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10 - Model Building with Belief Networks and Influence Diagrams

Published online by Cambridge University Press:  05 June 2012

By
Ross D. Shachter
Edited by
Ward Edwards ,
Ralph F. Miles Jr.  and
Detlof von Winterfeldt
Ross D. Shachter
Affiliation:
Department of Management Science and Engineering, Stanford University
Ralph F. Miles Jr.
Affiliation:
California Institute of Technology
Detlof von Winterfeldt
Affiliation:
University of Southern California
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Summary

ABSTRACT. Belief networks and influence diagrams use directed graphs to represent models for probabilistic reasoning and decision making under uncertainty. They have proven to be effective at facilitating communication with decision makers and with computers. Many of the important relationships among uncertainties, decisions, and values can be captured in the structure of these diagrams, explicitly revealing irrelevance and the flow of information. We explore a variety of examples illustrating some of these basic structures, along with an algorithm that efficiently analyzes their model structure. We also show how algorithms based on these structures can be used to resolve inference queries and determine the optimal policies for decisions.

We have all learned how to translate models, as we prefer to think of them, into arcane representations that our computers can understand, or to simplify away key subtleties for the benefit of clients or students. Thus it has been an immense pleasure to work with graphical models where the representation is natural for the novice, convenient for computation, and yet powerful enough to convey difficult concepts among analysts and researchers.

The graphical representations of belief networks and influence diagrams enable us to capture important relationships at the structural level of the graph where it easiest for people to see them and for algorithms to exploit them. Although the diagrams lend themselves to communication, there remains the challenge of synthesis, and building graphical models is still a challenging art.

Type
Chapter
Information
Advances in Decision Analysis
From Foundations to Applications
 , pp. 177 - 201
Publisher: Cambridge University Press
Print publication year: 2007

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References

Barza, M., and Pauker, S. G. (1980). The Decision to Biopsy, Treat, or Wait in Suspected Herpes encephalitis. Annals of Internal Medicine, 92(5), 641–649.CrossRefGoogle ScholarPubMed
Capen, E. C., Clapp, R. V., & Campbell, W. M. (1971). Competitive Bidding in High-Risk Situations. Journal of Petroleum Technology, 23(6), 641–653.CrossRefGoogle Scholar
Friedman, L. (1956). A Competitive Bidding Strategy. Operations Research, 4(1), 104–112.CrossRefGoogle Scholar
Good, I. J. (1961a). A Causal Calculus–I. British Journal of Philosophy of Science, 11, 305–318.CrossRefGoogle Scholar
Good, I. J. (1961b). A Causal Calculus–II. British Journal of Philosophy of Science, 12, 43–51.CrossRefGoogle Scholar
Heckerman, D., & Shachter, R. (1995). Decision-Theoretic Foundations for Causal Reasoning. Journal of Artificial Intelligence Research, 3, 405–430.Google Scholar
Heckerman, D. E., & Shachter, R. D. (1994). A Decision-Based View of Causality. In Mantaras, R. Lopez & Poole, D. (Eds.), Uncertainty in Artificial Intelligence: Proceedings of the Tenth Conference (pp. 302–310). San Mateo, CA: Morgan Kaufmann.Google Scholar
Henrion, M., & Druzdzel, M. J. (1990). Qualitative propagation and scenario-based approaches to explanation of probabiliistic reasoning. Paper presented at the Sixth Conference on Uncertainty in Artificial Intelligence, Cambridge, MA.Google Scholar
Howard, R. A. (1960). Dynamic Programming and Markov Processes. Cambridge, MA: MIT Press.Google Scholar
Howard, R. A. (1990). From Influence to Relevance to Knowledge. In Oliver, R. M. & Smith, J. Q. (Eds.), Influence Diagrams, Belief Nets, and Decision Analysis (pp. 3–23). Chichester: Wiley.Google Scholar
Howard, R. A., & Matheson, J. E. (1984). Influence Diagrams. In Howard, R. A. & Matheson, J. E. (Eds.), The Principles and Applications of Decision Analysis (Vol. II). Menlo Park, CA: Strategic Decisions Group.Google Scholar
Jensen, F., Jensen, F. V., & Dittmer, S. L. (1994). From Influence Diagrams to Junction Trees. In Mantaras, R. Lopez & Poole, D. (Eds.), Uncertainty in Artificial Intelligence: Proceedings of the Tenth Conference (pp. 367–373). San Mateo, CA: Morgan Kaufmann.Google Scholar
Jensen, F. V., Lauritzen, S. L., & Olesen, K. G. (1990). Bayesian Updating in Causal Probabilistic Networks by Local Computations. Comp. Stats. Q., 4, 269–282.Google Scholar
Keeney, R. L. (1992). Value-Focused Thinking. Cambridge, MA: Harvard University Press.Google Scholar
Kim, J. H., & Pearl, J. (1983). A computational model for causal and diagnostic reasoning in inference engines. Paper presented at the 8th International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany.Google Scholar
Lauritzen, S. L., & Spiegelhalter, D. J. (1988). Local Computations with Probabilities on Graphical Structures and Their Application to Expert Systems. JRSS B, 50(2), 157–224.Google Scholar
Matheson, J. E. (1990). Using Influence Diagrams to Value Information and Control. In Oliver, R. M. & Smith, J. Q. (Eds.), Influence Diagrams, Belief Nets, and Decision Analysis (pp. 25–48). Chichester: John Wiley.Google Scholar
Miller, A. C., Merkofer, M. M., Howard, R. A., Matheson, J. E., & Rice, T. R. (1976). Development of Automated Aids for Decision Analysis: Stanford Research Institute, Menlo Park, CA.CrossRefGoogle Scholar
Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. San Mateo, CA: Morgan Kaufmann.Google Scholar
Pearl, J. (2000). Causality: Models, Reasoning, and Inference: Cambridge University Press.Google Scholar
Raiffa, H. (1968). Decision Analysis. Reading, MA: Addison-Wesley.Google Scholar
Shachter, R. D. (1986). Evaluating Influence Diagrams. Operations Research, 34(November–December), 871–882.CrossRefGoogle Scholar
Shachter, R. D. (1988). Probabilistic Inference and Influence Diagrams. Operations Research, 36(July–August), 589–605.CrossRefGoogle Scholar
Shachter, R. D. (1990). An Ordered Examination of Influence Diagrams. Networks, 20, 535–563.CrossRefGoogle Scholar
Shachter, R. D. (1998). Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams). In Uncertainty in Artificial Intelligence: Proceedings of the Fourteenth Conference (pp. 480–487). San Francisco, CA: Morgan Kaufmann.Google Scholar
Shachter, R. D. (1999). Efficient Value of Information Computation. In Uncertainty in Artificial Intelligence: Proceedings of the Fifteenth Conference (pp. 594–601). San Francisco, CA: Morgan Kaufmann.Google Scholar
Shachter, R. D., & Heckerman, D. E. (1987). Thinking Backwards for Knowledge Acquisition. AI Magazine, 8(Fall), 55–61.Google Scholar
Shachter, R. D., & Peot, M. A. (1992). Decision Making Using Probabilistic Inference Methods. In Uncertainty in Artificial Intelligence: Proceedings of the Eighth Conference (pp. 276–283). San Mateo, CA: Morgan Kaufmann.Google Scholar
Shenoy, P. P., & Shafer, G. (1990). Axioms for Probability and Belief-Function Propagation. In Shachter, R. D., Levitt, T. S., Lemmer, J. F. & Kanal, L. N. (Eds.), Uncertainty in Artificial Intelligence 4 (pp. 169–198). Amsterdam: North-Holland.Google Scholar
Tatman, J. A., & Shachter, R. D. (1990). Dynamic Programming and Influence Diagrams. IEEE Transactions on Systems, Man, and Cybernetics, 20(2), 365–379.CrossRefGoogle Scholar
Wright, S. (1921). Correlation and Causation. Journal of Agricultural Research, 20, 557–585.Google Scholar
Wright, S. (1934). The Method of Path Coefficients. Annals of Mathematical Statistics, 5, 161–215.CrossRefGoogle Scholar

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