Evidence Against Evidence Theory (?!)

This paper is concerned with the apparent greatest weakness of the Mathematical Theory of Evidence (MTE) of Shafer \cite{Shafer:76}, which has been strongly criticized by Wasserman \cite{Wasserman:92ijar} - the relationship to frequencies. Weaknesses of various proposals of probabilistic interpretation of MTE belief functions are demonstrated. A new frequency-based interpretation is presented overcoming various drawbacks of earlier interpretations.Comment: 30 pages. arXiv admin note: substantial text overlap with arXiv:1704.0400

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

Mathematical Theory of Evidence (MTE), a foundation for reasoning under partial ignorance, is blamed to leave frequencies outside (or aside of) its framework. The seriousness of this accusation is obvious: no experiment may be run to compare the performance of MTE-based models of real world processes against real world data. In this paper we consider this problem from the point of view of conditioning in the MTE. We describe the class of belief functions for which marginal consistency with observed frequencies may be achieved and conditional belief functions are proper belief functions,%\ and deal with implications for (marginal) approximation of general belief functions by this class of belief functions and for inference models in MTE.Comment: M.A. K{\l}opotek, S.T. Wierzcho\'n: On Marginally Correct Approximations of Dempster-Shafer Belief Functions from Data. Proc. IPMU'96 (Information Processing and Management of Uncertainty), Grenada (Spain), Publisher: Universitaed de Granada, 1-5 July 1996, Vol II, pp. 769-77