MDL and MML: Similarities and differences

This paper continues the introduction to minimum encoding inductive inference given by Oliver and Hand. This series of papers was written with the objective of providing an introduction to this area for statisticians. We describe the message length estimates used in Wallace's Minimum Message Length (MML) inference and Rissanen's Minimum Description Length (MDL) inference. The diierences in the message length estimates of the two approaches are explained. The implications of these diierences for applications are discussed.