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Optimal Linear Opinion Pools

Author

Listed:
  • Morris H. DeGroot

    (Formerly with Carnegie Mellon University)

  • Julia Mortera

    (Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università degli Studi di Roma, "La Sapienza," 00185 Rome, Italy)

Abstract

Consider a decision problem involving a group of m Bayesians in which each member reports his/her posterior distribution for some random variable \theta . The individuals all share a common prior distribution for \theta and a common loss function, but form their posterior distributions based on different data sets. A single distribution of \theta must be chosen by combining the individual posterior distributions in some type of opinion pool. In this paper, the optimal pool is presented when the data observed by the different members of the group are conditionally independent given \theta . When the data are not conditionally independent, the optimal weights to be used in a linear opinion pool are determined for problems involving quadratic loss functions and arbitrary distributions for \theta and the data. Properties of the optimal procedure are developed and some examples are discussed.

Suggested Citation

  • Morris H. DeGroot & Julia Mortera, 1991. "Optimal Linear Opinion Pools," Management Science, INFORMS, vol. 37(5), pages 546-558, May.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:5:p:546-558
    DOI: 10.1287/mnsc.37.5.546
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    Citations

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    Cited by:

    1. A. Philip Dawid & Julia Mortera, 2020. "Resolving some contradictions in the theory of linear opinion pools," Theory and Decision, Springer, vol. 88(3), pages 453-456, April.
    2. Roopesh Ranjan & Tilmann Gneiting, 2010. "Combining probability forecasts," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 71-91, January.
    3. Pierre A. Balthazard & William R. Ferrell & Dorothy L. Aguilar, 1998. "Influence Allocation Methods in Group Decision Support Systems," Group Decision and Negotiation, Springer, vol. 7(4), pages 347-362, July.
    4. Yakov Babichenko & Dan Garber, 2021. "Learning Optimal Forecast Aggregation in Partial Evidence Environments," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 628-641, May.
    5. Marcello Basili & Alain Chateauneuf & Giuseppe Scianna, 2019. "A consistent representation of Keynes’s long-term expectation in ?nancial market," Department of Economics University of Siena 808, Department of Economics, University of Siena.
    6. David M. Pennock & Michael P. Wellman, 2005. "Graphical Models for Groups: Belief Aggregation and Risk Sharing," Decision Analysis, INFORMS, vol. 2(3), pages 148-164, September.
    7. Marcello Basili & Carlo Zappia, 2018. "Ellsberg’s Decision Rules and Keynes’s Long-Term Expectations," Department of Economics University of Siena 777, Department of Economics, University of Siena.
    8. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2019. "Density Forecasting," BEMPS - Bozen Economics & Management Paper Series BEMPS59, Faculty of Economics and Management at the Free University of Bozen.
    9. Stephen Hora & Erim Kardeş, 2015. "Calibration, sharpness and the weighting of experts in a linear opinion pool," Annals of Operations Research, Springer, vol. 229(1), pages 429-450, June.
    10. Garratt, Anthony & Henckel, Timo & Vahey, Shaun P., 2023. "Empirically-transformed linear opinion pools," International Journal of Forecasting, Elsevier, vol. 39(2), pages 736-753.
    11. Roberto Casarin & Giulia Mantoan & Francesco Ravazzolo, 2016. "Bayesian Calibration of Generalized Pools of Predictive Distributions," Econometrics, MDPI, vol. 4(1), pages 1-24, March.
    12. Donnacha Bolger & Brett Houlding, 2016. "Reliability updating in linear opinion pooling for multiple decision makers," Journal of Risk and Reliability, , vol. 230(3), pages 309-322, June.
    13. Marcello Basili & Alain Chateauneuf & Giuliano Antonio & Giuseppe Scianna, 2023. "A representation of Keynes's long-term expectation in financial markets," Working Papers hal-03999320, HAL.
    14. Ville A. Satopää & Robin Pemantle & Lyle H. Ungar, 2016. "Modeling Probability Forecasts via Information Diversity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1623-1633, October.
    15. Marcello Basili, 2013. "Ellsberg Rules and Keynes’s State of Long-Term Expectation: More Than an Accordance," Department of Economics University of Siena 685, Department of Economics, University of Siena.
    16. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, vol. 50(5), pages 561-574, May.

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