# Stein's Method Meets Computational Statistics: A Review of Some Recent Developments

arXiv: https://arxiv.org/abs/2105.03481 · HTML: https://mlsanity.com/paper/2105.03481/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2021.

## Built on by (most cited first, 30 of 32)

- [Particle Denoising Diffusion Sampler](https://mlsanity.com/paper/2402.06320/) (2024)
- [Composite Goodness-of-fit Tests with Kernels](https://mlsanity.com/paper/2111.10275/) (2021)
- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [Targeted Separation and Convergence with Kernel Discrepancies](https://mlsanity.com/paper/2209.12835/) (2022)
- [Generalised Bayesian Inference for Discrete Intractable Likelihood](https://mlsanity.com/paper/2206.08420/) (2022)
- [Controlling Moments with Kernel Stein Discrepancies](https://mlsanity.com/paper/2211.05408/) (2022)
- [Stein transport for Bayesian inference](https://mlsanity.com/paper/2409.01464/) (2024)
- [A kernel Stein test of goodness of fit for sequential models](https://mlsanity.com/paper/2210.10741/) (2022)
- [Conditional Bayesian Quadrature](https://mlsanity.com/paper/2406.16530/) (2024)
- [A Dictionary of Closed-Form Kernel Mean Embeddings](https://mlsanity.com/paper/2504.18830/) (2025)
- [Meta-learning Control Variates: Variance Reduction with Limited Data](https://mlsanity.com/paper/2303.04756/) (2023)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy](https://mlsanity.com/paper/2304.14762/) (2023)
- [Nystr"om Kernel Stein Discrepancy](https://mlsanity.com/paper/2406.08401/) (2024)
- [A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spaces](https://mlsanity.com/paper/2206.04552/) (2022)
- [Stein's method for marginals on large graphical models](https://mlsanity.com/paper/2410.11771/) (2024)
- [The Minimax Lower Bound of Kernel Stein Discrepancy Estimation](https://mlsanity.com/paper/2510.15058/) (2025)
- [Neural Stein critics with staged L2-regularization](https://mlsanity.com/paper/2207.03406/) (2022)
- [The Polynomial Stein Discrepancy for Assessing Moment Convergence](https://mlsanity.com/paper/2412.05135/) (2024)
- [Fast and Scalable Score-Based Kernel Calibration Tests](https://mlsanity.com/paper/2510.14711/) (2025)
- [Robust inference using density-powered Stein operators](https://mlsanity.com/paper/2511.03963/) (2025)
- [Efficient Learning of Stationary Diffusions with Stein-type Discrepancies](https://mlsanity.com/paper/2601.16597/) (2026)
- [Kernel Tests of Equivalence](https://mlsanity.com/paper/2603.10886/) (2026)
- [Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD](https://mlsanity.com/paper/2607.24235/) (2026)
- [Bayes Hilbert Spaces for Posterior Approximation](https://mlsanity.com/paper/2304.09053/) (2023)
- [Monte Carlo with kernel-based Gibbs measures: Guarantees for probabilistic herding](https://mlsanity.com/paper/2402.11736/) (2024)
- [Even Faster Kernel Matrix Linear Algebra via Density Estimation](https://mlsanity.com/paper/2510.02540/) (2025)
- [TASTE: Task-Aware Out-of-Distribution Detection via Stein Operators](https://mlsanity.com/paper/2602.07640/) (2026)
- [Stein Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2502.03587/) (2025)
- [Quenched large deviations for Monte Carlo integration with Coulomb gases](https://mlsanity.com/paper/2508.01392/) (2025)

## Abstract (arXiv)

Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to significant advances in computational statistics in recent years. The goal of this survey is to bring together some of these recent developments and, in doing so, to stimulate further research into the successful field of Stein's method and statistics. The topics we discuss include tools to benchmark and compare sampling methods such as approximate Markov chain Monte Carlo, deterministic alternatives to sampling methods, control variate techniques, parameter estimation and goodness-of-fit testing.