IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v207y2010i1p284-289.html
   My bibliography  Save this article

Merging experts' opinions: A Bayesian hierarchical model with mixture of prior distributions

Author

Listed:
  • Rufo, M.J.
  • Pérez, C.J.
  • Martín, J.

Abstract

In this paper, a general approach is proposed to address a full Bayesian analysis for the class of quadratic natural exponential families in the presence of several expert sources of prior information. By expressing the opinion of each expert as a conjugate prior distribution, a mixture model is used by the decision maker to arrive at a consensus of the sources. A hyperprior distribution on the mixing parameters is considered and a procedure based on the expected Kullback-Leibler divergence is proposed to analytically calculate the hyperparameter values. Next, the experts' prior beliefs are calibrated with respect to the combined posterior belief over the quantity of interest by using expected Kullback-Leibler divergences, which are estimated with a computationally low-cost method. Finally, it is remarkable that the proposed approach can be easily applied in practice, as it is shown with an application.

Suggested Citation

  • Rufo, M.J. & Pérez, C.J. & Martín, J., 2010. "Merging experts' opinions: A Bayesian hierarchical model with mixture of prior distributions," European Journal of Operational Research, Elsevier, vol. 207(1), pages 284-289, November.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:1:p:284-289
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00304-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. E. Gutiérrez-Peña & A. Smith & José Bernardo & Guido Consonni & Piero Veronese & E. George & F. Girón & M. Martínez & G. Letac & Carl Morris, 1997. "Exponential and bayesian conjugate families: Review and extensions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 1-90, June.
    2. Irene Valsecchi, 2008. "Learning from Experts," Working Papers 2008.35, Fondazione Eni Enrico Mattei.
    3. Korhonen, Pekka & Moskowitz, Herbert & Wallenius, Jyrki, 1992. "Multiple criteria decision support - A review," European Journal of Operational Research, Elsevier, vol. 63(3), pages 361-375, December.
    4. John C. Liechty, 2004. "Bayesian correlation estimation," Biometrika, Biometrika Trust, vol. 91(1), pages 1-14, March.
    5. Nicolas Bousquet, 2008. "Diagnostics of prior-data agreement in applied Bayesian analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(9), pages 1011-1029.
    6. Valsecchi, Irene, 2008. "Learning from Experts," International Energy Markets Working Papers 36756, Fondazione Eni Enrico Mattei (FEEM).
    7. Rufo, M.J. & Pérez, C.J. & Martín, J., 2009. "Local parametric sensitivity for mixture models of lifetime distributions," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1238-1244.
    8. Szwed, P. & Dorp, J. Rene van & Merrick, J.R.W. & Mazzuchi, T.A. & Singh, A., 2006. "A Bayesian paired comparison approach for relative accident probability assessment with covariate information," European Journal of Operational Research, Elsevier, vol. 169(1), pages 157-177, February.
    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. 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.
    2. Yingchun Xu & Xiaohu Zheng & Wen Yao & Ning Wang & Xiaoqian Chen, 2021. "A sequential multi-prior integration and updating method for complex multi-level system based on Bayesian melding method," Journal of Risk and Reliability, , vol. 235(5), pages 863-876, October.

    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. Rufo, M.J. & Martín, J. & Pérez, C.J., 2009. "Inference on exponential families with mixture of prior distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3271-3280, July.
    2. Consonni, Guido & Veronese, Piero & Gutiérrez-Peña, Eduardo, 2004. "Reference priors for exponential families with simple quadratic variance function," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 335-364, February.
    3. J. Granat & M. Makowski, 1998. "ISAAP - Interactive Specification and Analysis of Aspiration-Based Preferences," Working Papers ir98052, International Institute for Applied Systems Analysis.
    4. Rufo, M.J. & Pérez, C.J. & Martín, J., 2009. "Local parametric sensitivity for mixture models of lifetime distributions," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1238-1244.
    5. Haapalinna, Ilkka, 2003. "How to allocate funds within the army," European Journal of Operational Research, Elsevier, vol. 144(1), pages 224-233, January.
    6. Antão, P. & Sun, S. & Teixeira, A.P. & Guedes Soares, C., 2023. "Quantitative assessment of ship collision risk influencing factors from worldwide accident and fleet data," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    7. Matthew Reimherr & Xiao‐Li Meng & Dan L. Nicolae, 2021. "Prior sample size extensions for assessing prior impact and prior‐likelihood discordance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 413-437, July.
    8. Feng Dong & Xinqi Gao & Jingyun Li & Yuanqing Zhang & Yajie Liu, 2018. "Drivers of China’s Industrial Carbon Emissions: Evidence from Joint PDA and LMDI Approaches," IJERPH, MDPI, vol. 15(12), pages 1-28, December.
    9. Bo Cai & David B. Dunson, 2006. "Bayesian Covariance Selection in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 62(2), pages 446-457, June.
    10. M. Makowski, 1994. "Methodology and a Modular Tool for Multiple Criteria Analysis of LP Models," Working Papers wp94102, International Institute for Applied Systems Analysis.
    11. Luigi Spezia, 2019. "Modelling covariance matrices by the trigonometric separation strategy with application to hidden Markov models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 399-422, June.
    12. Nadja A. Leith & Richard E. Chandler, 2010. "A framework for interpreting climate model outputs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 279-296, March.
    13. Salo, Ahti A., 1995. "Interactive decision aiding for group decision support," European Journal of Operational Research, Elsevier, vol. 84(1), pages 134-149, July.
    14. Pitt, M.K. & Walker, S.G., 2001. "Construction of Stationary Time Series via the Giggs Sampler with Application to Volatility Models," The Warwick Economics Research Paper Series (TWERPS) 595, University of Warwick, Department of Economics.
    15. Kalaba, Robert & Tesfatsion, Leigh, 1996. "A multicriteria approach to model specification and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 21(2), pages 193-214, February.
    16. Suyi Li & Qiang Meng & Xiaobo Qu, 2012. "An Overview of Maritime Waterway Quantitative Risk Assessment Models," Risk Analysis, John Wiley & Sons, vol. 32(3), pages 496-512, March.
    17. Nicholas Generous & Kristen J Margevicius & Kirsten J Taylor-McCabe & Mac Brown & W Brent Daniel & Lauren Castro & Andrea Hengartner & Alina Deshpande, 2014. "Selecting Essential Information for Biosurveillance—A Multi-Criteria Decision Analysis," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-15, January.
    18. Viktor DOLIA & Irina ENGLEZI, 2015. "Determine the safe transport of dangerous goods route," Transport Problems, Silesian University of Technology, Faculty of Transport, vol. 10(1), pages 31-44, March.
    19. Gandibleux, Xavier, 1999. "Interactive multicriteria procedure exploiting a knowledge-based module to select electricity production alternatives: The CASTART system," European Journal of Operational Research, Elsevier, vol. 113(2), pages 355-373, March.
    20. Goerlandt, Floris & Montewka, Jakub, 2015. "Maritime transportation risk analysis: Review and analysis in light of some foundational issues," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 115-134.

    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:ejores:v:207:y:2010:i:1:p:284-289. 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: http://www.elsevier.com/locate/eor .

    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.