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

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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