The m-sophistication of a finite binary string x is introduced as a
generalization of some parameter in the proof that complexity of complexity is
rare. A probabilistic near sufficient statistic of x is given which length is
upper bounded by the m-sophistication of x within small additive terms. This
shows that m-sophistication is lower bounded by coarse sophistication and upper
bounded by sophistication within small additive terms. It is also shown that
m-sophistication and coarse sophistication can not be approximated by an upper
or lower semicomputable function, not even within very large error.Comment: 13 pages, draf