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Aggregating Point Estimates: A Flexible Modeling Approach


  • Robert T. Clemen

    (College of Business Administration, University of Oregon, Eugene, Oregon 97403)

  • Robert L. Winkler

    (Fuqua School of Business, Duke University, Durham, North Carolina 27706)


In many decision situations information is available from a number of different sources. Aggregating the diverse bits of information is an important aspect of the decision-making process but entails special statistical modeling problems in characterizing the information. Prior research in this area has relied primarily on the use of historical data as a basis for modeling the information sources. We develop a Bayesian framework that a decision maker can use to encode subjective knowledge about the information sources in order to aggregate point estimates of an unknown quantity of interest. This framework features a highly flexible environment for modeling the probabilistic nature and interrelationships of the information sources and requires straightforward and intuitive subjective judgments using proven decision-analysis assessment techniques. Analysis of the constructed model produces a posterior distribution for the quantity of interest. An example based on health risks due to ozone exposure demonstrates the technique.

Suggested Citation

  • Robert T. Clemen & Robert L. Winkler, 1993. "Aggregating Point Estimates: A Flexible Modeling Approach," Management Science, INFORMS, vol. 39(4), pages 501-515, April.
  • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:4:p:501-515
    DOI: 10.1287/mnsc.39.4.501

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    Cited by:

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    2. Enrique López Droguett & Ali Mosleh, 2013. "Integrated treatment of model and parameter uncertainties through a Bayesian approach," Journal of Risk and Reliability, , vol. 227(1), pages 41-54, February.
    3. de Menezes, Lilian M. & W. Bunn, Derek & Taylor, James W., 2000. "Review of guidelines for the use of combined forecasts," European Journal of Operational Research, Elsevier, vol. 120(1), pages 190-204, January.
    4. Osherson, Daniel & Vardi, Moshe Y., 2006. "Aggregating disparate estimates of chance," Games and Economic Behavior, Elsevier, vol. 56(1), pages 148-173, July.
    5. Enrique López Droguett & Ali Mosleh, 2008. "Bayesian Methodology for Model Uncertainty Using Model Performance Data," Risk Analysis, John Wiley & Sons, vol. 28(5), pages 1457-1476, October.
    6. Esteban Fernández-Vázquez & Blanca Moreno, 2017. "Entropy Econometrics for combining regional economic forecasts: A Data-Weighted Prior Estimator," Journal of Geographical Systems, Springer, vol. 19(4), pages 349-370, October.
    7. Weyant John, 2014. "Integrated assessment of climate change: state of the literature," Journal of Benefit-Cost Analysis, De Gruyter, vol. 5(3), pages 377-409, December.
    8. Mostaghimi, Mehdi, 1996. "Combining ranked mean value forecasts," European Journal of Operational Research, Elsevier, vol. 94(3), pages 505-516, November.
    9. Enrique López Droguett & Ali Mosleh, 2014. "Bayesian Treatment of Model Uncertainty for Partially Applicable Models," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 252-270, February.
    10. Troutt, M. D. & Pang, W. K. & Hou, S. H., 1999. "Performance of some boundary-seeking mode estimators on the dome bias model," European Journal of Operational Research, Elsevier, vol. 119(1), pages 209-218, November.
    11. 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.
    12. Buehler, Roger & Messervey, Deanna & Griffin, Dale, 2005. "Collaborative planning and prediction: Does group discussion affect optimistic biases in time estimation?," Organizational Behavior and Human Decision Processes, Elsevier, vol. 97(1), pages 47-63, May.
    13. Thomas Weber, 2010. "Simple methods for evaluating and comparing binary experiments," Theory and Decision, Springer, vol. 69(2), pages 257-288, August.
    14. Joseph Lipscomb & Giovanni Parmigiani & Vic Hasselblad, 1998. "Combining Expert Judgment by Hierarchical Modeling: An Application to Physician Staffing," Management Science, INFORMS, vol. 44(2), pages 149-161, February.
    15. Robert T. Clemen & Robert L. Winkler, 1999. "Combining Probability Distributions From Experts in Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 19(2), pages 187-203, April.
    16. James Taylor & Derek Bunn, 1998. "Combining forecast quantiles using quantile regression: Investigating the derived weights, estimator bias and imposing constraints," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(2), pages 193-206.
    17. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, vol. 50(5), pages 561-574, May.
    18. Joseph Kadane & Javier Girón & Daniel Peña & Peter Fishburn & Simon French & D. Lindley & Giovanni Parmigiani & Robert Winkler, 1993. "Several Bayesians: A review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(1), pages 1-32, December.


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