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Valuation-Based Systems for Bayesian Decision Analysis

Author

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  • Prakash P. Shenoy

    (The University of Kansas, Lawrence, Kansas)

Abstract

This paper proposes a new method for representing and solving Bayesian decision problems. The representation is called a valuation-based system and has some similarities to influence diagrams. However, unlike influence diagrams which emphasize conditional independence among random variables, valuation-based systems emphasize factorizations of joint probability distributions. Also, whereas influence diagram representation allows only conditional probabilities, valuation-based system representation allows all probabilities. The solution method is a hybrid of local computational methods for the computation of marginals of joint probability distributions and the local computational methods for discrete optimization problems. We briefly compare our representation and solution methods to those of influence diagrams.

Suggested Citation

  • Prakash P. Shenoy, 1992. "Valuation-Based Systems for Bayesian Decision Analysis," Operations Research, INFORMS, vol. 40(3), pages 463-484, June.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:3:p:463-484
    DOI: 10.1287/opre.40.3.463
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    Citations

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    Cited by:

    1. Hu, Ye & Li, Xinxin, 2011. "Context-Dependent Product Evaluations: An Empirical Analysis of Internet Book Reviews," Journal of Interactive Marketing, Elsevier, vol. 25(3), pages 123-133.
    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. Erik Jørgensen & Anders Kristensen & Dennis Nilsson, 2014. "Markov Limid processes for representing and solving renewal problems," Annals of Operations Research, Springer, vol. 219(1), pages 63-84, August.
    4. Prakash Shenoy, 1998. "Game Trees For Decision Analysis," Theory and Decision, Springer, vol. 44(2), pages 149-171, April.
    5. 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.
    6. C. L. Smith & E. Borgonovo, 2007. "Decision Making During Nuclear Power Plant Incidents—A New Approach to the Evaluation of Precursor Events," Risk Analysis, John Wiley & Sons, vol. 27(4), pages 1027-1042, August.
    7. 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.
    8. Apiruk Detwarasiti & Ross D. Shachter, 2005. "Influence Diagrams for Team Decision Analysis," Decision Analysis, INFORMS, vol. 2(4), pages 207-228, December.
    9. 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.
    10. Domenica Mirauda & Marco Ostoich, 2018. "Assessment of Pressure Sources and Water Body Resilience: An Integrated Approach for Action Planning in a Polluted River Basin," IJERPH, MDPI, vol. 15(2), pages 1-19, February.
    11. 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.
    12. 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.
    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. Steffen L. Lauritzen & Dennis Nilsson, 2001. "Representing and Solving Decision Problems with Limited Information," Management Science, INFORMS, vol. 47(9), pages 1235-1251, September.
    15. Finn Jensen & Thomas Nielsen, 2013. "Probabilistic decision graphs for optimization under uncertainty," Annals of Operations Research, Springer, vol. 204(1), pages 223-248, April.
    16. 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.
    17. Koller, Daphne & Milch, Brian, 2003. "Multi-agent influence diagrams for representing and solving games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 181-221, October.
    18. 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.

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