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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. 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.
    2. Irene Valsecchi, 2008. "Learning from Experts," Working Papers 2008.35, Fondazione Eni Enrico Mattei.
    3. Valsecchi, Irene, 2008. "Learning from Experts," International Energy Markets Working Papers 36756, Fondazione Eni Enrico Mattei (FEEM).
    4. Agresti, Alan & Caffo, Brian, 2002. "Measures of relative model fit," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 127-136, April.
    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. 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.
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    Cited by:

    1. 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.
    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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