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

arXiv: https://arxiv.org/abs/2609.39712 · HTML: https://mlsanity.com/paper/2609.39712/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 43 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
- [Sequential Neural Posterior and Likelihood Approximation](https://mlsanity.com/paper/2102.06522/) (2021)
- [Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2107.01214/) (2021)
- [Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.05120/) (2023)
- [Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimation](https://mlsanity.com/paper/2208.13624/) (2022)
- [Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison](https://mlsanity.com/paper/2103.10522/) (2021)
- [Elastic Net Regularization Paths for All Generalized Linear Models](https://mlsanity.com/paper/2103.03475/) (2021)
- [Partially Exchangeable Networks and Architectures for Learning Summary Statistics in Approximate Bayesian Computation](https://mlsanity.com/paper/1901.10230/) (2019)
- [High-Dimensional Regression with Gaussian Mixtures and Partially-Latent Response Variables](https://mlsanity.com/paper/1308.2302/) (2013)
- [ABC of the Future](https://mlsanity.com/paper/2112.12841/) (2021)
- [A Comprehensive Guide to Simulation-based Inference in Computational Biology](https://mlsanity.com/paper/2409.19675/) (2024)
- [Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings](https://mlsanity.com/paper/2403.07454/) (2024)
- [Posterior SBC: Simulation-Based Calibration Checking Conditional on Data](https://mlsanity.com/paper/2502.03279/) (2025)
- [Simulation-based inference for stochastic nonlinear mixed-effects models with applications in systems biology](https://mlsanity.com/paper/2504.11279/) (2025)

## Abstract (arXiv)

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 to estimate the posterior, incorporating an importance sampling step that introduces a locally amortized likelihood-to-evidence ratio estimator. The local amortization allows the ratio estimator to be evaluated at new parameter--data pairs from a local (data-dependent) design, without re-estimation, which is particularly convenient for our second contribution. The second contribution is localized simulation-based calibration (SBC). Localized SBC provides a graphical diagnostic of 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.