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

## TL;DR

This paper investigates how to approximate Dempster-Shafer belief functions from data, focusing on marginal consistency and proper conditioning, to improve the practical application of the Mathematical Theory of Evidence.

## Contribution

It characterizes belief functions that can be marginally consistent with observed frequencies and discusses implications for approximating general belief functions.

## Key findings

- Identifies class of belief functions with marginal consistency
- Provides conditions for proper conditional belief functions
- Discusses implications for inference in MTE

## Abstract

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.