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Regression models with fat-tailed error terms are an increasingly popularchoice to obtain more robust inference to the presence of outlyingobservations. This article focuses on Bayesian inference for the Student-$t$linear regression model under objective priors that are based on the Jeffreysrule. Posterior propriety results presented in Fonseca et al. (2008) arerevisited and corrected. In particular, it is shown that the standardJeffreys-rule prior precludes the existence of a proper posterior distribution.

On posterior propriety for the Student-$t$ linear regression model under Jeffreys priors