ROBUST BAYESIAN-INFERENCE IN ELLIPTIC REGRESSION-MODELS

Broadening the stochastic assumptions on the error terms of regression models was prompted by the analysis of linear multivariate t models in Zellner (1976). We consider a possibly nonlinear regression model under any multivariate elliptical data density, and examine Bayesian posterior and predictive results. The latter are shown to be robust with respect to the specific choice of a sampling density within this elliptical class. In particular, sufficient conditions for such model robustness are that we single out a precision factor tau2 on which we can specify an improper prior density. Apart from the posterior distribution of this nuisance parameter tau2, the entire analysis will then be completely unaffected by departures from Normality. Similar results hold in finite mixtures of such elliptical densities, which can be used to average out specification uncertainty.