Stein S Method And Applications
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Normal Approximation By Stein S Method
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Author : Louis H.Y. Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-13
Normal Approximation By Stein S Method written by Louis H.Y. Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-13 with Mathematics categories.
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
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Author : Andrew Barbour
language : en
Publisher: World Scientific
Release Date : 2005-04-14
An Introduction To Stein S Method written by Andrew Barbour and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-14 with Mathematics categories.
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
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Author : A. D. Barbour
language : en
Publisher: World Scientific
Release Date : 2005
Stein S Method And Applications written by A. D. Barbour and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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.
Stein S Method And Applications
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Author : Louis Hsiao Yun Chen
language : en
Publisher: World Scientific
Release Date : 2005-05-03
Stein S Method And Applications written by Louis Hsiao Yun Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-03 with Mathematics categories.
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 2003, 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
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Author : Benjamin Arras
language : en
Publisher: Springer
Release Date : 2019-04-24
On Stein S Method For Infinitely Divisible Laws With Finite First Moment written by Benjamin Arras and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-24 with Mathematics categories.
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 classicalweak limit theorems for sums of independent random variables. This book is aimed at graduate students and researchers working in probability theory and mathematical statistics.
Poisson Approximation
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Author : A. D. Barbour
language : en
Publisher:
Release Date : 2023
Poisson Approximation written by A. D. Barbour and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Approximation theory categories.
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. 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.
Normal Approximation And Asymptotic Expansions
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Author : Rabi N. Bhattacharya
language : en
Publisher: SIAM
Release Date : 2010-11-11
Normal Approximation And Asymptotic Expansions written by Rabi N. Bhattacharya and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-11 with Mathematics categories.
-Fourier analysis, --
The Geometric Process And Its Applications
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Author : Yeh Lam
language : en
Publisher: World Scientific
Release Date : 2007-07-26
The Geometric Process And Its Applications written by Yeh Lam and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-26 with Mathematics categories.
A geometric process is a simple monotone process that was first introduced by the author in 1988. It is a generalization of renewal process. This book captures the extensive research work on geometric processes that has been done since then in both probability and statistics theory and various applications. Some results are published for the first time.A reference book for researchers and a handbook for practitioners, it is also a useful textbook for postgraduate or senior undergraduate students.
Risk Assessment
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Author : Marvin Rausand
language : en
Publisher: John Wiley & Sons
Release Date : 2020-03-31
Risk Assessment written by Marvin Rausand and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-31 with Mathematics categories.
Introduces risk assessment with key theories, proven methods, and state-of-the-art applications Risk Assessment: Theory, Methods, and Applications remains one of the few textbooks to address current risk analysis and risk assessment with an emphasis on the possibility of sudden, major accidents across various areas of practice—from machinery and manufacturing processes to nuclear power plants and transportation systems. Updated to align with ISO 31000 and other amended standards, this all-new 2nd Edition discusses the main ideas and techniques for assessing risk today. The book begins with an introduction of risk analysis, assessment, and management, and includes a new section on the history of risk analysis. It covers hazards and threats, how to measure and evaluate risk, and risk management. It also adds new sections on risk governance and risk-informed decision making; combining accident theories and criteria for evaluating data sources; and subjective probabilities. The risk assessment process is covered, as are how to establish context; planning and preparing; and identification, analysis, and evaluation of risk. Risk Assessment also offers new coverage of safe job analysis and semi-quantitative methods, and it discusses barrier management and HRA methods for offshore application. Finally, it looks at dynamic risk analysis, security and life-cycle use of risk. Serves as a practical and modern guide to the current applications of risk analysis and assessment, supports key standards, and supplements legislation related to risk analysis Updated and revised to align with ISO 31000 Risk Management and other new standards and includes new chapters on security, dynamic risk analysis, as well as life-cycle use of risk analysis Provides in-depth coverage on hazard identification, methodologically outlining the steps for use of checklists, conducting preliminary hazard analysis, and job safety analysis Presents new coverage on the history of risk analysis, criteria for evaluating data sources, risk-informed decision making, subjective probabilities, semi-quantitative methods, and barrier management Contains more applications and examples, new and revised problems throughout, and detailed appendices that outline key terms and acronyms Supplemented with a book companion website containing Solutions to problems, presentation material and an Instructor Manual Risk Assessment: Theory, Methods, and Applications, Second Edition is ideal for courses on risk analysis/risk assessment and systems engineering at the upper-undergraduate and graduate levels. It is also an excellent reference and resource for engineers, researchers, consultants, and practitioners who carry out risk assessment techniques in their everyday work.
The Preparation Of Dispersions In Liquids
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Author : H.N. Stein
language : en
Publisher: CRC Press
Release Date : 1995-11-08
The Preparation Of Dispersions In Liquids written by H.N. Stein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-08 with Science categories.
This work details the preparation of dispersions in liquids. It sets out to bridge the gap in information for the chemist who is not applications oriented and the chemical engineer who needs to solve problems in the field based on theoretical methods of dispersions of solids, liquids and gases. Insights are provided into many topics, including the transportation and handling of finely divided soils or highly viscous liquids; the reactions between reactants dissolved in immiscible phases; the formation of porous materials; and filtration.