Introduction to minimum message length inference

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.