SMML estimators for 1-dimensional continuous data

The minimum message length(MML) principle[4] is an information theoretic criterion that links data compression with statistical inference [3]. It has a number of useful properties and it has close connections with Kolmogorov complexity [5]. Using the MML principle to construct estimators is known to be NPhard in general [1] so it is common to use approximations in practice [3]. The term'strict minimum message length' (SMML) is used to distinguish the exact MML criterion from these approximations. The only known algorithm for calculating an SMML estimator is Farr's algorithm [1] which applies to data taking values in a finite set which is (in some sense) 1-dimensional.