Does anybody have suggestions on what to read to learn more about couplings pertaining to statistics?


I'm working on a research project on Poisson approximations and am looking to perform a coupling on the unknown distribution. However, I cannot find much material on how to perform a coupling and the general calculations for it. I haven't had formal training on measure theory or intense probability theory, just upper level statistics courses. Any suggestions?



Reading Material on Couplings
My friend Marty suggests the Lindvall book as well as


H. Thorisson, Coupling, Stationarity, and Regeneration. Springer, New York, 2000. 


<http://www.springer.com/mathematics/probability/book/978-0-387-98779-8>


and points out that coupling is used now in basic textbooks in stochastic processes to prove the ergodic theorem for Markov Chains. So he recommends 


Geoffrey Grimmett and David Stirzaker, Probability and Random Processes, 3rd edition, Oxford University Press, 2001. 


<http://ukcatalogue.oup.com/product/9780198572220.do>


A monograph that presents the 1975 Stein-Chen method: 


A. D. Barbour, Lars Holst, and Svante Janson, Poisson Approximation 


<http://ukcatalogue.oup.com/product/academic/series/mathematics/osip/9780198522355.do?sortby=bookTitleAscend>


A rare accessible discussion is in chapter 2 of:


Ross, Sheldon and Peköz, Erol (2007). A second course in probability. www.ProbabilityBookstore.com. ISBN 978-0979570407.


Link to page for Peköz, which gives further link for book purchase to Amazon:


<http://smgpublish.bu.edu/pekoz/>


A number of useful links at 


<http://www.math.lsa.umich.edu/~fomin/525w07.html> 


and see


<http://en.wikipedia.org/wiki/Stein%27s_method> 


<http://en.wikipedia.org/wiki/Coupling_%28probability%29>


