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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
    DOI: 10.1287/mnsc.45.7.995
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Tahir Ekin & Stephen Walker & Paul Damien, 2023. "Augmented simulation methods for discrete stochastic optimization with recourse," Annals of Operations Research, Springer, vol. 320(2), pages 771-793, January.
    2. Insua, Insua Rios & Rios, Jesus & Banks, David, 2009. "Adversarial Risk Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 841-854.
    3. Michael Macgregor Perry & Hadi El-Amine, 2021. "Computational Efficiency in Multivariate Adversarial Risk Analysis Models," Papers 2110.12572, arXiv.org.
    4. 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.
    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. Jesus Rios & David Rios Insua, 2012. "Adversarial Risk Analysis for Counterterrorism Modeling," Risk Analysis, John Wiley & Sons, vol. 32(5), pages 894-915, May.
    7. 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.
    8. Tahir Ekin & Nicholas G. Polson & Refik Soyer, 2017. "Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(8), pages 613-627, December.
    9. Ekin, Tahir, 2018. "Integrated maintenance and production planning with endogenous uncertain yield," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 52-61.
    10. Tevfik Aktekin & Tahir Ekin, 2016. "Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(6), pages 460-478, September.
    11. Ekin, Tahir & Aktekin, Tevfik, 2021. "Decision making under uncertain and dependent system rates in service systems," European Journal of Operational Research, Elsevier, vol. 291(1), pages 335-348.
    12. Insua, David Rios & Ruggeri, Fabrizio & Soyer, Refik & Wilson, Simon, 2020. "Advances in Bayesian decision making in reliability," European Journal of Operational Research, Elsevier, vol. 282(1), pages 1-18.
    13. 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.
    14. 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.
    15. Tahir Ekin & Nicholas G. Polson & Refik Soyer, 2014. "Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse," Decision Analysis, INFORMS, vol. 11(4), pages 250-264, December.
    16. Michael Perry & Hadi El-Amine, 2019. "Computational Efficiency in Multivariate Adversarial Risk Analysis Models," Decision Analysis, INFORMS, vol. 16(4), pages 314-332, December.
    17. E Ballestero & C Bielza & D Pla-Santamaría, 2006. "A decision approach to competitive electronic sealed-bid auctions for land," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(9), pages 1126-1133, September.
    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. César Gil & David Rios Insua & Jesus Rios, 2016. "Adversarial Risk Analysis for Urban Security Resource Allocation," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 727-741, April.
    20. 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.
    21. Jason R. W. Merrick, 2009. "Bayesian Simulation and Decision Analysis: An Expository Survey," Decision Analysis, INFORMS, vol. 6(4), pages 222-238, December.
    22. González-Ortega, Jorge & Ríos Insua, David & Cano, Javier, 2019. "Adversarial risk analysis for bi-agent influence diagrams: An algorithmic approach," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1085-1096.
    23. 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.
    24. Ekin, Tahir & Naveiro, Roi & Ríos Insua, David & Torres-Barrán, Alberto, 2023. "Augmented probability simulation methods for sequential games," European Journal of Operational Research, Elsevier, vol. 306(1), pages 418-430.

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