  In this paper reference and probability-matching priors are derived for the
univariate Student $t$-distribution. These priors generally lead to procedures
with properties frequentists can relate to while still retaining Bayes
validity. The priors are tested by performing simulation studies. The focus is
on the relative mean squared error from the posterior median ($MSE(\nu)/\nu$)
and on the frequentist coverage of the 95\% credibility intervals for a sample
size of $n=30$. Average interval lengths of the credibility intervals as well
as the modes of the interval lengths based on 2000 simulations are also
considered. The performance of the priors are also tested on real data, namely
daily logarithmic returns of IBM stocks.
