Multivariate Student -t Regression Models: Pitfalls and Inference

We consider likelihood-based inference from multivariate regression models with independent Student-t errors. Some very intruiging pitfalls of both Bayesian and classical methods on the basis of point observations are uncovered. Bayesian inference may be precluded as a consequence of the coarse nature of the data. Global maximization of the likelihood function is a vacuous exercise since the likelihood function is unbounded as we tend to the boundary of the parameter space. A Bayesian analysis on the basis of set observations is proposed and illustrated by several examples.