  We analyze differences between two information-theoretically motivated
approaches to statistical inference and model selection: the Minimum
Description Length (MDL) principle, and the Minimum Message Length (MML)
principle. Based on this analysis, we present two revised versions of MML: a
pointwise estimator which gives the MML-optimal single parameter model, and a
volumewise estimator which gives the MML-optimal region in the parameter space.
Our empirical results suggest that with small data sets, the MDL approach
yields more accurate predictions than the MML estimators. The empirical results
also demonstrate that the revised MML estimators introduced here perform better
than the original MML estimator suggested by Wallace and Freeman.
