  The aim of this manuscript is to introduce the Bayesian minimum message
length principle of inductive inference to a general statistical audience that
may not be familiar with information theoretic statistics. We describe two key
minimum message length inference approaches and demonstrate how the principle
can be used to develop a new Bayesian alternative to the frequentist $t$-test
as well as new approaches to hypothesis testing for the correlation
coefficient. Lastly, we compare the minimum message length approach to the
closely related minimum description length principle and discuss similarities
and differences between both approaches to inference.
