# Stein's Method: Expository Lectures and Applications

@inproceedings{Diaconis2004SteinsME, title={Stein's Method: Expository Lectures and Applications}, author={Persi Diaconis and Susan P. Holmes}, year={2004} }

This article presents a review of Stein’s method applied to the case of discrete random variables. [... ] Key Method Then the case where one of the distributions has an unknown characterizing operator is tackled. This is done for the hypergeometric which is then compared to a binomial. Finally the general case of the comparison of two probability distributions that can be seen as the stationary distributions of two birth and death chains is treated and conditions of the validity of the method are conjectured. Expand

## 83 Citations

### 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…

### Stein's method for normal approximation

- Mathematics
- 2005

Stein’s method originated in 1972 in a paper in the Proceedings of the Sixth Berkeley Symposium. In that paper, he introduced the method in order to determine the accuracy of the normal approximation…

### 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…

### 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 OF NORMAL APPROXIMATION: SOME RECOLLECTIONS AND REFLECTIONS BY LOUIS

- Mathematics
- 2021

This paper is a short exposition of Stein’s method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of…

### Stein's method for Conditional Central Limit Theorem

- Mathematics
- 2021

In the seventies, Charles Stein revolutionized the way of proving the Central Limit Theorem by introducing a method that utilizes a characterization equation for Gaussian distribution. In the last 50…

### Contributions to Stein's method and some limit theorems in probability

- Mathematics
- 2010

Author(s): Dey, Partha Sarathi | Advisor(s): Chatterjee, Sourav; Evans, Steven N | Abstract: In this dissertation we investigate three different problems related to (1) concentration inequalities…

### Stein’s method of normal approximation: Some recollections and reflections

- MathematicsThe Annals of Statistics
- 2021

This paper is a short exposition of Stein’s method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of…

### Fundamentals of Stein's method

- Mathematics
- 2011

This survey article discusses the main concepts and techniques of Stein's method for distributional approximation by the normal, Poisson, exponential, and geometric distributions, and also its…

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

- Mathematics
- 2021

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…

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