mlsanityData to 14 Oct 2026

Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks

arXiv 2112.08866 ↗First posted 16 Dec 2021stat.ME cs.LG stat.MLcited by 49

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Abstract (arXiv)

Neural density estimators have proven remarkably powerful in performing efficient simulation-based Bayesian inference in various research domains. In particular, the BayesFlow framework uses a two-step approach to enable amortized parameter estimation in settings where the likelihood function is implicitly defined by a simulation program. But how faithful is such inference when simulations are poor representations of reality? In this paper, we conceptualize the types of model misspecification arising in simulation-based inference and systematically investigate the performance of the BayesFlow framework under these misspecifications. We propose an augmented optimization objective which imposes a probabilistic structure on the latent data space and utilize maximum mean discrepancy (MMD) to detect potentially catastrophic misspecifications during inference undermining the validity of the obtained results. We verify our detection criterion on a number of artificial and realistic misspecifications, ranging from toy conjugate models to complex models of decision making and disease outbreak dynamics applied to real data. Further, we show that posterior inference errors increase as a function of the distance between the true data-generating distribution and the typical set of simulations in the latent summary space. Thus, we demonstrate the dual utility of MMD as a method for detecting model misspecification and as a proxy for verifying the faithfulness of amortized Bayesian inference.

Key facts. Cited by 49 papers in the map (data through 14 Oct 2026). Builds on 35 of its 85 references that are in the map. First posted on arXiv 16 Dec 2021.

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35 of 85 references.

References · 35

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  11. 2021Benchmarking Simulation-Based Inferencecited by 162
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23 more
  1. 2020BayesFlow: Learning complex stochastic models with invertible neural networkscited by 144
  2. 2018Validating Bayesian Inference Algorithms with Simulation-Based Calibrationcited by 124
  3. 2020On Contrastive Learning for Likelihood-free Inferencecited by 98
  4. 2014Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing Itcited by 95
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  17. 2020OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germanycited by 18
  18. 2019Robust Approximate Bayesian Inference with Synthetic Likelihoodcited by 14
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Citing papers per year: 2022: 3; 2023: 8; 2024: 9; 2025: 16; 2026: 13.

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  1. 2023Learning Robust Statistics for Simulation-based Inference under Model Misspecificationcited by 48
  2. 2023JANA: Jointly Amortized Neural Approximation of Complex Bayesian Modelscited by 41
  3. 2024Neural Methods for Amortized Inferencecited by 39
  4. 2023BayesFlow: Amortized Bayesian Workflows With Neural Networkscited by 32
  5. 2025Simulation-Based Inference: A Practical Guidecited by 32
  6. 2024Addressing Misspecification in Simulation-based Inference through Data-driven Calibrationcited by 27
  7. 2022Reliable amortized variational inference with physics-based latent distribution correctioncited by 25
  8. 2024Amortized Probabilistic Conditioning for Optimization, Simulation and Inferencecited by 23
  9. 2023Sensitivity-Aware Amortized Bayesian Inferencecited by 20
  10. 2023Adversarial robustness of amortized Bayesian inferencecited by 17
  11. 2024Amortized Bayesian Multilevel Modelscited by 14
  12. 2025Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Datacited by 11
37 more
  1. 2025Does Unsupervised Domain Adaptation Improve the Robustness of Amortized Bayesian Inference? A Systematic Evaluationcited by 10
  2. 2025Simulation-based Bayesian inference under model misspecificationcited by 9
  3. 2026BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Pythoncited by 9
  4. 2023Misspecification-robust Sequential Neural Likelihood for Simulation-based Inferencecited by 8
  5. 2024Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigationcited by 8
  6. 2025G-Sim: Generative Simulations with Large Language Models and Gradient-Free Calibrationcited by 8
  7. 2024Domain-Adaptive Neural Posterior Estimation for Strong Gravitational Lens Analysiscited by 7
  8. 2024Preconditioned Neural Posterior Estimation for Likelihood-free Inferencecited by 6
  9. 2022Meta-Uncertainty in Bayesian Model Comparisoncited by 5
  10. 2025Robust Simulation-Based Inference under Missing Data via Neural Processescited by 5
  11. 2025Improving the Accuracy of Amortized Model Comparison with Self-Consistencycited by 5
  12. 2024Demonstrating the power and flexibility of variational assumptions for amortized neural posterior estimation in environmental applicationscited by 4
  13. 2025Inductive Domain Transfer In Misspecified Simulation-Based Inferencecited by 4
  14. 2023Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inferencecited by 3
  15. 2024Amortized Bayesian Workflowcited by 3
  16. 2025Amortized Bayesian Mixture Modelscited by 3
  17. 2025Posterior SBC: Simulation-Based Calibration Checking Conditional on Datacited by 3
  18. 2025PriorGuide: Test-Time Prior Adaptation for Simulation-Based Inferencecited by 3
  19. 2022Improving the Accuracy of Marginal Approximations in Likelihood-Free Inference via Localisationcited by 2
  20. 2025Cryo-em images are intrinsically low dimensionalcited by 2
  21. 2025Representative, Informative, and De-Amplifying: Requirements for Robust Bayesian Active Learning under Model Misspecificationcited by 2
  22. 2025Flow Matching Calibration for Simulation-Based Inference under Model Misspecificationcited by 2
  23. 2023Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Modelscited by 1
  24. 2025Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Modelscited by 1
  25. 2025Simulation-based population inference of LISA's Galactic binaries: Bypassing the global fitcited by 1
  26. 2026Conditional Neural Bayes Ratio Estimation for Experimental Design Optimisationcited by 1
  27. 2026An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learningcited by 1
  28. 2026Amortized Bayesian Inference on Multilevel Models of Arbitrary Structurecited by 1
  29. 2026Preconditioned Robust Neural Posterior Estimation for Misspecified Simulatorscited by 0
  30. 2026Unsupervised Continual Learning for Amortized Bayesian Inferencecited by 0
  31. 2026Improving moment tensor solutions under Earth structure uncertainty with simulation-based inferencecited by 0
  32. 2026Overcoming Selection Bias in Statistical Studies With Amortized Bayesian Inferencecited by 0
  33. 2026Information-Preserving Domain Transfer with Unlabeled Data in Misspecified Simulation-Based Inferencecited by 0
  34. 2026Amortized Probabilistic Retrieval of Atmospheric CO2 from OCO-2 Spectra Using Deep Learning with Laplace Approximations and Normalizing Flowscited by 0
  35. 2026Wrong Operator or Blind Design? A Post-Training Diagnostic for Physics-Informed Coefficient Learningcited by 0
  36. 2026Mitigating Representation Gaps in Amortized Bayesian Inference with Auxiliary Supervisioncited by 0
  37. 2026How Well Do Prior-Data Fitted Networks Amortize Bayesian Inference?cited by 0