Robust Bayesian inference on scale parameters

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)-dimension al space Y. By fixing the distribution of either R or Y while imposing inde pendence between them, different classes of distributions on R-n can be gen erated. As examples. the spherical. I-q-spherical, b-spherical and anisotro pic classes can be interpreted in this unifying framework, We present a rob ust Bayesian analysis on a scale parameter in the purr scale model and in t he regression model. In particular, we consider robustness of posterior inf erence on the scale parameter when the sampling distribution ranges over cl asses related to those mentioned above. Some links between Bayesian and sam pling-theory results are also highlighted. (C) 2001 Academic Press.