IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v73y2012i4p605-619.html
   My bibliography  Save this article

Combining expert probabilities using the product of odds

Author

Listed:
  • Patrizio Frederic
  • Mario Di Bacco
  • Frank Lad

Abstract

We resolve a useful formulation of the question how a statistician can coherently incorporate the information in a consulted expert’s probability assessment for an event into a personal posterior probability assertion. Using a framework that recognises the total information available as composed of units available only to each of them along with units available to both, we show: that a sufficient statistic for all the information available to both the expert and the statistician is the product of their odds ratios in favour of the event; that the geometric mean of their two probabilities specifies a contour of pairs of assertions in the unit-square that yield the same posterior probability; that the information-combining function is parameterised by an unknown probability for the event conditioned only on the unspecified information common to both the statistician and the expert; and that an assessable mixing distribution over this unspecified probability allows an integrable mixture distribution to represent a computable posterior probability. The exact results allow the identification of the subclass of coherent probabilities that are externally Bayesian operators. This subclass is equivalent to the class of combining functions that honour the principles of uniformity and compromise. Copyright Springer Science+Business Media New York 2012

Suggested Citation

  • Patrizio Frederic & Mario Di Bacco & Frank Lad, 2012. "Combining expert probabilities using the product of odds," Theory and Decision, Springer, vol. 73(4), pages 605-619, October.
    • Handle: RePEc:kap:theord:v:73:y:2012:i:4:p:605-619
    DOI: 10.1007/s11238-012-9320-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11238-012-9320-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-012-9320-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Robert L. Winkler, 1981. "Combining Probability Distributions from Dependent Information Sources," Management Science, INFORMS, vol. 27(4), pages 479-488, April.
    2. Peter A. Morris, 1986. "Observations on Expert Aggregation," Management Science, INFORMS, vol. 32(3), pages 321-328, March.
    3. Peter A. Morris, 1974. "Decision Analysis Expert Use," Management Science, INFORMS, vol. 20(9), pages 1233-1241, May.
    4. Robert T. Clemen, 1987. "Combining Overlapping Information," Management Science, INFORMS, vol. 33(3), pages 373-380, March.
    5. Robert L. Winkler, 1968. "The Consensus of Subjective Probability Distributions," Management Science, INFORMS, vol. 15(2), pages 61-75, October.
    6. Robert T. Clemen & Robert L. Winkler, 1990. "Unanimity and Compromise Among Probability Forecasters," Management Science, INFORMS, vol. 36(7), pages 767-779, July.
    7. Dennis Lindley, 1983. "Reconciliation of Probability Distributions," Operations Research, INFORMS, vol. 31(5), pages 866-880, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. S. Cerreia-Vioglio & F. Maccheroni & M. Marinacci & A. Rustichini, 2017. "Multinomial logit processes and preference discovery: inside and outside the black box," Working Papers 615, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, vol. 50(5), pages 561-574, May.
    2. 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.
    3. Paola Monari & Patrizia Agati, 2001. "Fiducial inference in combining expert judgements," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 81-97, January.
    4. Jason R. W. Merrick, 2008. "Getting the Right Mix of Experts," Decision Analysis, INFORMS, vol. 5(1), pages 43-52, March.
    5. Robert J. Budnitz & George Apostolakis & David M. Boore & Lloyd S. Cluff & Kevin J. Coppersmith & C. Allin Cornell & Peter A. Morris, 1998. "Use of Technical Expert Panels: Applications to Probabilistic Seismic Hazard Analysis," Risk Analysis, John Wiley & Sons, vol. 18(4), pages 463-469, August.
    6. Jason R. W. Merrick & J. Rene van Dorp & Amita Singh, 2005. "Analysis of Correlated Expert Judgments from Extended Pairwise Comparisons," Decision Analysis, INFORMS, vol. 2(1), pages 17-29, March.
    7. Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2010. "Combining forecast densities from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 621-634.
    8. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    9. Dr. James Mitchell, 2009. "Measuring Output Gap Uncertainty," National Institute of Economic and Social Research (NIESR) Discussion Papers 342, National Institute of Economic and Social Research.
    10. 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.
    11. Wang, Xiaoqian & Hyndman, Rob J. & Li, Feng & Kang, Yanfei, 2023. "Forecast combinations: An over 50-year review," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1518-1547.
    12. Erin Baker & Olaitan Olaleye, 2013. "Combining Experts: Decomposition and Aggregation Order," Risk Analysis, John Wiley & Sons, vol. 33(6), pages 1116-1127, June.
    13. Garratt, Anthony & Mise, Emi, 2014. "Forecasting exchange rates using panel model and model averaging," Economic Modelling, Elsevier, vol. 37(C), pages 32-40.
    14. 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.
    15. Ali E. Abbas, 2009. "A Kullback-Leibler View of Linear and Log-Linear Pools," Decision Analysis, INFORMS, vol. 6(1), pages 25-37, March.
    16. Li, Yongquan & Zhu, Kaijie, 2009. "Information acquisition in new product introduction," European Journal of Operational Research, Elsevier, vol. 198(2), pages 618-625, October.
    17. Fu, Qi & Zhu, Kaijie, 2010. "Endogenous information acquisition in supply chain management," European Journal of Operational Research, Elsevier, vol. 201(2), pages 454-462, March.
    18. Wang, W., 1997. "Subjective estimation of the delay time distribution in maintenance modelling," European Journal of Operational Research, Elsevier, vol. 99(3), pages 516-529, June.
    19. Lichtendahl Jr., Kenneth C., 2009. "Random quantiles of the Dirichlet process," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 501-507, February.
    20. Julia R. Falconer & Eibe Frank & Devon L. L. Polaschek & Chaitanya Joshi, 2022. "Methods for Eliciting Informative Prior Distributions: A Critical Review," Decision Analysis, INFORMS, vol. 19(3), pages 189-204, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:73:y:2012:i:4:p:605-619. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.