Reproduce “A Domain-Theoretic Foundation for Imprecise Probability and Credal Sets” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Abbas Edalat, Pietro Di Gianantonio, Amin Farjudian
A domain-theoretic foundation is established for imprecise probability and credal sets, introducing Scott-continuous mappings for interval probabilities, conditional probabilities, and Bayesian updating on general topological spaces. The framework provides sound and complete logical predicates for inference, enhancing the robustness and computational tractability of probabilistic reasoning under uncertainty.
Key insights
- Domain theory offers a unified mathematical foundation that intrinsically supports approximation, computability, and verifiable reasoning for imprecise probability, bridging measure theory, topology, and logic.
- The monotonicity properties of the classical Bayesian update function enable a 'sharp interval extension' for exact computation of posterior interval bounds from imprecise priors and likelihoods.
- The framework provides a systematic and logically rigorous extension of classical probabilistic concepts, allowing for robust inference in systems with partial or ambiguous information.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.