116-133, July.
    4. C. L. Smith & E. Borgonovo, 2007. "Decision Making During Nuclear Power Plant Incidents—A New Approach to the Evaluation of Precursor Events," Risk Analysis, John Wiley & Sons, vol. 27(4), pages 1027-1042, August.
    5. Apiruk Detwarasiti & Ross D. Shachter, 2005. "Influence Diagrams for Team Decision Analysis," Decision Analysis, INFORMS, vol. 2(4), pages 207-228, December.
    6. Domenica Mirauda & Marco Ostoich, 2018. "Assessment of Pressure Sources and Water Body Resilience: An Integrated Approach for Action Planning in a Polluted River Basin," IJERPH, MDPI, vol. 15(2), pages 1-19, February.
    7. Özgür-Ünlüakın, Demet & Bilgiç, Taner, 2017. "Performance analysis of an aggregation and disaggregation solution procedure to obtain a maintenance plan for a partially observable multi-component system," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 652-662.
    8. Yu, Oliver S., 1990. "5.0. Interface between mental and computer models," Energy, Elsevier, vol. 15(7), pages 621-629.
    9. David M. Pennock & Michael P. Wellman, 2005. "Graphical Models for Groups: Belief Aggregation and Risk Sharing," Decision Analysis, INFORMS, vol. 2(3), pages 148-164, September.
    10. Jesus Rios & David Rios Insua, 2009. "Supporting Negotiations over Influence Diagrams," Decision Analysis, INFORMS, vol. 6(3), pages 153-171, September.
    11. 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.
    12. Frank A. Sonnenberg & C. Greg Hagerty & Casimir A. Kulikowski, 1994. "An Architecture for Knowledge-based Construction of Decision Models," Medical Decision Making, , vol. 14(1), pages 27-39, February.
    13. Stephen G. Pauker & John B. Wong, 2005. "The Influence of Influence Diagrams in Medicine," Decision Analysis, INFORMS, vol. 2(4), pages 238-244, December.
    14. M Berkan Sesen & Ann E Nicholson & Rene Banares-Alcantara & Timor Kadir & Michael Brady, 2013. "Bayesian Networks for Clinical Decision Support in Lung Cancer Care," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-1, December.
    15. Pontus Johnson & Robert Lagerström & Per Närman & Mårten Simonsson, 2007. "Enterprise architecture analysis with extended influence diagrams," Information Systems Frontiers, Springer, vol. 9(2), pages 163-180, July.
    16. Cho, Sungbin, 2009. "A linear Bayesian stochastic approximation to update project duration estimates," European Journal of Operational Research, Elsevier, vol. 196(2), pages 585-593, July.
    17. Douglas K. Owens & Ross D. Shachter & Robert F. Nease JR, 1997. "Representation and Analysis of Medical Decision Problems with Influence Diagrams," Medical Decision Making, , vol. 17(3), pages 241-262, July.
    18. Sue McNeil & Sci‐Chang Oh, 1991. "A Note on the Influence of Rail Defects on the Risk Associated with Shipping Hazardous Materials by Rail," Risk Analysis, John Wiley & Sons, vol. 11(2), pages 333-338, June.
    19. Byun, Ji-Eun & Song, Junho, 2020. "Efficient probabilistic multi-objective optimization of complex systems using matrix-based Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 200(C).
    20. VanDerHorn, Eric & Mahadevan, Sankaran, 2018. "Bayesian model updating with summarized statistical and reliability data," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 12-24.
    21. Farrokh Alemi & Manaf Zargoush & Jee Vang, 2017. "Using observed sequence to orient causal networks," Health Care Management Science, Springer, vol. 20(4), pages 590-599, December.
    22. Dennis M. Buede, 2005. "Influence Diagrams: A Practitioner's Perspective," Decision Analysis, INFORMS, vol. 2(4), pages 235-237, December.
    23. Concha Bielza & Peter Müller & David Ríos Insua, 1999. "Decision Analysis by Augmented Probability Simulation," Management Science, INFORMS, vol. 45(7), pages 995-1007, July.
    24. Salo, Ahti & Andelmin, Juho & Oliveira, Fabricio, 2022. "Decision programming for mixed-integer multi-stage optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 299(2), pages 550-565.

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