Exchangeable pairs and Poisson approximation

By Sourav Chatterjee, Persi Diaconis, Elizabeth Meckes. 2004

106 citations recorded by the source corpus.

This is a survery paper on Poisson approximation using Stein's method of exchangeable pairs. We illustrate using Poisson-binomial trials and many variations on three classical problems of combinatorial probability: the matching problem, the coupon collector's problem, and the birthday problem. While many details are new, the results are closely related to a body of work developed by Andrew Barbour, Louis Chen, Richard Arratia, Lou Gordon, Larry Goldstein, and their collaborators. Some comparison with these other approaches is offered.

Subfields: Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c96113491db75ba1828dc24bd6751659c4ce1029

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In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

A short survey of Stein's method (2014, methodology): “A relatively recent survey of Poisson approximation by Stein’s method is given in my paper [26] with Diaconis and Meckes.”
Fundamentals of Stein's method (2011, methodology): “Exchangeable pairs In this section, we develop Stein’s method for Poisson approximation using exchangeable pairs as detailed in [20].”
On fixed points of permutations (2007, background): “See Takács [Ta] for its history, Chapter 4 of Barbour, Holst, Janson [BHJ] or Chatterjee, Diaconis, Meckes [CDM] for modern versions.”
Limit theorems for Betti numbers of random simplicial complexes (2010, methodology): “(For an introduction to topological combinatorics see [4]; for a survey of Stein’s method in proving Poisson approximation theorems see [5], and for an introduction to Stein’s method for normal approximation, see [17].”
MULTIVARIATE NORMAL APPROXIMATION USING EXCHANGEABLE PAIRS (2007, unknown): “The method of exchangeable pairs was extended to Poisson approximation by Chatterjee, Diaconis and Meckes in the survey paper [13], and to a general method of normal approximation for arbitrary functions of independent random variables in [12].”