Statistical inference with belief functions: A survey

TL;DR

This survey reviews methods for statistical inference using belief functions, emphasizing their role in uncertainty quantification when data is insufficient for traditional probability learning.

Contribution

It provides a comprehensive overview of the most significant approaches to belief function inference from statistical data, highlighting recent developments.

Findings

Belief functions effectively model uncertainty with limited data.

Various inference techniques have been developed for belief measures.

The survey identifies key challenges and future directions in the field.

Abstract

Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first step in a reasoning chain based on belief functions is inference: how to learn a belief measure from the available data. In this survey we focus, in particular, on making inference from statistical data, and review the most significant contributions in the area.