# Misspecification-robust Sequential Neural Likelihood for Simulation-based Inference

arXiv: https://arxiv.org/abs/2301.13368 · HTML: https://mlsanity.com/paper/2301.13368/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 112 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 30 of 55)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (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)
- [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)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Bayesian Workflow](https://mlsanity.com/paper/2011.01808/) (2020)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)

## Built on by (most cited first, 8 of 8)

- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [Generalized Bayesian Inference for Scientific Simulators via Amortized Cost Estimation](https://mlsanity.com/paper/2305.15208/) (2023)
- [Does Unsupervised Domain Adaptation Improve the Robustness of Amortized Bayesian Inference? A Systematic Evaluation](https://mlsanity.com/paper/2502.04949/) (2025)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigation](https://mlsanity.com/paper/2406.03154/) (2024)
- [Preconditioned Neural Posterior Estimation for Likelihood-free Inference](https://mlsanity.com/paper/2404.13557/) (2024)
- [Bayesian calibration of differentiable agent-based models](https://mlsanity.com/paper/2305.15340/) (2023)

## Abstract (arXiv)

Simulation-based inference techniques are indispensable for parameter estimation of mechanistic and simulable models with intractable likelihoods. While traditional statistical approaches like approximate Bayesian computation and Bayesian synthetic likelihood have been studied under well-specified and misspecified settings, they often suffer from inefficiencies due to wasted model simulations. Neural approaches, such as sequential neural likelihood (SNL) avoid this wastage by utilising all model simulations to train a neural surrogate for the likelihood function. However, the performance of SNL under model misspecification is unreliable and can result in overconfident posteriors centred around an inaccurate parameter estimate. In this paper, we propose a novel SNL method, which through the incorporation of additional adjustment parameters, is robust to model misspecification and capable of identifying features of the data that the model is not able to recover. We demonstrate the efficacy of our approach through several illustrative examples, where our method gives more accurate point estimates and uncertainty quantification than SNL.