# Product Monte Carlo

Expectations under a product of densities become a regression on a consensus and a discrepancy: using only Monte Carlo draws from each component and no density evaluations, the method estimates arbitrary expectations. On 11 million simulated HIGGS collision events, PMC-MLP reaches an estimation error of 0.0001 with 0.1092 minutes of merge time, about 10% of full-data MCMC runtime; in a privacy-restricted respiratory clinical trial, every PMC variant merges more cheaply than GBF.

Expectations under a product of densities become a regression on a consensus and a discrepancy: using only Monte Carlo draws from each component and no density evaluations, the method estimates arbitrary expectations. On 11 million simulated HIGGS collision events, PMC-MLP reaches an estimation error of 0.0001 with 0.1092 minutes of merge time, about 10% of full-data MCMC runtime; in a privacy-restricted respiratory clinical trial, every PMC variant merges more cheaply than GBF.