A New Sampling Method via Approximate Bayesian Computation with Correlated Random Numbers

Bayesian inference for hierarchical and latent-variable models often faces challenges with intractable likelihoods and the complexity of tuning backward-mode posterior samplers. This paper leverages the forward data generative process to achieve exact posterior sampling without direct likelihood evaluation. Starting from a forward-mode validator that produces independent posterior draws, we integrate Approximate Bayesian Computation with non-centered parameterization to induce correlation in latent variables, improving acceptance and mixing. Applications to Bayesian Lasso, random-effects models, and stochastic volatility demonstrate that the correlated sampler achieves substantial computational gains while recovering the exact posterior.