IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v50y2004i3p405-418.html
   My bibliography  Save this article

Multistage Monte Carlo Method for Solving Influence Diagrams Using Local Computation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1030.0138
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1030.0138?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Prakash P. Shenoy, 1992. "Valuation-Based Systems for Bayesian Decision Analysis," Operations Research, INFORMS, vol. 40(3), pages 463-484, June.
    2. 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.
    3. Concha Bielza & Peter Müller & David Ríos Insua, 1999. "Decision Analysis by Augmented Probability Simulation," Management Science, INFORMS, vol. 45(7), pages 995-1007, July.
    4. Ross D. Shachter & C. Robert Kenley, 1989. "Gaussian Influence Diagrams," Management Science, INFORMS, vol. 35(5), pages 527-550, May.
    5. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    6. Ross D. Shachter, 1986. "Evaluating Influence Diagrams," Operations Research, INFORMS, vol. 34(6), pages 871-882, December.
    7. Ronald A. Howard, 1971. "Proximal Decision Analysis," Management Science, INFORMS, vol. 17(9), pages 507-541, May.
    8. Allen C. Miller, III & Thomas R. Rice, 1983. "Discrete Approximations of Probability Distributions," Management Science, INFORMS, vol. 29(3), pages 352-362, March.
    9. James E. Smith, 1993. "Moment Methods for Decision Analysis," Management Science, INFORMS, vol. 39(3), pages 340-358, March.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. Prakash Shenoy, 1998. "Game Trees For Decision Analysis," Theory and Decision, Springer, vol. 44(2), pages 149-171, April.
    12. Donald L. Keefer, 1994. "Certainty Equivalents for Three-Point Discrete-Distribution Approximations," Management Science, INFORMS, vol. 40(6), pages 760-773, June.
    13. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. 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.
    4. Concha Bielza & Peter Müller & David Ríos Insua, 1999. "Decision Analysis by Augmented Probability Simulation," Management Science, INFORMS, vol. 45(7), pages 995-1007, July.
    5. 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.
    6. 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.
    7. Robert K. Hammond & J. Eric Bickel, 2013. "Reexamining Discrete Approximations to Continuous Distributions," Decision Analysis, INFORMS, vol. 10(1), pages 6-25, March.
    8. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    9. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    10. Prakash Shenoy, 1998. "Game Trees For Decision Analysis," Theory and Decision, Springer, vol. 44(2), pages 149-171, April.
    11. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    12. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    13. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    14. 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.
    15. De Reyck, Bert & Degraeve, Zeger & Vandenborre, Roger, 2008. "Project options valuation with net present value and decision tree analysis," European Journal of Operational Research, Elsevier, vol. 184(1), pages 341-355, January.
    16. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    17. Woodruff, Joshua & Dimitrov, Nedialko B., 2018. "Optimal discretization for decision analysis," Operations Research Perspectives, Elsevier, vol. 5(C), pages 288-305.
    18. Barry R. Cobb, 2007. "Influence Diagrams with Continuous Decision Variables and Non-Gaussian Uncertainties," Decision Analysis, INFORMS, vol. 4(3), pages 136-155, September.
    19. Debarun Bhattacharjya & Ross D. Shachter, 2012. "Formulating Asymmetric Decision Problems as Decision Circuits," Decision Analysis, INFORMS, vol. 9(2), pages 138-145, June.
    20. Konstantin Pavlikov & Stan Uryasev, 2018. "CVaR distance between univariate probability distributions and approximation problems," Annals of Operations Research, Springer, vol. 262(1), pages 67-88, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:50:y:2004:i:3:p:405-418. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.