Normal Approximation by Stein's Method by Louis Hy Chen
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.-
Probability Models for DNA Sequence Evolution
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An Introduction to Stochastic Integration
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Invariant Probabilities of Transition Functions
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Associated Sequences, Demimartingales and Nonparametric Inference
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Continuous-Time Markov Jump Linear Systems
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Quasi-Stationary Distributions
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Stochastic Partial Differential Equations
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Self-Normalized Processes
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Laws of Chaos
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Stochastic Differential Equations in Infinite Dimensions
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Invariant Random Fields on Spaces with a Group Action
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Noise-Induced Phenomena in Slow-Fast Dynamical Systems
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Schrodinger Diffusion Processes
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Probability Measures on Semigroups
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Stochastic Control in Insurance
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Measure-Valued Branching Markov Processes
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Stochastic Processes
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The Doctrine of Chances
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An Introduction to the Theory of Point Processes
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Eigenvalues, Inequalities, and Ergodic Theory
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Theory of Random Sets
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Feynman-Kac Formulae
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Mass Transportation Problems
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Stochastic Calculus for Fractional Brownian Motion and Applications
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Renewal Theory for Perturbed Random Walks and Similar Processes
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Discrete-Time Markov Jump Linear Systems
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Basics of Applied Stochastic Processes
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Limit Theorems for Randomly Stopped Stochastic Processes
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Point Process Theory and Applications
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Excursions of Markov Processes
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Decoupling
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The Malliavin Calculus and Related Topics
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Discrete-Time Semi-Markov Random Evolutions and Their Applications
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Stochastic Neutron Transport
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Diffusions and Elliptic Operators
From the reviews:
“This book gives a complete and comprehensive overview of normal approximation using Stein’s methodIt serves both as an introductory textbook to graduate students who aim at becoming more familiar with Stein’s method and as a research book taking into account the most recent advances in this area. … To conclude, the authors present in this book the foundations and the main developments of Stein’s method … . The book is very pleasant to read and suitable for both graduate students and experienced researchers.” (Anthony Réveillac, Mathematical Reviews, Issue 2012 b)
Louis Chen's research interests are in probability and computational biology, focusing largely on Stein's method. He is well-known for his pioneering work on Poisson approximation. He is an elected Fellow of the Institute of Mathematical Statistics and of the Academy of Sciences for the Developing World. He has also served as Associate Editor of Statistica Sinica and Bernoulli. Larry Goldstein has studied Stein's method since 1989, and is a noted researcher in the field. He was elected Fellow of the Institute of Mathematical Statistics in 2003, and serves on the editorial board of Bernoulli. Qi-Man Shao has been working on limit theory in probability and statistics, especially on self-normalized large and moderate deviations and Stein's method for normal and non-normal approximation. He is an invited speaker (45 minutes) at the International Congress of Mathematicians 2010. He is an elected Fellow of the Institute of Mathematical Statistics, and has served on the editorial board of The Annals of Statistics and The Annals of Applied Probability.
| SKU | Unavailable |
| ISBN 13 | 9783642265655 |
| ISBN 10 | 3642265650 |
| Title | Normal Approximation by Stein's Method |
| Author | Louis Hy Chen |
| Series | Probability And Its Applications |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 2012-12-01 |
| Number of pages | 408 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |