On Marginally Correct Approximations of Dempster-Shafer Belief Functions from Data
This work tackles a foundational issue in the Mathematical Theory of Evidence, allowing for empirical comparison of models against real-world data, which is crucial for researchers in uncertainty reasoning.
The paper addresses the problem of reconciling Dempster-Shafer belief functions with observed frequencies, enabling experimental validation of MTE-based models. It identifies a class of belief functions that achieve marginal consistency with data and explores implications for approximation and inference.
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.