Stein’s method for birth and death chains

@inproceedings{Holmes2004SteinsMF,
title={Stein’s method for birth and death chains},
author={Susan P. Holmes},
year={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 chapter 6 of his book. This is illustrated by first studying the mechanics of comparison between two distributions whose characterizing operators are known, for example the binomial and the Poisson. Then the case where one of the distributions has an unknown characterizing operator is tackled. This is…

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 FOR DISCRETE GIBBS MEASURES 1

• Mathematics
• 2008
Stein’s method provides a way of bounding the distance of a probability distribution to a target distribution μ . Here we develop Stein’s method for the class of discrete Gibbs measures with a

Stein's Method and Stochastic Orderings

• Mathematics
Advances in Applied Probability
• 2012
A stochastic ordering approach is applied with Stein's method for approximation by the equilibrium distribution of a birth-death process. The usual stochastic order and the more general s-convex

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

Stein's Method for the Beta Distribution and the Pólya-Eggenberger Urn

• Mathematics, Computer Science
Journal of Applied Probability
• 2013
Using a characterizing equation for the beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number

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 Meets Statistics: A Review of Some Recent Developments

• Mathematics
• 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

Stein's method for the Beta distribution and the P\'olya-Eggenberger Urn

• Mathematics
• 2012
Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number

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

• Mathematics
Statistical Science
• 2022
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

MULTIVARIATE NORMAL APPROXIMATION USING EXCHANGEABLE PAIRS

• Mathematics
• 2007
Since the introduction of Stein's method in the early 1970s, much research has been done in extending and strengthening it; however, there does not exist a version of Stein's original method of

References

SHOWING 1-10 OF 23 REFERENCES

Stein's Method: Expository Lectures and Applications

• Mathematics
• 2004
A review of Stein’s method applied to the case of discrete random variables and attempt to complete one of Stein's open problems, that of providing a discrete version for chapter 6 of his book.

Nash inequalities for finite Markov chains

• Mathematics
• 1996
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

• Mathematics
• 1991
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