An Introduction to Stein's Method - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Stein's Method write by A. D. Barbour. This book was released on 2005. An Introduction to Stein's Method available in PDF, EPUB and Kindle. A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.
Normal Approximation by Stein’s Method
Normal Approximation by Stein’s Method - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Normal Approximation by Stein’s Method write by Louis H.Y. Chen. This book was released on 2010-10-13. Normal Approximation by Stein’s Method available in PDF, EPUB and Kindle. Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.
Stein's Method and Applications
Stein's Method and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stein's Method and Applications write by A. D. Barbour. This book was released on 2005. Stein's Method and Applications available in PDF, EPUB and Kindle. 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.
On Stein's Method for Infinitely Divisible Laws with Finite First Moment
On Stein's Method for Infinitely Divisible Laws with Finite First Moment - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Stein's Method for Infinitely Divisible Laws with Finite First Moment write by Benjamin Arras. This book was released on 2019-04-24. On Stein's Method for Infinitely Divisible Laws with Finite First Moment available in PDF, EPUB and Kindle. This book focuses on quantitative approximation results for weak limit theorems when the target limiting law is infinitely divisible with finite first moment. Two methods are presented and developed to obtain such quantitative results. At the root of these methods stands a Stein characterizing identity discussed in the third chapter and obtained thanks to a covariance representation of infinitely divisible distributions. The first method is based on characteristic functions and Stein type identities when the involved sequence of random variables is itself infinitely divisible with finite first moment. In particular, based on this technique, quantitative versions of compound Poisson approximation of infinitely divisible distributions are presented. The second method is a general Stein's method approach for univariate selfdecomposable laws with finite first moment. Chapter 6 is concerned with applications and provides general upper bounds to quantify the rate of convergence in classical weak limit theorems for sums of independent random variables. This book is aimed at graduate students and researchers working in probability theory and mathematical statistics.
Approximate Computation of Expectations
Approximate Computation of Expectations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximate Computation of Expectations write by Charles Stein. This book was released on 1986. Approximate Computation of Expectations available in PDF, EPUB and Kindle.
