# Generalized Bayesian Inference for Scientific Simulators via Amortized Cost Estimation

arXiv: https://arxiv.org/abs/2305.15208 · HTML: https://mlsanity.com/paper/2305.15208/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 62 references that are in the map.
- First posted on arXiv 24 May 2023.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [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)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Epistemic Neural Networks](https://mlsanity.com/paper/2107.08924/) (2021)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models](https://mlsanity.com/paper/1501.03291/) (2015)
- [Likelihood-free inference with emulator networks](https://mlsanity.com/paper/1805.09294/) (2018)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Robust Neural Posterior Estimation and Statistical Model Criticism](https://mlsanity.com/paper/2210.06564/) (2022)
- [Investigating the Impact of Model Misspecification in Neural Simulation-based Inference](https://mlsanity.com/paper/2209.01845/) (2022)
- [Variational methods for simulation-based inference](https://mlsanity.com/paper/2203.04176/) (2022)
- [Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap](https://mlsanity.com/paper/2202.04744/) (2022)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancy](https://mlsanity.com/paper/1909.13339/) (2019)
- [Sequential Neural Posterior and Likelihood Approximation](https://mlsanity.com/paper/2102.06522/) (2021)
- [A comparison of learning rate selection methods in generalized Bayesian inference](https://mlsanity.com/paper/2012.11349/) (2020)
- [Generalized Posteriors in Approximate Bayesian Computation](https://mlsanity.com/paper/2011.08644/) (2020)
- [Misspecification-robust Sequential Neural Likelihood for Simulation-based Inference](https://mlsanity.com/paper/2301.13368/) (2023)
- [Error-guided likelihood-free MCMC](https://mlsanity.com/paper/2010.06735/) (2020)

## Built on by (most cited first, 17 of 17)

- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [sbi reloaded: a toolkit for simulation-based inference workflows](https://mlsanity.com/paper/2411.17337/) (2024)
- [Effortless, Simulation-Efficient Bayesian Inference using Tabular Foundation Models](https://mlsanity.com/paper/2504.17660/) (2025)
- [A Probabilistic Framework for LLM-Based Model Discovery](https://mlsanity.com/paper/2602.18266/) (2026)
- [Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data](https://mlsanity.com/paper/2501.13483/) (2025)
- [Does Unsupervised Domain Adaptation Improve the Robustness of Amortized Bayesian Inference? A Systematic Evaluation](https://mlsanity.com/paper/2502.04949/) (2025)
- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [Robust Simulation-Based Inference under Missing Data via Neural Processes](https://mlsanity.com/paper/2503.01287/) (2025)
- [Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings](https://mlsanity.com/paper/2403.07454/) (2024)
- [Neural timescales from a computational perspective](https://mlsanity.com/paper/2409.02684/) (2024)
- [Minimum Distance Summaries for Robust Neural Posterior Estimation](https://mlsanity.com/paper/2602.09161/) (2026)
- [Amortized Simulation-Based Inference in Generalized Bayes via Neural Posterior Estimation](https://mlsanity.com/paper/2601.22367/) (2026)
- [Amortized Bayesian Decision Making for simulation-based models](https://mlsanity.com/paper/2312.02674/) (2023)
- [Generalized Bayes for Causal Inference](https://mlsanity.com/paper/2603.03035/) (2026)
- [Identifiability and amortized inference limitations in Kuramoto models](https://mlsanity.com/paper/2603.21752/) (2026)

## Abstract (arXiv)

Simulation-based inference (SBI) enables amortized Bayesian inference for simulators with implicit likelihoods. But when we are primarily interested in the quality of predictive simulations, or when the model cannot exactly reproduce the observed data (i.e., is misspecified), targeting the Bayesian posterior may be overly restrictive. Generalized Bayesian Inference (GBI) aims to robustify inference for (misspecified) simulator models, replacing the likelihood-function with a cost function that evaluates the goodness of parameters relative to data. However, GBI methods generally require running multiple simulations to estimate the cost function at each parameter value during inference, making the approach computationally infeasible for even moderately complex simulators. Here, we propose amortized cost estimation (ACE) for GBI to address this challenge: We train a neural network to approximate the cost function, which we define as the expected distance between simulations produced by a parameter and observed data. The trained network can then be used with MCMC to infer GBI posteriors for any observation without running additional simulations. We show that, on several benchmark tasks, ACE accurately predicts cost and provides predictive simulations that are closer to synthetic observations than other SBI methods, especially for misspecified simulators. Finally, we apply ACE to infer parameters of the Hodgkin-Huxley model given real intracellular recordings from the Allen Cell Types Database. ACE identifies better data-matching parameters while being an order of magnitude more simulation-efficient than a standard SBI method. In summary, ACE combines the strengths of SBI methods and GBI to perform robust and simulation-amortized inference for scientific simulators.