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Inference on exponential families with mixture of prior distributions

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

Abstract

A Bayesian analysis of the natural exponential families with quadratic variance function when there are several sources of prior information is considered. The belief of each source is expressed as a conjugate prior distribution. Then, a mixture of them is considered to represent a consensus of the sources. A unified framework considering unknown weights is presented. Firstly, a general procedure based on Kullback-Leibler (K-L) distance to obtain the weights is proposed. The main advantage is that the weights can be analytically calculated. In addition, expressions that allow a direct implementation for these families are shown. Secondly, the experts' prior beliefs are calibrated with respect to the combined posterior belief by using K-L distances. A straightforward Monte Carlo-based approach to estimate these distances is proposed. Finally, two illustrative examples are presented to show the ease of application of the proposed technique, as well as its usefulness in a Bayesian framework.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3271-3280
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    References listed on IDEAS

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    1. Irene Valsecchi, 2008. "Learning from Experts," Working Papers 2008.35, Fondazione Eni Enrico Mattei.
    2. 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.
    3. Al-Saleh, Jamal A. & Agarwal, Satish K., 2007. "Finite mixture of gamma distributions: A conjugate prior," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4369-4378, May.
    4. Valsecchi, Irene, 2008. "Learning from Experts," International Energy Markets Working Papers 36756, Fondazione Eni Enrico Mattei (FEEM).
    5. Agresti, Alan & Caffo, Brian, 2002. "Measures of relative model fit," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 127-136, April.
    6. M. Rufo & J. Martín & C. Pérez, 2006. "Bayesian analysis of finite mixture models of distributions from exponential families," Computational Statistics, Springer, vol. 21(3), pages 621-637, December.
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    Citations

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    Cited by:

    1. 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.
    2. Rufo, M.J. & Martín, J. & Pérez, C.J., 2016. "A Bayesian negotiation model for quality and price in a multi-consumer context," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 132-141.

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