Robust Bayesian Inference on Scale Parameters

Abstract

We represent random vectors Z that take values in Rn−{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 Rn can be generated. As examples, the spherical, lq-spherical, υ-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.