# 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…

## 35 Citations

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

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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

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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…

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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…

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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

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- 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…

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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

- MathematicsStatistical Science
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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

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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…

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