Reasoning with random sets: An agenda for the future
This work proposes foundational advancements in uncertainty theory, potentially impacting fields such as climate science and AI, but it is incremental as it builds on existing random set frameworks.
The paper outlines a future research agenda for developing a comprehensive theory of statistical reasoning with random sets and belief functions, aiming to generalize logistic regression and probability laws, enhance geometric uncertainty approaches, and apply these to high-impact areas like climate change and machine learning.
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.