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Decision Analysis by Augmented Probability Simulation

Author

Listed:
  • Concha Bielza

    (Decision Analysis Group, Madrid Technical University, Spain)

  • Peter Müller

    (Institute of Statistics and Decision Sciences, Duke University, Durham, North Carolina 27706)

  • David Ríos Insua

    (School of Engineering, Universidad Rey Juan Carlos, Spain)

Abstract

We provide a generic Monte Carlo method to find the alternative of maximum expected utility in a decision analysis. We define an artificial distribution on the product space of alternatives and states, and show that the optimal alternative is the mode of the implied marginal distribution on the alternatives. After drawing a sample from the artificial distribution, we may use exploratory data analysis tools to approximately identify the optimal alternative. We illustrate our method for some important types of influence diagrams.

Suggested Citation

  • Concha Bielza & Peter Müller & David Ríos Insua, 1999. "Decision Analysis by Augmented Probability Simulation," Management Science, INFORMS, vol. 45(7), pages 995-1007, July.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:7:p:995-1007
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    File URL: http://dx.doi.org/10.1287/mnsc.45.7.995
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    References listed on IDEAS

    as
    1. Izhar Matzkevich & Bruce Abramson, 1995. "Decision Analytic Networks in Artificial Intelligence," Management Science, INFORMS, vol. 41(1), pages 1-22, January.
    2. Allen C. Miller, III & Thomas R. Rice, 1983. "Discrete Approximations of Probability Distributions," Management Science, INFORMS, vol. 29(3), pages 352-362, March.
    3. James E. Smith, 1993. "Moment Methods for Decision Analysis," Management Science, INFORMS, vol. 39(3), pages 340-358, March.
    4. Shenoy, Prakash P., 1994. "A comparison of graphical techniques for decision analysis," European Journal of Operational Research, Elsevier, vol. 78(1), pages 1-21, October.
    5. Brewer, M. J. & Aitken, C. G. G. & Talbot, M., 1996. "A comparison of hybrid strategies for Gibbs sampling in mixed graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 21(3), pages 343-365, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. Ryan, Elizabeth G. & Drovandi, Christopher C. & Thompson, M. Helen & Pettitt, Anthony N., 2014. "Towards Bayesian experimental design for nonlinear models that require a large number of sampling times," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 45-60.
    3. 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.
    4. 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.
    5. repec:pal:jorsoc:v:57:y:2006:i:9:d:10.1057_palgrave.jors.2602097 is not listed on IDEAS
    6. Elizabeth G. Ryan & Christopher C. Drovandi & James M. McGree & Anthony N. Pettitt, 2016. "A Review of Modern Computational Algorithms for Bayesian Optimal Design," International Statistical Review, International Statistical Institute, vol. 84(1), pages 128-154, April.

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