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On Robust Bayesian Analysis for Location and Scale Parameters

Author

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  • Haro-López, Rubén A.
  • Smith, Adrian F. M.

Abstract

Dawid (1973,Biometrika60, 664-666) stated conditions in the univariate location model with known scale parameter needed for there to be either vanishing likelihood or prior influence on the posterior distribution when there is a conflict between likelihood and prior. More recently, Pericchi and Sansó (1995,Biometrika82, 223-225) noted that there are distributions that partially satisfy Dawid's conditions but have bounded rather than vanishing influence on the posterior distribution. In this paper, we present the extension of these results for the location and scale model using the multivariatev-spherical distributions. We show that when thev(·)=||·|| function is a norm, the || ||-spherical distributions, exponential power, and logistic power provide a robust analysis for the location model with known scale parameter, whereas Student's powertprovides a robust analysis for the location and scale model. Robust analyses are illustrated for normal-gamma prior location and scale models. Numerical computations are implemented via the Gibbs sampler.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:70:y:1999:i:1:p:30-56
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    Cited by:

    1. Arslan, Olcay, 2005. "A new class of multivariate distributions: Scale mixture of Kotz-type distributions," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 18-28, November.
    2. 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.

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