# Factorization of Dempster-Shafer Belief Functions Based on Data

## TL;DR

This paper introduces a new measure within Dempster-Shafer Theory that enables statistical testing of belief function independence, overcoming previous difficulties caused by negative belief values.

## Contribution

A novel measure F is proposed that relates to conditional independence in DST, facilitating the use of standard statistical tests for dependence detection.

## Key findings

- The measure F allows testing independence in belief functions.
- Negative belief values no longer hinder statistical analysis.
- The approach bridges DST with conventional statistical methods.

## Abstract

One important obstacle in applying Dempster-Shafer Theory (DST) is its relationship to frequencies. In particular, there exist serious difficulties in finding factorizations of belief functions from data. In probability theory factorizations are usually related to notion of (conditional) independence and their possibility tested accordingly. However, in DST conditional belief distributions prove to be non-proper belief functions (that is ones connected with negative "frequencies"). This makes statistical testing of potential conditional independencies practically impossible, as no coherent interpretation could be found so far for negative belief function values. In this paper a novel attempt is made to overcome this difficulty. In the proposal no conditional beliefs are calculated, but instead a new measure F is introduced within the framework of DST, closely related to conditional independence, allowing to apply conventional statistical tests for detection of dependence/independence.