IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v31y1983i5p866-880.html
   My bibliography  Save this article

Reconciliation of Probability Distributions

Author

Listed:
  • Dennis Lindley

    (Decision Sciences Consortium, Inc., Falls Church, Virginia)

Abstract

Several people each express their opinion of an uncertain quantity by providing their mean and standard deviation of it. In this paper we discuss the problem of incorporating all these opinions into a single, reconciled, probability distribution for the quantity. The usual procedure is least squares, based on normality. The paper illustrates the advantages of using t -distributions, instead, and clarifies the role of the information provided by the standard deviations. Suitable approximations are provided for many cases.

Suggested Citation

  • Dennis Lindley, 1983. "Reconciliation of Probability Distributions," Operations Research, INFORMS, vol. 31(5), pages 866-880, October.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:5:p:866-880
    DOI: 10.1287/opre.31.5.866
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.31.5.866
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.31.5.866?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
    ---><---

    Citations

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


    Cited by:

    1. Saralees Nadarajah & Samuel Kotz, 2007. "Moments of a product Pearson type VII density distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 91(4), pages 441-448, December.
    2. 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.
    3. Refik Soyer & M. Murat Tarimcilar, 2008. "Modeling and Analysis of Call Center Arrival Data: A Bayesian Approach," Management Science, INFORMS, vol. 54(2), pages 266-278, February.
    4. Hurley, W. J. & Lior, D. U., 2002. "Combining expert judgment: On the performance of trimmed mean vote aggregation procedures in the presence of strategic voting," European Journal of Operational Research, Elsevier, vol. 140(1), pages 142-147, July.
    5. Erin Baker & Olaitan Olaleye, 2013. "Combining Experts: Decomposition and Aggregation Order," Risk Analysis, John Wiley & Sons, vol. 33(6), pages 1116-1127, June.
    6. Wolden Bache, Ida & Sofie Jore, Anne & Mitchell, James & Vahey, Shaun P., 2011. "Combining VAR and DSGE forecast densities," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1659-1670, October.
    7. Das Sourish & Yang Hongxia & Banks David, 2012. "Synthetic Priors that Merge Opinion from Multiple Experts," Statistics, Politics and Policy, De Gruyter, vol. 4(1), pages 1-26, December.
    8. Saralees Nadarajah, 2009. "The product t density distribution arising from the product of two Student’s t PDFs," Statistical Papers, Springer, vol. 50(3), pages 605-615, June.
    9. A. Charisse Farr & Kerrie Mengersen & Fabrizio Ruggeri & Daniel Simpson & Paul Wu & Prasad Yarlagadda, 2020. "Combining Opinions for Use in Bayesian Networks: A Measurement Error Approach," International Statistical Review, International Statistical Institute, vol. 88(2), pages 335-353, August.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Anthony Garratt & James Mitchell & Shaun P. Vahey, 2009. "Measuring Output Gap Uncertainty," Birkbeck Working Papers in Economics and Finance 0909, Birkbeck, Department of Economics, Mathematics & Statistics.
    15. Jason R. W. Merrick, 2008. "Getting the Right Mix of Experts," Decision Analysis, INFORMS, vol. 5(1), pages 43-52, March.
    16. Ali E. Abbas, 2009. "A Kullback-Leibler View of Linear and Log-Linear Pools," Decision Analysis, INFORMS, vol. 6(1), pages 25-37, March.
    17. Garratt, Anthony & Mise, Emi, 2014. "Forecasting exchange rates using panel model and model averaging," Economic Modelling, Elsevier, vol. 37(C), pages 32-40.
    18. Lichtendahl Jr., Kenneth C., 2009. "Random quantiles of the Dirichlet process," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 501-507, February.
    19. 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.
    20. Francesco Billari & Rebecca Graziani & Eugenio Melilli, 2014. "Stochastic Population Forecasting Based on Combinations of Expert Evaluations Within the Bayesian Paradigm," Demography, Springer;Population Association of America (PAA), vol. 51(5), pages 1933-1954, October.
    21. 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.
    22. 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.
    23. 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.
    24. Frederik Herzberg, 2015. "Aggregating infinitely many probability measures," Theory and Decision, Springer, vol. 78(2), pages 319-337, February.
    25. Basak, Indrani, 1998. "Probabilistic judgments specified partially in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 108(1), pages 153-164, July.

    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:inm:oropre:v:31:y:1983:i:5:p:866-880. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.