  Strict Minimum Message Length (SMML) is an information-theoretic statistical
inference method widely cited (but only with informal arguments) as providing
estimations that are consistent for general estimation problems. It is,
however, almost invariably intractable to compute, for which reason only
approximations of it (known as MML algorithms) are ever used in practice. Using
novel techniques that allow for the first time direct, non-approximated
analysis of SMML solutions, we investigate the Neyman-Scott estimation problem,
an oft-cited showcase for the consistency of MML, and show that even with a
natural choice of prior neither SMML nor its popular approximations are
consistent for it, thereby providing a counterexample to the general claim.
This is the first known explicit construction of an SMML solution for a
natural, high-dimensional problem.
