Steins Method

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Normal Approximation by Stein’s Method

Author : Louis H.Y. Chen
Publisher : Springer Science & Business Media
ISBN 13 : 3642150071
Total Pages : 411 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Normal Approximation by Stein’s Method by : Louis H.Y. Chen

Download or read book Normal Approximation by Stein’s Method written by Louis H.Y. Chen and published by Springer Science & Business Media. This book was released on 2010-10-13 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Stein's Method

Author : A. D. Barbour
Publisher : World Scientific
ISBN 13 : 981256280X
Total Pages : 240 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis An Introduction to Stein's Method by : A. D. Barbour

Download or read book An Introduction to Stein's Method written by A. D. Barbour and published by World Scientific. This book was released on 2005 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stein's Method

Author : Persi Diaconis
Publisher : IMS
ISBN 13 : 9780940600621
Total Pages : 154 pages
Book Rating : 4.6/5 (6 download)

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Book Synopsis Stein's Method by : Persi Diaconis

Download or read book Stein's Method written by Persi Diaconis and published by IMS. This book was released on 2004 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: "These papers were presented and developed as expository talks at a summer-long workshop on Stein's method at Stanford's Department of Statistics in 1998."--P. iii.

On Stein's Method for Infinitely Divisible Laws with Finite First Moment

Author : Benjamin Arras
Publisher : Springer
ISBN 13 : 3030150178
Total Pages : 104 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis On Stein's Method for Infinitely Divisible Laws with Finite First Moment by : Benjamin Arras

Download or read book On Stein's Method for Infinitely Divisible Laws with Finite First Moment written by Benjamin Arras and published by Springer. This book was released on 2019-04-24 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction To Stein's Method

Author : Andrew Barbour
Publisher : World Scientific
ISBN 13 : 9814480657
Total Pages : 239 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis An Introduction To Stein's Method by : Andrew Barbour

Download or read book An Introduction To Stein's Method written by Andrew Barbour and published by World Scientific. This book was released on 2005-04-14 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stein's Method and Applications

Author : A. D. Barbour
Publisher : World Scientific
ISBN 13 : 9812562818
Total Pages : 320 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Stein's Method and Applications by : A. D. Barbour

Download or read book Stein's Method and Applications written by A. D. Barbour and published by World Scientific. This book was released on 2005 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Normal Approximations with Malliavin Calculus

Author : Ivan Nourdin
Publisher : Cambridge University Press
ISBN 13 : 1107017777
Total Pages : 255 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Normal Approximations with Malliavin Calculus by : Ivan Nourdin

Download or read book Normal Approximations with Malliavin Calculus written by Ivan Nourdin and published by Cambridge University Press. This book was released on 2012-05-10 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.

Approximate Computation of Expectations

Author : Charles Stein
Publisher : IMS
ISBN 13 : 9780940600089
Total Pages : 172 pages
Book Rating : 4.6/5 ( download)

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Book Synopsis Approximate Computation of Expectations by : Charles Stein

Download or read book Approximate Computation of Expectations written by Charles Stein and published by IMS. This book was released on 1986 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Method and Message of Jesus' Teachings

Author : Robert H. Stein
Publisher : Westminster John Knox Press
ISBN 13 : 9780664255138
Total Pages : 228 pages
Book Rating : 4.2/5 (551 download)

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Book Synopsis The Method and Message of Jesus' Teachings by : Robert H. Stein

Download or read book The Method and Message of Jesus' Teachings written by Robert H. Stein and published by Westminster John Knox Press. This book was released on 1994-01-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This useful and practical book provides the college student, seminarian, church study group, and interested lay person with a much-needed introductory guide on the "how" (method) and the "what" (message) of Jesus' teachings. In this revised edition, Robert Stein updates his classic work, adds a new bibliography, and introduces use of the New Revised Standard Version of the Bible, bringing this important text to a new generation of students.

Poisson Approximation

Author : A. D. Barbour
Publisher :
ISBN 13 :
Total Pages : 298 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Poisson Approximation by : A. D. Barbour

Download or read book Poisson Approximation written by A. D. Barbour and published by . This book was released on 1992 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Poisson "law of small numbers" is a central principle in modern theories of reliability, insurance, and the statistics of extremes. It also has ramifications in apparently unrelated areas, such as the description of algebraic and combinatorial structures, and the distribution of prime numbers. Yet despite its importance, the law of small numbers is only an approximation. In 1975, however, a new technique was introduced, the Stein-Chen method, which makes it possible to estimate the accuracy of the approximation in a wide range of situations. This book provides an introduction to the method, and a varied selection of examples of its application, emphasizing the flexibility of the technique when combined with a judicious choice of coupling. It also contains more advanced material, in particular on compound Poisson and Poisson process approximation, where the reader is brought to the boundaries of current knowledge. The study will be of special interest to postgraduate students and researchers in applied probability as well as computer scientists.

Stein On Writing

Author : Sol Stein
Publisher : St. Martin's Press
ISBN 13 : 1466864990
Total Pages : 324 pages
Book Rating : 4.4/5 (668 download)

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Book Synopsis Stein On Writing by : Sol Stein

Download or read book Stein On Writing written by Sol Stein and published by St. Martin's Press. This book was released on 2014-02-11 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Your future as a writer is in your hands. Whether you are a newcomer or an accomplished professional, a novelist, story writer, or a writer of nonfiction, you will find this book a wealth of immediately useful guidance not available anywhere else. As Sol Stein, renowned editor, author, and instructor, explains, "This is not a book of theory. It is a book of useable solutions-- how to fix writing that is flawed, how to improve writing that is good, how to create interesting writing in the first place." You will find one of the great unspoken secrets of craftsmanship in Chapter 5, called "Markers: The Key to Swift Characterization." In Chapter 7, Stein reveals for he first time in print the wonderful system for creating instant conflict developed in the Playwrights Group of the Actors Studio, of which he was a founder. In "Secrets of Good Dialogue," the premier teacher of dialogue gives you the instantly useable techniques that not only make verbal exchanges exciting but that move the story forward immediately. You won't need to struggle with flashbacks or background material after you've read Chapter 14, which shows you how to bring background into the foreground. Writers of both fiction and nonfiction will relish the amphetamines for speeding up pace, and the many ways to liposuction flab, as well as how to tap originality and recognize what successful titles have in common. You'll discover literary values that enhance writing, providing depth and resonance. You'll bless the day you read Chapters 32 and 33 and discover why revising by starting at page one can be a serious mistake, and how to revise without growing cold on your manuscript. In the pages of this book, nonfiction writers will find a passport to the new revolution in journalism and a guide to using the techniques of fiction to enhance nonfiction. Fresh, useful, informative, and fun to read and reread, Stein on Writing is a book you will mark up, dog-ear, and cherish.

Handbook of Phycological Methods: Culture methods and growth measurements, edited by J. R. Stein

Author : Janet R. Stein-Taylor
Publisher : Cambridge University Press
ISBN 13 : 9780521200493
Total Pages : 536 pages
Book Rating : 4.2/5 (4 download)

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Book Synopsis Handbook of Phycological Methods: Culture methods and growth measurements, edited by J. R. Stein by : Janet R. Stein-Taylor

Download or read book Handbook of Phycological Methods: Culture methods and growth measurements, edited by J. R. Stein written by Janet R. Stein-Taylor and published by Cambridge University Press. This book was released on 1973 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Isolation and purification; General equipment and methods; Special culture methods; Growth measurements; Bioassay.

Modular Forms, a Computational Approach

Author : William A. Stein
Publisher : American Mathematical Soc.
ISBN 13 : 0821839608
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Modular Forms, a Computational Approach by : William A. Stein

Download or read book Modular Forms, a Computational Approach written by William A. Stein and published by American Mathematical Soc.. This book was released on 2007-02-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.

Complex Stochastic Systems

Author : O.E. Barndorff-Nielsen
Publisher : CRC Press
ISBN 13 : 9781420035988
Total Pages : 306 pages
Book Rating : 4.0/5 (359 download)

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Book Synopsis Complex Stochastic Systems by : O.E. Barndorff-Nielsen

Download or read book Complex Stochastic Systems written by O.E. Barndorff-Nielsen and published by CRC Press. This book was released on 2000-08-09 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex stochastic systems comprises a vast area of research, from modelling specific applications to model fitting, estimation procedures, and computing issues. The exponential growth in computing power over the last two decades has revolutionized statistical analysis and led to rapid developments and great progress in this emerging field. In Complex Stochastic Systems, leading researchers address various statistical aspects of the field, illustrated by some very concrete applications. A Primer on Markov Chain Monte Carlo by Peter J. Green provides a wide-ranging mixture of the mathematical and statistical ideas, enriched with concrete examples and more than 100 references. Causal Inference from Graphical Models by Steffen L. Lauritzen explores causal concepts in connection with modelling complex stochastic systems, with focus on the effect of interventions in a given system. State Space and Hidden Markov Models by Hans R. Künschshows the variety of applications of this concept to time series in engineering, biology, finance, and geophysics. Monte Carlo Methods on Genetic Structures by Elizabeth A. Thompson investigates special complex systems and gives a concise introduction to the relevant biological methodology. Renormalization of Interacting Diffusions by Frank den Hollander presents recent results on the large space-time behavior of infinite systems of interacting diffusions. Stein's Method for Epidemic Processes by Gesine Reinert investigates the mean field behavior of a general stochastic epidemic with explicit bounds. Individually, these articles provide authoritative, tutorial-style exposition and recent results from various subjects related to complex stochastic systems. Collectively, they link these separate areas of study to form the first comprehensive overview of this rapidly developing field.

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Complex Analysis

Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 1400831156
Total Pages : 398 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Complex Analysis by : Elias M. Stein

Download or read book Complex Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2010-04-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Theory of Stein Spaces

Author : H. Grauert
Publisher : Springer Science & Business Media
ISBN 13 : 1475743572
Total Pages : 269 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Theory of Stein Spaces by : H. Grauert

Download or read book Theory of Stein Spaces written by H. Grauert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. The classical theorem of Mittag-Leffler was generalized to the case of several complex variables by Cousin in 1895. In its one variable version this says that, if one prescribes the principal parts of a merom orphic function on a domain in the complex plane e, then there exists a meromorphic function defined on that domain having exactly those principal parts. Cousin and subsequent authors could only prove the analogous theorem in several variables for certain types of domains (e. g. product domains where each factor is a domain in the complex plane). In fact it turned out that this problem can not be solved on an arbitrary domain in em, m ~ 2. The best known example for this is a "notched" bicylinder in 2 2 e . This is obtained by removing the set { (z , z ) E e 11 z I ~ !, I z 1 ~ !}, from 1 2 1 2 2 the unit bicylinder, ~ :={(z , z ) E e llz1