Probability Surveys

Fundamentals of Stein’s method

Nathan Ross

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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 relation to concentration of measure inequalities. The material is presented at a level accessible to beginning graduate students studying probability with the main emphasis on the themes that are common to these topics and also to much of the Stein’s method literature.

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Probab. Surveys Volume 8 (2011), 210-293.

First available in Project Euclid: 28 October 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60C05: Combinatorial probability
Secondary: 05C80: Random graphs [See also 60B20]

Stein’s method distributional approximation concentration of measure inequalities size-bias distribution exchangeable pairs


Ross, Nathan. Fundamentals of Stein’s method. Probab. Surveys 8 (2011), 210--293. doi:10.1214/11-PS182.

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