Compositional imprecise probability: a solution from graded monads and Markov categories
summary
Provides a fully compositional semantic for imprecise probability by naming nondeterministic choices and tracking them with graded monads, giving a dataflow-friendly model in Markov-category style. The construction recovers the usual convex-set semantics (via a map inducing an uplax functor to the convex powerset), yields strictly tighter uncertainty bounds than direct convex-monad composition, and proves maximality: any further quotient breaks compositionality or the imprecise-probability interpretation. Also sketches how sampling and conditioning are interpreted and where extension to infinite cases fails.
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chapters (9)
- 0:00Imprecise probability intro
- 2:26What is imprecise probability
- 5:58Language for imprecise probability
- 8:05Desirable language properties
- 10:31Solving paradox with choices
- 11:55Graded monads for semantics
- 12:38Better uncertainty bounds
- 14:01Conclusion and future work
- 14:45Q&A
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