Guaranteed Bounds for Posterior Inference in Universal Probabilistic Programming. (arXiv:2204.02948v1 [cs.PL])

We propose a new method to approximate the posterior distribution of
probabilistic programs by means of computing guaranteed bounds. The starting
point of our work is an interval-based trace semantics for a recursive,
higher-order probabilistic programming language with continuous distributions.
Taking the form of (super-/subadditive) measures, these lower/upper bounds are
non-stochastic and provably correct: using the semantics, we prove that the
actual posterior of a given program is sandwiched between the lower and upper
bounds (soundness); moreover the bounds converge …

arxiv pl posterior programming