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On Robust Bayesian Analysis for Location and Scale Parameters

✍ Scribed by Rubén A. Haro-López; Adrian F.M. Smith

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
327 KB
Volume
70
Category
Article
ISSN
0047-259X

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✦ Synopsis

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 Sanso (1995, Biometrika 82, 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 multivariate v-spherical distributions. We show that when the v( } )=& }& 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 power t provides 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.

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