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

2026-09-30

AI Summary

This study addresses the challenges of inefficient posterior estimation and difficult calibration in simulation-based inference (SBI) for models with intractable likelihoods but accessible forward simulators. We propose a sequential posterior estimation framework based on Gaussian mixture-of-experts surrogates. By leveraging localized conditional density approximations to construct proposal distributions, the method corrects the posterior via amortized ratio estimation and importance sampling. Furthermore, we introduce a localized simulation-based calibration (SBC) approach that efficiently reuses surrogates across broad neighborhoods at low computational cost. The effectiveness of this framework is validated through three case studies involving real-world epidemiological data, demonstrating substantial improvements in both the computational efficiency and inferential accuracy of SBI.

Abstract

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.

Problem

• simulation-based inference
• intractable likelihoods
• posterior estimation
• calibration
• importance sampling

Innovation

• Simulation-based inference
• Amortized ratio estimation
• Importance sampling
• Localized simulation-based calibration
• Intractable likelihoods