Bayesian sensitivity analysis in elliptical linear regression models

Abstract

Bayesian influence measures for linear regression models have been developed mostly for normal regression models with noninformative prior distributions for the unknown parameters. In this work we extend existing results in several directions. First, we review influence measures for the ordinary normal regression model under conjugate prior distributions in unified framework. Second, we consider elliptical regression models with noninformative prior distributions for the model parameters and investigate the influence of a given subset of observations on the posterior distributions of the location and scale parameters. We found that these influence measures are Bayesian versions of classical counterparts to identify outliers or influential observations. Finally, we show that departures from normality within the multivariate elliptical family of distributions only affect the posterior distribution of the scale parameter. (C) 2000 Elsevier Science B.V. All rights reserved.