Static Posterior Inference of Bayesian Probabilistic Programming via Polynomial ...
summary
Automated method derives guaranteed upper and lower bounds on a probabilistic program’s normalized posterior by reducing NPD bounding to bounds on the normalizing constant and solving polynomial optimization problems via sum‑of‑squares style polynomial solving. It handles continuous distributions with infinite support and unbounded while loops by classifying programs into score‑at‑end and score‑recursive, proving a fixed‑point theorem for the former and a multiplicative OST for the latter. Evaluated examples match simulation and run up to 15× faster.
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