Amortized ratio-estimation importance sampling and localized simulation-based calibration for intractable likelihoods

We consider simulation-based Bayesian inference (SBI) for the parameters of models with intractable likelihoods but tractable forward simulation. Building on Gaussian mixtures-of-experts surrogates, as a first contribution we develop a sequential procedure for posterior estimation in which progressively localized, data informed, conditional density approximations are used as proposal distributions. A final surrogate of the posterior distribution is then corrected using an importance sampling step that introduces a locally amortized likelihood-to-evidence ratio estimator. A second contribution is localized simulation-based calibration (SBC). Localized SBC probe calibration over neighborhoods that are deliberately broader than the available posterior, at low additional computational cost. Rather than repeatedly running the full inference procedure for each simulated pseudo-observation, localized SBC fits the local surrogate and ratio estimator only once for each local design, and reuses them across all pseudo-observations. This approach is particularly appealing for SBI applications. We evaluate both contributions on three case studies, including a real-data epidemiological application.