Editing Minimum message length (section)

==Key features of MML==
* MML can be used to compare models of different structure. For example, its earliest application was in finding [[mixture model]]s with the optimal number of classes. Adding extra classes to a mixture model will always allow the data to be fitted to greater accuracy, but according to MML this must be weighed against the extra bits required to encode the parameters defining those classes. 
* MML is a method of [[Bayesian model comparison]]. It gives every model a score.
* MML is scale-invariant and statistically invariant. Unlike many Bayesian selection methods, MML doesn't care if you change from measuring length to volume or from Cartesian co-ordinates to polar co-ordinates.
* MML is statistically consistent.  For problems like the [[#{{harvid|Dowe|Wallace|1997}}|Neyman-Scott]] (1948) problem or factor analysis where the amount of data per parameter is bounded above, MML can estimate all parameters with [[statistical consistency]].
* MML accounts for the precision of measurement. It uses the [[Fisher information]] (in the Wallace-Freeman 1987 approximation, or other hyper-volumes in [[#{{harvid|Wallace (posthumous)|2005}}|other approximations]]) to optimally discretize continuous parameters. Therefore the posterior is always a probability, not a probability density.
* MML has been in use since 1968. MML coding schemes have been developed for several distributions, and many kinds of machine learners including unsupervised classification, decision trees and graphs, DNA sequences, [[Bayesian network]]s, neural networks (one-layer only so far), image compression, image and function segmentation, etc.