# Sampling-Based Accuracy Testing of Posterior Estimators for General Inference

arXiv: https://arxiv.org/abs/2302.03026 · HTML: https://mlsanity.com/paper/2302.03026/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 74 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [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)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [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)
- [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)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [Likelihood-free inference with emulator networks](https://mlsanity.com/paper/1805.09294/) (2018)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [GATSBI: Generative Adversarial Training for Simulation-Based Inference](https://mlsanity.com/paper/2203.06481/) (2022)
- [Conditional Density Estimation Tools in Python and R with Applications to Photometric Redshifts and Likelihood-Free Cosmological Inference](https://mlsanity.com/paper/1908.11523/) (2019)
- [Posterior samples of source galaxies in strong gravitational lenses with score-based priors](https://mlsanity.com/paper/2211.03812/) (2022)
- [Mining for Dark Matter Substructure: Inferring subhalo population properties from strong lenses with machine learning](https://mlsanity.com/paper/1909.02005/) (2019)
- [Towards constraining warm dark matter with stellar streams through neural simulation-based inference](https://mlsanity.com/paper/2011.14923/) (2020)
- [A neural simulation-based inference approach for characterizing the Galactic Center γ-ray excess](https://mlsanity.com/paper/2110.06931/) (2021)
- [Diagnostic tools of approximate Bayesian computation using the coverage property](https://mlsanity.com/paper/1301.3166/) (2013)

## Built on by (most cited first, 30 of 46)

- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [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)
- [Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability](https://mlsanity.com/paper/2310.13402/) (2023)
- [Balancing Simulation-based Inference for Conservative Posteriors](https://mlsanity.com/paper/2304.10978/) (2023)
- [Multifidelity Simulation-based Inference for Computationally Expensive Simulators](https://mlsanity.com/paper/2502.08416/) (2025)
- [PQMass: Probabilistic Assessment of the Quality of Generative Models using Probability Mass Estimation](https://mlsanity.com/paper/2402.04355/) (2024)
- [A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)](https://mlsanity.com/paper/2407.16550/) (2024)
- [Conditional diffusions for amortized neural posterior estimation](https://mlsanity.com/paper/2410.19105/) (2024)
- [Variational Inference with Coverage Guarantees in Simulation-Based Inference](https://mlsanity.com/paper/2305.14275/) (2023)
- [Field-level simulation-based inference with galaxy catalogs: the impact of systematic effects](https://mlsanity.com/paper/2310.15234/) (2023)
- [Training-Free Bayesian Filtering with Generative Emulators](https://mlsanity.com/paper/2605.20028/) (2026)
- [Simulation-based Inference with the Generalized Kullback-Leibler Divergence](https://mlsanity.com/paper/2310.01808/) (2023)
- [Bayesian Imaging for Radio Interferometry with Score-Based Priors](https://mlsanity.com/paper/2311.18012/) (2023)
- [Discriminative calibration: Check Bayesian computation from simulations and flexible classifier](https://mlsanity.com/paper/2305.14593/) (2023)
- [Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature](https://mlsanity.com/paper/2408.11065/) (2024)
- [Full-waveform earthquake source inversion using simulation-based inference](https://mlsanity.com/paper/2410.23238/) (2024)
- [Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Models](https://mlsanity.com/paper/2511.04792/) (2025)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [Simulation-based inference with scattering representations: scattering is all you need](https://mlsanity.com/paper/2410.11883/) (2024)
- [Conformal C2ST: Turning weak classifiers into strong two-sample tests](https://mlsanity.com/paper/2507.17026/) (2025)
- [Trustworthy scientific inference with generative models](https://mlsanity.com/paper/2508.02602/) (2025)
- [On Uncertainty Calibration for Equivariant Functions](https://mlsanity.com/paper/2510.21691/) (2025)
- [Bridging Simulators with Conditional Optimal Transport](https://mlsanity.com/paper/2510.24631/) (2025)
- [First Estimation of Model Parameters for Neutrino-Induced Nucleon Knockout Using Simulation-Based Inference](https://mlsanity.com/paper/2603.09778/) (2026)
- [Tokenised Flow Matching for Hierarchical Simulation Based Inference](https://mlsanity.com/paper/2604.20723/) (2026)
- [MIRA: A Score for Conditional Distribution Accuracy and Model Comparison](https://mlsanity.com/paper/2605.02014/) (2026)
- [Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problems](https://mlsanity.com/paper/2605.22891/) (2026)
- [An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning](https://mlsanity.com/paper/2607.21702/) (2026)
- [Exposing Disparities in Flood Adaptation for Equitable Future Interventions](https://mlsanity.com/paper/2312.03843/) (2023)

## Abstract (arXiv)

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.