Bayesian inference for elliptical linear models: Conjugate analysis and model comparison

In this work, we review and extend some results presented in the literature related to Bayesian analysis in elliptical (symmetric) linear models. A new class of prior distributions is considered, which generalizes the normal-chi-squared family. It is shown that for this class, the posterior analysis is simple to perform under some conditions, and conjugacy is achieved for phi. One aspect of the models studied in detail is the invariance of some distributions with respect to changes in the generator. In particular, it is shown that some Bayes estimators and Bayes factors do not depend on the generator function of an elliptical model. We also discuss practical implications of these results.