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MML and Bayesianism: similarities and differences: introduction to minimum encoding inference Part

This paper continues the introduction to minimum encoding inference given by Oliver and Hand. This series of papers were written with the objective of providing an introduction to this area for statisticians. We examine the relationship between Bayesianism and Minimum Message Length (MML) inference. We argue that MML augments Bayesian methods by providing a sound Bayesian method for point estimation which is invariant under non-linear transformations. We explore the issues of invariance of estimators under non-linear transformations, the role of the Fisher Information matrix in MML inference, and the apparent similarity between MML and the adoption of a Jeereys' Prior. We then compare MML to an approximate method of Bayesian Model Class Selection. Despite apparent similarities in their expressions, the properties of the two approaches can be diierent.