arXiv Machine Learning October 12, 2026 By Pietro Carlotti, Sifan Liu, Yuling Yao

Product Monte Carlo: Expectation Under a Product of Densities

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Product Monte Carlo (PMC) is an algorithm that estimates expectations under a product of densities using only Monte Carlo samples from each individual density. By reformulating the intractable product expectation as a regression problem involving computable conditional expectations, PMC provides both point estimates and coherent Bayesian uncertainty quantification. The method achieves higher accuracy, better-calibrated uncertainty, and improved scalability compared to existing techniques, and it does not require density evaluations, enabling its use in simulation‑based inference such as protein image analysis.

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