• Corpus ID: 61361369

Stein's Method: Expository Lectures and Applications

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

Stein’s method for birth and death chains

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

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

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

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


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

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

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

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

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

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



Nash inequalities for finite Markov chains

This paper develops bounds on the rate of decay of powers of Markov kernels on finite state spaces. These are combined with eigenvalue estimates to give good bounds on the rate of convergence to

A bound for the error in the normal approximation to the distribution of a sum of dependent random variables

This paper has two aims, one fairly concrete and the other more abstract. In Section 3, bounds are obtained under certain conditions for the departure of the distribution of the sum of n terms of a

Closed Form Summation for Classical Distributions: Variations on Theme of De Moivre

De Moivre gave a simple closed form expression for the mean absolute deviation of the binomial distribution. Later authors showed that similar closed form expressions hold for many of the other

On the binary expansion of a random integer

Permutation Groups

Whatever you have to do with a structure-endowed entity Σ try to determine its group of automorphisms. .. You can expect to gain a deep insight into the constitution of Σ in this way. 1 Automorphism

Distance Regular Graphs

Inequalities are obtained between the various parameters of a distance-regular graph. In particular, if k1 is the valency and k2 is the number of vertices at distance two from a given vertex, then in

The Distribution of Leading Digits and Uniform Distribution Mod 1

Approximate computation of expectations