Statistical inference with belief functions: A survey

2026-05-08

AI Summary

This study addresses the critical challenge of effectively constructing belief functions to characterize uncertainty in data-scarce scenarios where accurate estimation of probability distributions is difficult. It presents a systematic review and, for the first time, a comprehensive integration of research at the intersection of statistical inference and Dempster–Shafer belief function theory. By tracing the evolution from classical to modern representative approaches, the work clarifies the theoretical foundations and applicability boundaries of various methods. Furthermore, it synthesizes multiple effective strategies for learning belief measures from limited data, thereby offering a coherent methodological framework and theoretical reference for uncertainty modeling and reasoning under data scarcity.

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.

Problem

• belief functions
• statistical inference
• uncertainty
• data scarcity
• belief measure

Innovation

• belief functions
• statistical inference
• uncertainty quantification
• data scarcity
• evidence theory