  This paper applies the minimum message length principle to inference of
linear regression models with Student-t errors. A new criterion for variable
selection and parameter estimation in Student-t regression is proposed. By
exploiting properties of the regression model, we derive a suitable
non-informative proper uniform prior distribution for the regression
coefficients that leads to a simple and easy-to-apply criterion. Our proposed
criterion does not require specification of hyperparameters and is invariant
under both full rank transformations of the design matrix and linear
transformations of the outcomes. We compare the proposed criterion with several
standard model selection criteria, such as the Akaike information criterion and
the Bayesian information criterion, on simulations and real data with promising
results.
