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Mathematical Theory of Evidence (MTE), a foundation for reasoning underpartial ignorance, is blamed to leave frequencies outside (or aside of) itsframework. The seriousness of this accusation is obvious: no experiment may berun to compare the performance of MTE-based models of real world processesagainst real world data.  In this paper we consider this problem from the point of view of conditioningin the MTE. We describe the class of belief functions for which marginalconsistency with observed frequencies may be achieved and conditional belieffunctions are proper belief functions,%\ and deal with implications for(marginal) approximation of general belief functions by this class of belieffunctions and for inference models in MTE.

On Marginally Correct Approximations of Dempster-Shafer Belief Functions from Data