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Robust Bayesian Inference on Scale Parameters

✍ Scribed by Carmen Fernández; Jacek Osiewalski; Mark F.J Steel

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
160 KB
Volume
77
Category
Article
ISSN
0047-259X

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✦ Synopsis

We represent random vectors Z that take values in R n &[0] as Z=RY, where R is a positive random variable and Y takes values in an (n&1)-dimensional space Y. By fixing the distribution of either R or Y, while imposing independence between them, different classes of distributions on R n can be generated. As examples, the spherical, l q -spherical, "-spherical and anisotropic classes can be interpreted in this unifying framework. We present a robust Bayesian analysis on a scale parameter in the pure scale model and in the regression model. In particular, we consider robustness of posterior inference on the scale parameter when the sampling distribution ranges over classes related to those mentioned above. Some links between Bayesian and sampling-theory results are also highlighted.

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