Graphical Models for Groups: Belief Aggregation and Risk Sharing

References

• Arrow K. J. The role of securities in the optimal allocation of risk-bearing. Rev. Econom. Stud. (1964) 31(2):91–96Crossref, Google Scholar
• Benediktsson J. A., Swain P. H. Consensus theoretic classification methods. IEEE Trans. Systems, Man, Cybernetics (1992) 22(4):688–704Crossref, Google Scholar
• Bonduelle Y. Aggregating expert opinions by resolving sources of disagreement. (1987) . Unpublished doctoral thesis, Stanford University, Stanford, CAGoogle Scholar
• Cesa-Bianchi N., Freund Y., Haussler D., Helmbold D. P., Schapire R. E., Warmuth M. K. How to use expert advice. J. ACM (1997) 44(3):427–485Crossref, Google Scholar
• Chyu C. C. Decomposable probabilistic influence diagrams. Probab. Engrg. Inform. Sci. (1991) 5:229–243Crossref, Google Scholar
• Clemen R. T., Winkler R. L. Aggregation of point estimates: A flexible modeling approach. Management Sci. (1993) 39(4):501–515Link, Google Scholar
• Cooke R. M.Experts in Uncertainty: Opinion and Subjective Probability in Science (1991) (Oxford University Press, New York) Environmental Ethics and Science Policy SeriesCrossref, Google Scholar
• Cooper G. The computational complexity of probabilistic inference using Bayes belief networks. Artificial Intelligence (1990) 42:393–405Crossref, Google Scholar
• Dalkey N. C., Linstone H. A., Turoff M. Toward a theory of group estimation. The Delphi Method: Techniques and Applications (1975) (Addison-Wesley, Reading, MA) 236–261Google Scholar
• Darroch J. N., Lauritzen S. L., Speed T. P. Markov fields and log-linear interaction models for contingency tables. Ann. Statist. (1980) 8(3):522–539Crossref, Google Scholar
• de Finetti B.Theory of Probability: A Critical Introductory Treatment (1974) 1(Wiley, New York) Google Scholar
• Degroot M. H. Reaching a consensus. J. Amer. Statist. Association (1974) 69(345):118–121Crossref, Google Scholar
• Degroot M. H., Mortera J. Optimal linear opinion pools. Management Sci. (1991) 37(5):546–558Link, Google Scholar
• Faria A. E., Smith J. Q. Conditional external Bayesianity in decomposable influence diagrams. Bayesian Statist. (1996) 5:551–560Google Scholar
• French S. Group consensus probability distributions: A critical survey. Bayesian Statist. (1985) 2:183–202Google Scholar
• Genest C. A characterization theorem for externally Bayesian groups. Ann. Statist. (1984a) 12(3):1100–1105Crossref, Google Scholar
• Genest C. A conflict between two axioms for combining subjective distributions. J. Roy. Statist. Soc. (1984b) 46(3):403–405Google Scholar
• Genest C. Pooling operators with the marginalization property. Canadian J. Statist. (1984c) 12(2):153–163Crossref, Google Scholar
• Genest C., Wagner C. G. Further evidence against independence preservation in expert judgement synthesis. Aequationes Mathematicae (1987) 32(1):74–86Crossref, Google Scholar
• Genest C., Zidek J. V. Combining probability distributions: A critique and an annotated bibliography. Statist. Sci. (1986) 1(1):114–148Crossref, Google Scholar
• Genest C., McConway K. J., Schervish M. J. Characterization of externally Bayesian pooling operators. Ann. Statist. (1986) 14(2):487–501Crossref, Google Scholar
• Huang C.-F., Litzenberger R. H.Foundations for Financial Economics (1988) (Elsevier, Amsterdam, The Netherlands) Google Scholar
• Jacobs R. A. Methods for combining experts’ probability assessments. Neural Comput. (1995) 7(5):867–888Crossref, Google Scholar
• Jensen F. V.An Introduction to Bayesian Networks (1996) (Springer, New York) Google Scholar
• Kadane J. B., Winkler R. L. Separating probability elicitation from utilities. J. Amer. Statist. Association (1988) 83(402):357–363Crossref, Google Scholar
• Kloks T.Treewidth: Computations and Approximations (1994) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Laddaga R. Lehrer and the consensus proposal. Synthese (1977) 36:473–477Crossref, Google Scholar
• Lauritzen S. L., Spiegelhalter D. J. Local computations with probabilities on graphical structures and their application to expert systems. J. Roy. Statist. Soc. Ser. B (1988) 50:157–224Google Scholar
• Lehrer K., Wagner C. G. Probability amalgamation and the independence issue: A reply to Laddaga. Synthese (1983) 55(3):339–346Crossref, Google Scholar
• Levy W. B., Delic H. Maximum entropy aggregation of individual opinions. IEEE Trans. Systems, Man, Cybernetics (1994) 24(4):606–613Crossref, Google Scholar
• Lindley D. V., Bernando J. M., Degroot M. H., Lindley D. V., Smith A. F. M. Reconciliation of discrete probability distributions. Bayesian Statistics 2 (1985) (North-Holland, Amsterdam, The Netherlands) 375–390Google Scholar
• Lindley D. V., Clarotti C. A., Lindley D. V. The use of probability statements. Accelerated Life Testing and Experts’ Opinions in Reliability (1988) (Elsevier, Amsterdam, The Netherlands) 25–57Google Scholar
• Matzkevich I., Abramson B. The topological fusion of Bayes nets. 8th Conf. Uncertainty Artificial Intelligence (1992) 152–158Google Scholar
• Matzkevich I., Abramson B. Some complexity considerations in the combination of belief networks. 9th Conf. Uncertainty Artificial Intelligence (1993) 152–158Crossref, Google Scholar
• Morris P. A. Decision analysis expert use. Management Sci. (1974) 20(9):1233–1241Link, Google Scholar
• Morris P. A. Combining expert judgments: A Bayesian approach. Management Sci. (1977) 23(7):679–693Link, Google Scholar
• Myung I. J., Ramamoorti S., Bailey A. D. Maximum entropy aggregation of expert predictions. Management Sci. (1996) 42(10):1420–1436Link, Google Scholar
• Nau R. F. Coherent decision analysis with inseparable probabilities and utilities. J. Risk Uncertainty (1995) 10(1):71–91Crossref, Google Scholar
• Nau R. F., McCardle K. F. Arbitrage, rationality, and equilibrium. Theory Decision (1991) 31:199–240Crossref, Google Scholar
• Neapo litan R. E.Probabilistic Reasoning in Expert Systems: Theory and Algorithms (1990) (Wiley, New York) Google Scholar
• Ng K.-C., Abramson B. Consensus diagnosis—A simulation study. IEEE Trans. Systems, Man, Cybernetics (1992) 22(5):916–928Crossref, Google Scholar
• Ng K.-C., Abramson B. Probabilistic multi-knowledge-base systems. Appl. Intelligence (1994) 4(2):219–236Crossref, Google Scholar
• Pearl J.Probabilistic Reasoning in Intelligent Systems (1988) (Morgan Kaufmann, San Francisco, CA) Google Scholar
• Pennock D. M., Wellman M. P. Representing aggregate belief through the competitive equilibrium of a securities market. 13th Conf. Uncertainty Artificial Intelligence (1997) Providence, RI:392–400Google Scholar
• Pennock D. M., Wellman M. P. Graphical representations of consensus belief. 15th Conf. Uncertainty Artificial Intelligence (1999) San Francisco, CA:531–540Google Scholar
• Pennock D. M., Wellman M. P. Compact securities markets for Pareto optimal reallocation of risk. 16th Conf. Uncertainty Artificial Intelligence (2000) San Francisco, CA:481–488Google Scholar
• Pennock D. M., Wellman M. P. A market framework for pooling opinions. (2001) . Technical report 2001-081, NEC Research Institute, Princeton, NJGoogle Scholar
• Raiffa H.Decision Analysis: Introductory Lectures on Choices under Uncertainty (1968) (Addison-Wesley, Reading, MA) Google Scholar
• Rosenblueth E., Ordaz M. Combination of expert opinions. J. Scientific Indust. Res. (1992) 51:572–580Google Scholar
• Savage L. J.The Foundations of Statistics (1954) (Wiley, New York) Google Scholar
• Shachter R. D. Probabilistic inference and influence diagrams. Oper. Res. (1988) 36(4):589–604Link, Google Scholar
• Shachter R. D., Andersen S. K., Poh K. L. Directed reduction algorithms and decomposable graphs. Uncertainty in Artificial Intelligence (1991) 6(North Holland, Amsterdam, The Netherlands) 197–208Google Scholar
• Varian H. R. The arbitrage principle in financial economics. J. Econom. Perspectives (1987) 1(2):55–72Crossref, Google Scholar
• von Neumann J., Morgenstern O.Theory of Games and Economic Behavior (1953) (Princeton University Press, Princeton, NJ) Google Scholar
• Wagner C. Aggregating subjective probabilities: Some limitative theorems. Notre Dame J. Formal Logic (1984) 25(3):233–240Crossref, Google Scholar
• West M., Crosse J. Modeling probabilistic agent opinion. J. Roy. Statist. Soc. Ser. B. Methodological (1992) 54(1):285–299Google Scholar
• Whittaker J.Graphical Models in Applied Multivariate Statistics (1990) (Wiley, Chichester, England) Google Scholar
• Winkler R. L. The consensus of subjective probability distributions. Management Sci. (1968) 15(2):B61–B75Link, Google Scholar
• Winkler R. L. Combining probability distributions from dependent sources. Management Sci. (1981) 27(4):479–488Link, Google Scholar
• Winkler R. L. Expert resolution. Management Sci. (1986) 32(3):298–303Link, Google Scholar
• Wolfers J., Zitzewitz E. Interpreting prediction market prices as probabilities. (2005) . Technical report, http://bpp.wharton.upenn.edu/jwolfers/Papers/InterpretingPredictionMarketPrices.pdfGoogle Scholar
• Xiang Y. A probabilistic framework for cooperative multi-agent distributed interpretation and optimization of communication. Artificial Intelligence (1996) 87(1–2):295–342Crossref, Google Scholar
• Yule G. U. Notes on the theory of association of attributes in statistics. Biometrika (1903) 2:121–134Crossref, Google Scholar