  We study objective Bayesian inference for linear regression models with
residual errors distributed according to the class of two-piece scale mixtures
of normal distributions. These models allow for capturing departures from the
usual assumption of normality of the errors in terms of heavy tails, asymmetry,
and certain types of heteroscedasticity. We propose a general noninformative,
scale-invariant, prior structure and provide sufficient conditions for the
propriety of the posterior distribution of the model parameters, which cover
cases when the response variables are censored. These results allow us to apply
the proposed models in the context of survival analysis. This paper represents
an extension to the Bayesian framework of the models proposed in Rubio and Hong
(2015). We present a simulation study that shows good frequentist properties of
the posterior credible intervals as well as point estimators associated to the
proposed priors. We illustrate the performance of these models with real data
in the context of survival analysis of cancer patients.
