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Multistage Monte Carlo Method for Solving Influence Diagrams Using Local Computation

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  • John M. Charnes

    (School of Business, University of Kansas, 1300 Sunnyside Avenue, Summerfield Hall, Lawrence, Kansas 66045-7585)

  • Prakash P. Shenoy

    (School of Business, University of Kansas, 1300 Sunnyside Avenue, Summerfield Hall, Lawrence, Kansas 66045-7585)

Abstract

The main goal of this paper is to describe a new multistage Monte Carlo (MMC) simulation method for solving influence diagrams using local computation. Global methods have been proposed by others that sample from the joint probability distribution of all the variables in the influence diagram. However, for influence diagrams having many variables, the state space of all variables grows exponentially, and the sample sizes required for good estimates may be too large to be practical. In this paper, we develop a MMC method, which samples only a small set of chance variables for each decision node in the influence diagram. MMC is akin to methods developed for exact solution of influence diagrams in that we limit the number of chance variables sampled at any time. Because influence diagrams model each chance variable with a conditional probability distribution, the MMC method lends itself well to influence diagram representations.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:3:p:405-418
    DOI: 10.1287/mnsc.1030.0138
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Finn Jensen & Thomas Nielsen, 2013. "Probabilistic decision graphs for optimization under uncertainty," Annals of Operations Research, Springer, vol. 204(1), pages 223-248, April.
    5. Barry R. Cobb, 2007. "Influence Diagrams with Continuous Decision Variables and Non-Gaussian Uncertainties," Decision Analysis, INFORMS, vol. 4(3), pages 136-155, September.

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