Stein's Method and Applications (Lecture Notes Series, Institute for Mathematical Sciences, Vol. 5) (Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore) | 
 enlarge | Author: A. D. Barbour
Publisher: World Scientific Publishing Company
Category: Book
List Price: $82.00
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Sales Rank: 1852743
Media: Hardcover
Pages: 320
Number Of Items: 1
Shipping Weight (lbs): 1.3
Dimensions (in): 9 x 6 x 0.9
ISBN: 9812562818
Dewey Decimal Number: 519.24
EAN: 9789812562814
Publication Date: May 2005
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Product Description
Stein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 1983, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers in the collection include applications to the study of random binary search trees, Brownian motion on manifolds, Monte-Carlo integration, Edgeworth expansions, regenerative phenomena, the geometry of random point sets, and random matrices.
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| Customer Reviews:
collection of papers on specialized probability topic September 1, 2007
Michael R. Chernick (Holland PA)
27 out of 27 found this review helpful
This book is a collection of papers presented at a conference in Singapore honoring Charles Stein and his interesting probability trick that has found many applications in the asymptotic theory of averages (CLT) and point process limit theorems (Poisson limit) for both independent variables and weakly dependent stochastic processes. Stein's original work was published in the 6th Berkeley Symposium in 1972 and the conference was a celebration of thirty years of research that has shown the method to be surprisingly powerful. The book editors Barbour and Chen are both major contributors to the theory and the articles are expository presentations of results. Chen was a student of Stein's who showed how the method could be used to develop limit theorems and approximations in the case of point process convergence to a Poisson limit. The book is interesting because of its development of an extension of classical probability results to weakly dependent cases. A colleague of mine was particularly interested in finding a Berry-Esseen bound for a stationary Markov process. I believe that the theorem in one of the papers that uses weak dependence conditions with Stein's method to prove a Berry-Esseen bound. This book will be of interest to probabilists and statisticians who are interested in applying asymptotic theory. However it requires knowledge of probability theory at an advanced level.
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