Rigorous Approximation of Posterior Inference for Probabilistic Programs
summary
Claims rigorous, nonstochastic posterior bounds for a universal probabilistic language that allows recursion, continuous distributions and conditioning. Method uses interval traces, interval arithmetic, an interval type system (widening for fixed points) and fallback symbolic execution with VINCI volumes and linear optimization. Soundness and (under mild continuity and usage) completeness are proved; a prototype flags wrong HMC on a random walk, reveals multimodality in a Gaussian mixture, handles unbounded loops, and degrades on heavy branching or very high-dimensional models.
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