IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v158y2017icp41-49.html
   My bibliography  Save this article

Deriving the probability of a linear opinion pooling method being superior to a set of alternatives

Author

Listed:
  • Bolger, Donnacha
  • Houlding, Brett

Abstract

Linear opinion pools are a common method for combining a set of distinct opinions into a single succinct opinion, often to be used in a decision making task. In this paper we consider a method, termed the Plug-in approach, for determining the weights to be assigned in this linear pool, in a manner that can be deemed as rational in some sense, while incorporating multiple forms of learning over time into its process. The environment that we consider is one in which every source in the pool is herself a decision maker (DM), in contrast to the more common setting in which expert judgments are amalgamated for use by a single DM. We discuss a simulation study that was conducted to show the merits of our technique, and demonstrate how theoretical probabilistic arguments can be used to exactly quantify the probability of this technique being superior (in terms of a probability density metric) to a set of alternatives. Illustrations are given of simulated proportions converging to these true probabilities in a range of commonly used distributional cases.

Suggested Citation

  • Bolger, Donnacha & Houlding, Brett, 2017. "Deriving the probability of a linear opinion pooling method being superior to a set of alternatives," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 41-49.
    • Handle: RePEc:eee:reensy:v:158:y:2017:i:c:p:41-49
    DOI: 10.1016/j.ress.2016.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832016306639
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2016.10.008?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. A. Dawid & M. DeGroot & J. Mortera & R. Cooke & S. French & C. Genest & M. Schervish & D. Lindley & K. McConway & R. Winkler, 1995. "Coherent combination of experts' opinions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(2), pages 263-313, December.
    2. Flandoli, F. & Giorgi, E. & Aspinall, W.P. & Neri, A., 2011. "Comparison of a new expert elicitation model with the Classical Model, equal weights and single experts, using a cross-validation technique," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1292-1310.
    3. Wisse, Bram & Bedford, Tim & Quigley, John, 2008. "Expert judgement combination using moment methods," Reliability Engineering and System Safety, Elsevier, vol. 93(5), pages 675-686.
    4. Peter A. Morris, 1983. "An Axiomatic Approach to Expert Resolution," Management Science, INFORMS, vol. 29(1), pages 24-32, January.
    5. Eggstaff, Justin W. & Mazzuchi, Thomas A. & Sarkani, Shahram, 2014. "The effect of the number of seed variables on the performance of Cooke′s classical model," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 72-82.
    6. 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.
    7. Chauncey Starr, 1981. "Risk Criteria for Nuclear Power Plants: A Pragmatic Proposal," Risk Analysis, John Wiley & Sons, vol. 1(2), pages 113-120, June.
    8. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    9. Peter A. Morris, 1977. "Combining Expert Judgments: A Bayesian Approach," Management Science, INFORMS, vol. 23(7), pages 679-693, March.
    10. Kenneth C. Lichtendahl & Yael Grushka-Cockayne & Robert L. Winkler, 2013. "Is It Better to Average Probabilities or Quantiles?," Management Science, INFORMS, vol. 59(7), pages 1594-1611, July.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Colson, Abigail R. & Cooke, Roger M., 2017. "Cross validation for the classical model of structured expert judgment," Reliability Engineering and System Safety, Elsevier, vol. 163(C), pages 109-120.
    4. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    5. Makariou, Despoina & Barrieu, Pauline & Tzougas, George, 2021. "A finite mixture modelling perspective for combining experts’ opinions with an application to quantile-based risk measures," LSE Research Online Documents on Economics 110763, London School of Economics and Political Science, LSE Library.
    6. Despoina Makariou & Pauline Barrieu & George Tzougas, 2021. "A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures," Risks, MDPI, vol. 9(6), pages 1-25, June.
    7. Taylor, James W. & Taylor, Kathryn S., 2023. "Combining probabilistic forecasts of COVID-19 mortality in the United States," European Journal of Operational Research, Elsevier, vol. 304(1), pages 25-41.
    8. 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.
    9. Patrick Afflerbach & Christopher Dun & Henner Gimpel & Dominik Parak & Johannes Seyfried, 2021. "A Simulation-Based Approach to Understanding the Wisdom of Crowds Phenomenon in Aggregating Expert Judgment," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 63(4), pages 329-348, August.
    10. Konrad Bogner & Katharina Liechti & Luzi Bernhard & Samuel Monhart & Massimiliano Zappa, 2018. "Skill of Hydrological Extended Range Forecasts for Water Resources Management in Switzerland," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(3), pages 969-984, February.
    11. Malte Knüppel & Fabian Krüger, 2022. "Forecast uncertainty, disagreement, and the linear pool," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 23-41, January.
    12. Weronika Nitka & Rafał Weron, 2023. "Combining predictive distributions of electricity prices. Does minimizing the CRPS lead to optimal decisions in day-ahead bidding?," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(3), pages 105-118.
    13. Yang, Dazhi & van der Meer, Dennis, 2021. "Post-processing in solar forecasting: Ten overarching thinking tools," Renewable and Sustainable Energy Reviews, Elsevier, vol. 140(C).
    14. Jason R. W. Merrick, 2008. "Getting the Right Mix of Experts," Decision Analysis, INFORMS, vol. 5(1), pages 43-52, March.
    15. Yael Grushka-Cockayne & Kenneth C. Lichtendahl Jr. & Victor Richmond R. Jose & Robert L. Winkler, 2017. "Quantile Evaluation, Sensitivity to Bracketing, and Sharing Business Payoffs," Operations Research, INFORMS, vol. 65(3), pages 712-728, June.
    16. Stephen C. Hora & Benjamin R. Fransen & Natasha Hawkins & Irving Susel, 2013. "Median Aggregation of Distribution Functions," Decision Analysis, INFORMS, vol. 10(4), pages 279-291, December.
    17. Ali E. Abbas, 2009. "A Kullback-Leibler View of Linear and Log-Linear Pools," Decision Analysis, INFORMS, vol. 6(1), pages 25-37, March.
    18. Ray, Evan L. & Brooks, Logan C. & Bien, Jacob & Biggerstaff, Matthew & Bosse, Nikos I. & Bracher, Johannes & Cramer, Estee Y. & Funk, Sebastian & Gerding, Aaron & Johansson, Michael A. & Rumack, Aaron, 2023. "Comparing trained and untrained probabilistic ensemble forecasts of COVID-19 cases and deaths in the United States," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1366-1383.
    19. 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.
    20. Aitazaz Ali Raja & Pierre Pinson & Jalal Kazempour & Sergio Grammatico, 2022. "A Market for Trading Forecasts: A Wagering Mechanism," Papers 2205.02668, arXiv.org, revised Oct 2022.

    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:eee:reensy:v:158:y:2017:i:c:p:41-49. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.