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Modelling conflicting information using subexponential distributions and related classes

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  • J. Andrade
  • Edward Omey

Abstract

In the Bayesian modelling the data and the prior information concerning a certain parameter of interest may conflict, in the sense that the information carried by them disagree. The most common form of conflict is the presence of outlying information in the data, which may potentially lead to wrong posterior conclusions. To prevent this problem we use robust models which aim to control the influence of the atypical information in the posterior distribution. Roughly speaking, we conveniently use heavy-tailed distributions in the model in order to resolve conflicts in favour of those sources of information which we believe is more credible. The class of heavy-tailed distributions is quite wide and the literature have been concerned in establishing conditions on the data and prior distributions in order to reject the outlying information. In this work we focus on the subexponential and $$\mathfrak L $$ classes of heavy-tailed distributions, in which we establish sufficient conditions under which the posterior distribution automatically rejects the conflicting information. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • J. Andrade & Edward Omey, 2013. "Modelling conflicting information using subexponential distributions and related classes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 491-511, June.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:3:p:491-511
    DOI: 10.1007/s10463-012-0380-y
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    References listed on IDEAS

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    1. Haro-López, Rubén A. & Smith, Adrian F. M., 1999. "On Robust Bayesian Analysis for Location and Scale Parameters," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 30-56, July.
    2. Jose Ailton Alencar Andrade & Anthony O'Hagan, 2011. "Bayesian Robustness Modelling of Location and Scale Parameters," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(4), pages 691-711, December.
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    Cited by:

    1. Kevin McNally, 2023. "How Valuable Are Small Measurement Datasets in Supplementing Occupational Exposure Models? A Numerical Study Using the Advanced Reach Tool," IJERPH, MDPI, vol. 20(7), pages 1-14, April.
    2. J. A. A. Andrade & Edward Omey, 2017. "Bayesian robustness modelling using the O-regularly varying distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(3), pages 168-183, August.

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