Bayesian estimation for spherically symmetric distributions

The theory of Bayesian least squares is developed for a general and more ta ngible notion of conjugacy than in models which make the more conventional assumption of normality. This paper is primarily concerned with extending t he results of classical conjugate normal-normal Bayesian analysis to the ca nonical setting of the generalized linear model when, at the same time, the sampling distribution and the prior are spherically symmetric. In order to underline the intrinsic aspect of our results, the approach of multivariat e analysis adopted here is coordinate free. Examples which illustrate the t heory are also presented. (C) 1999 Academic Press.