The Geometry of Uncertainty: The Geometry of Imprecise Probabilities

Geometry Meets Uncertainty

Fabio Cuzzolin’s The Geometry of Uncertainty: The Geometry of Imprecise Probabilities brings a fresh mathematical perspective to the study of uncertainty. Part of Springer’s Artificial Intelligence series, the book addresses a central tension in modern reasoning: classical probability theory and Bayesian methods, while powerful, often fall short when dealing with missing data, set-valued observations, or ignorance. Cuzzolin explores how imprecise probability formalisms can model these richer forms of uncertainty.

Inside the Book

The volume builds a rigorous geometric framework for understanding imprecise probabilities. It examines key theories that extend classical probability, including belief functions, random sets, credal sets, possibility theory, and lower previsions. Rather than treating these approaches as disconnected tools, Cuzzolin demonstrates their shared mathematical structure and their relationships within a unified geometric landscape.

• The limitations of additive probability and Bayesian inference for second-order uncertainty
• The hierarchy of imprecise probability theories and their historical development
• Belief functions and the Dempster–Shafer theory of evidence
• Connections between random sets, capacities, and credal sets
• Geometric interpretations that link different uncertainty formalisms

Why This Matters

For researchers and graduate students working in artificial intelligence, statistics, or decision theory, understanding uncertainty is foundational. This book provides a detailed, mathematically careful treatment of the tools needed to represent incomplete or conflicting evidence. The geometric viewpoint offers new intuition for how these formalisms interact, making advanced concepts more accessible.

Who Should Read This Book

The text is best suited to readers with a solid background in probability and mathematics. It will be especially relevant to those studying machine learning, knowledge representation, risk analysis, and formal methods where uncertainty plays a critical role.