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Structuring Conditional Relationships in Influence Diagrams

Author

Listed:
  • James E. Smith

    (Duke University, Durham, North Carolina)

  • Samuel Holtzman

    (Strategic Decisions Group, Menlo Park, California)

  • James E. Matheson

    (Strategic Decisions Group, Menlo Park, California)

Abstract

An influence diagram is a graphical representation of a decision problem that is at once a formal description of a decision problem that can be treated by computers and a representation that is easily understood by decision makers who may be unskilled in the art of complex probabilistic modeling. The power of an influence diagram, both as an analysis tool and a communication tool, lies in its ability to concisely summarize the structure of a decision problem. However, when confronted with highly asymmetric problems in which particular acts or events lead to very different possibilities, many analysts prefer decision trees to influence diagrams. In this paper, we extend the definition of an influence diagram by introducing a new representation for its conditional probability distributions. This extended influence diagram representation, combining elements of the decision tree and influence diagram representations, allows one to clearly and efficiently represent asymmetric decision problems and provides an attractive alternative to both the decision tree and conventional influence diagram representations.

Suggested Citation

  • James E. Smith & Samuel Holtzman & James E. Matheson, 1993. "Structuring Conditional Relationships in Influence Diagrams," Operations Research, INFORMS, vol. 41(2), pages 280-297, April.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:2:p:280-297
    DOI: 10.1287/opre.41.2.280
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    Citations

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    Cited by:

    1. Guo, Rui & Shenoy, Prakash P., 1996. "A note on Kirkwood's algebraic method for decision problems," European Journal of Operational Research, Elsevier, vol. 93(3), pages 628-638, September.
    2. 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.
    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. Shenoy, Prakash P., 2000. "Valuation network representation and solution of asymmetric decision problems," European Journal of Operational Research, Elsevier, vol. 121(3), pages 579-608, March.
    5. Rodriguez-Muniz, Luis J. & Lopez-Diaz, Miguel & Gil, Maria Angeles, 2005. "Solving influence diagrams with fuzzy chance and value nodes," European Journal of Operational Research, Elsevier, vol. 167(2), pages 444-460, December.
    6. Debarun Bhattacharjya & Ross D. Shachter, 2012. "Formulating Asymmetric Decision Problems as Decision Circuits," Decision Analysis, INFORMS, vol. 9(2), pages 138-145, June.
    7. David Matheson & James E. Matheson, 2005. "Describing and Valuing Interventions That Observe or Control Decision Situations," Decision Analysis, INFORMS, vol. 2(3), pages 165-181, September.
    8. Prakash Shenoy, 1998. "Game Trees For Decision Analysis," Theory and Decision, Springer, vol. 44(2), pages 149-171, April.
    9. 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.
    10. Baker, Erin & Keisler, Jeffrey M., 2011. "Cellulosic biofuels: Expert views on prospects for advancement," Energy, Elsevier, vol. 36(1), pages 595-605.
    11. 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.
    12. Lopez-Diaz, Miguel & Rodriguez-Muniz, Luis J., 2007. "Influence diagrams with super value nodes involving imprecise information," European Journal of Operational Research, Elsevier, vol. 179(1), pages 203-219, May.
    13. 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.
    14. Thwaites, Peter A. & Smith, Jim Q., 2018. "A graphical method for simplifying Bayesian games," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 3-11.
    15. Freeman, G. & Smith, J.Q., 2011. "Bayesian MAP model selection of chain event graphs," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1152-1165, August.
    16. Demirer, Riza & Shenoy, Prakash P., 2006. "Sequential valuation networks for asymmetric decision problems," European Journal of Operational Research, Elsevier, vol. 169(1), pages 286-309, February.
    17. 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.

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