# Addressing Misspecification in Simulation-based Inference through Data-driven Calibration

arXiv: https://arxiv.org/abs/2405.08719 · HTML: https://mlsanity.com/paper/2405.08719/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 70 references that are in the map.
- First posted on arXiv 14 May 2024.

## Builds on (most cited first, 30 of 44)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Learning Transferable Features with Deep Adaptation Networks](https://mlsanity.com/paper/1502.02791/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [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)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Using Simulation and Domain Adaptation to Improve Efficiency of Deep Robotic Grasping](https://mlsanity.com/paper/1709.07857/) (2017)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [Optimal Transport Tools (OTT): A JAX Toolbox for all things Wasserstein](https://mlsanity.com/paper/2201.12324/) (2022)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [Sinkhorn Divergences for Unbalanced Optimal Transport](https://mlsanity.com/paper/1910.12958/) (2019)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)
- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [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)

## Built on by (most cited first, 27 of 27)

- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [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)
- [G-Sim: Generative Simulations with Large Language Models and Gradient-Free Calibration](https://mlsanity.com/paper/2506.09272/) (2025)
- [CP4SBI: Local Conformal Calibration of Credible Sets in Simulation-Based Inference](https://mlsanity.com/paper/2508.17077/) (2025)
- [Tests for model misspecification in simulation-based inference: from local distortions to global model checks](https://mlsanity.com/paper/2412.15100/) (2024)
- [Inductive Domain Transfer In Misspecified Simulation-Based Inference](https://mlsanity.com/paper/2508.15593/) (2025)
- [Flow Matching Calibration for Simulation-Based Inference under Model Misspecification](https://mlsanity.com/paper/2509.23385/) (2025)
- [Inferring Optical Tissue Properties from Photoplethysmography using Hybrid Amortized Inference](https://mlsanity.com/paper/2510.02073/) (2025)
- [Synthesizing 3D Abstractions by Inverting Procedural Buildings with Transformers](https://mlsanity.com/paper/2501.17044/) (2025)
- [Simulation-based population inference of LISA's Galactic binaries: Bypassing the global fit](https://mlsanity.com/paper/2506.22543/) (2025)
- [Trustworthy scientific inference with generative models](https://mlsanity.com/paper/2508.02602/) (2025)
- [An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning](https://mlsanity.com/paper/2607.21702/) (2026)
- [Unknown Unknowns: Model Misspecification in Machine Learning for Physics](https://mlsanity.com/paper/2608.13633/) (2026)
- [PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers](https://mlsanity.com/paper/2609.20794/) (2026)
- [Calibrated Multivariate Regression with Localized PIT Mappings](https://mlsanity.com/paper/2409.10855/) (2024)
- [Deep Neural Network Driven Simulation Based Inference Method for Pole Position Estimation under Model Misspecification](https://mlsanity.com/paper/2507.18824/) (2025)
- [Misspecification-robust amortised simulation-based inference using variational methods](https://mlsanity.com/paper/2509.05724/) (2025)
- [Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimation](https://mlsanity.com/paper/2602.06837/) (2026)
- [Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators](https://mlsanity.com/paper/2602.18004/) (2026)
- [Unsupervised Continual Learning for Amortized Bayesian Inference](https://mlsanity.com/paper/2602.22884/) (2026)
- [Information-Preserving Domain Transfer with Unlabeled Data in Misspecified Simulation-Based Inference](https://mlsanity.com/paper/2605.05652/) (2026)
- [MA-SBI: Misspecification-Aware Simulation-Based Inference via Side-Channel Guidance](https://mlsanity.com/paper/2606.16923/) (2026)
- [Simulation-Based Quantum System Inference with Neural Posterior Estimation](https://mlsanity.com/paper/2609.34995/) (2026)
- [A Missing Latent, Not a Missing Simulator: Radius-Augmented Inference for Real JWST Retrieval](https://mlsanity.com/paper/2610.02245/) (2026)

## Abstract (arXiv)

Driven by steady progress in deep generative modeling, simulation-based inference (SBI) has emerged as the workhorse for inferring the parameters of stochastic simulators. However, recent work has demonstrated that model misspecification can compromise the reliability of SBI, preventing its adoption in important applications where only misspecified simulators are available. This work introduces robust posterior estimation~(RoPE), a framework that overcomes model misspecification with a small real-world calibration set of ground-truth parameter measurements. We formalize the misspecification gap as the solution of an optimal transport~(OT) problem between learned representations of real-world and simulated observations, allowing RoPE to learn a model of the misspecification without placing additional assumptions on its nature. RoPE demonstrates how OT and a calibration set provide a controllable balance between calibrated uncertainty and informative inference, even under severely misspecified simulators. Results on four synthetic tasks and two real-world problems with ground-truth labels demonstrate that RoPE outperforms baselines and consistently returns informative and calibrated credible intervals.