Statistical inference for probabilistic programming with imprecise probability

Develop methods for performing statistical inference in a probabilistic programming language that supports imprecise probability modeled via named Knightian choices and graded monads, including principled procedures to condition on observations and compute posterior convex sets of distributions.

Background

The paper provides a fully compositional semantics for imprecise probability by naming Knightian choices and using graded monads/Markov categories, yielding improved uncertainty bounds and a maximal equational theory.

While the semantic framework is established, the authors point out that practical inference—central to probabilistic programming—remains unresolved for this imprecise-probability setting, motivating research into conditioning and posterior computation over convex sets of distributions in such languages.