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

@inproceedings{Anastasiou2021SteinsMM, title={Stein’s Method Meets Statistics: A Review of Some Recent Developments}, author={Andreas Anastasiou and Alessandro Barp and François-Xavier Briol and Bruno Ebner and Robert E. Gaunt and Fatemeh Ghaderinezhad and Jackson Gorham and Arthur and Gretton and Christophe Ley and Qiang Liu and Lester W. Mackey and Chris. J. Oates and Gesine Reinert and Yvik Swan}, year={2021} }

Stein’s method is a collection of tools for analysing distributional comparisons through the study of a class of linear operators called Stein operators. Originally studied in probability, Stein’s method has also enabled some important developments in statistics. This early success has led to a high research activity in this area in recent years. The goal of this survey is to bring together some of these developments in theoretical statistics as well as in computational statistics and, in doing…

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## 24 Citations

### Normal approximation for the posterior in exponential families

- Mathematics
- 2022

In this paper we obtain quantitative Bernstein-von Mises type bounds on the normal approximation of the posterior distribution in exponential family models when centering either around the posterior…

### An asymptotic approach to proving sufficiency of Stein characterisations

- Mathematics
- 2021

In extending Stein’s method to new target distributions, the first step is to find a Stein operator that suitably characterises the target distribution. In this paper, we introduce a widely…

### A Spectral Representation of Kernel Stein Discrepancy with Application to Goodness-of-Fit Tests for Measures on Infinite Dimensional Hilbert Spaces

- Computer Science
- 2022

A novel spectral representation of KSD is provided, making KSD applicable to Hilbert-valued data and revealing the impact of kernel and Stein operator choice on the KSD.

### A Framework for Improving the Characterization Scope of Stein's Method on Riemannian Manifolds

- Mathematics
- 2022

Stein’s method has been widely used to achieve distributional approximations for probability distributions deﬁned in Euclidean spaces. Recently, techniques to extend Stein’s method to manifold-valued…

### A Riemann–Stein kernel method

- MathematicsBernoulli
- 2022

This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation…

### Bayesian data selection

- Computer Science
- 2021

It is proved that the Stein volume criterion is consistent for both data selection and model selection, and consistency and asymptotic normality (Bernstein-von Mises) of the corresponding generalized posterior on parameters are established.

### Ergodic variational flows

- Mathematics
- 2022

This work presents a new class of variational family— ergodic variational ﬂows — that not only enables tractable i.i.d. sampling and density evaluation, but also comes with MCMC-like convergence…

### Vector-Valued Control Variates

- Computer Science
- 2021

Control variates are post-processing tools for Monte Carlo estimators which can lead to significant variance reduction. This approach usually requires a large number of samples, which can be…

### Weibull or not Weibull?

- Mathematics
- 2022

unknown These tests are based on an alternative characterizing representation of the Laplace transform related to the approach in the of Stein’s method. Asymptotic theory of the tests is derived,…

### Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents

- MathematicsArXiv
- 2022

## References

SHOWING 1-10 OF 200 REFERENCES

### Convergence rates for a class of estimators based on Stein’s method

- MathematicsBernoulli
- 2019

Gradient information on the sampling distribution can be used to reduce the variance of Monte Carlo estimators via Stein's method. An important application is that of estimating an expectation of a…

### Stein’s method for discrete Gibbs measures

- Mathematics
- 2008

Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. Here we develop Stein's method for the class of discrete Gibbs measures with a…

### Stein’s method for the bootstrap

- Mathematics
- 2004

This paper gives new proofs for many known results about the convergence in law of the bootstrap distribution to the true distribution of smooth statistics, whether the samples studied come from…

### A short survey of Stein's method

- Mathematics
- 2014

Stein's method is a powerful technique for proving central limit theorems in probability theory when more straightforward approaches cannot be implemented easily. This article begins with a survey of…

### Stein's method, self-normalized limit theory and applications

- Mathematics
- 2011

Stein’s method is a powerful tool in estimating accuracy of various probability approximations. It works for both independent and dependent random variables. It works for normal approximation and…

### Stein’s method for birth and death chains

- Mathematics
- 2004

This article presents a review of Stein's method applied to the case of discrete random variables. We attempt to complete one of Stein's open problems, that of providing a discrete version for…

### Chi-square approximation by Stein's method with application to Pearson's statistic

- Mathematics
- 2015

This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein…

### Stein's method for comparison of univariate distributions

- Mathematics
- 2014

We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on…

### Stein's Method and Birth-Death Processes

- Mathematics, Computer Science
- 2001

The methods introduced here apply to a very large class of approximating distributions on the non-negative integers, among which there is a natural class for higher-order approximations by probability distributions rather than signed measures (as previously).