Reasoning with random sets: An agenda for the future

TL;DR

This paper outlines a future research agenda for the theory of random sets and belief functions, emphasizing the development of statistical reasoning, geometric approaches, and applications in climate change and machine learning.

Contribution

It proposes new directions for advancing the theory of random sets, including generalizing probabilistic laws and expanding geometric uncertainty models.

Findings

Identifies key areas for theoretical development

Suggests applications in climate change and machine learning

Highlights the need for generalized uncertainty measures

Abstract

In this paper, we discuss a potential agenda for future work in the theory of random sets and belief functions, touching upon a number of focal issues: the development of a fully-fledged theory of statistical reasoning with random sets, including the generalisation of logistic regression and of the classical laws of probability; the further development of the geometric approach to uncertainty, to include general random sets, a wider range of uncertainty measures and alternative geometric representations; the application of this new theory to high-impact areas such as climate change, machine learning and statistical learning theory.