Normal Approximation by Stein’s Method

Normal Approximation by Stein’s Method
Author: Louis H.Y. Chen
Publisher: Springer Science & Business Media
Total Pages: 411
Release: 2010-10-13
Genre: Mathematics
ISBN: 3642150071

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.

The Basic Practice of Statistics

The Basic Practice of Statistics
Author: David S. Moore
Publisher: Palgrave Macmillan
Total Pages: 975
Release: 2010
Genre: Mathematics
ISBN: 1429224266

This is a clear and innovative overview of statistics which emphasises major ideas, essential skills and real-life data. The organisation and design has been improved for the fifth edition, coverage of engaging, real-world topics has been increased and content has been updated to appeal to today's trends and research.

Introductory Econometrics

Introductory Econometrics
Author: Humberto Barreto
Publisher: Cambridge University Press
Total Pages: 810
Release: 2006
Genre: Business & Economics
ISBN: 9780521843195

This highly accessible and innovative text with supporting web site uses Excel (R) to teach the core concepts of econometrics without advanced mathematics. It enables students to use Monte Carlo simulations in order to understand the data generating process and sampling distribution. Intelligent repetition of concrete examples effectively conveys the properties of the ordinary least squares (OLS) estimator and the nature of heteroskedasticity and autocorrelation. Coverage includes omitted variables, binary response models, basic time series, and simultaneous equations. The authors teach students how to construct their own real-world data sets drawn from the internet, which they can analyze with Excel (R) or with other econometric software. The accompanying web site with text support can be found at www.wabash.edu/econometrics.

Probability

Probability
Author: Jim Pitman
Publisher: Springer Science & Business Media
Total Pages: 564
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461243742

This is a text for a one-quarter or one-semester course in probability, aimed at students who have done a year of calculus. The book is organised so a student can learn the fundamental ideas of probability from the first three chapters without reliance on calculus. Later chapters develop these ideas further using calculus tools. The book contains more than the usual number of examples worked out in detail. The most valuable thing for students to learn from a course like this is how to pick up a probability problem in a new setting and relate it to the standard body of theory. The more they see this happen in class, and the more they do it themselves in exercises, the better. The style of the text is deliberately informal. My experience is that students learn more from intuitive explanations, diagrams, and examples than they do from theorems and proofs. So the emphasis is on problem solving rather than theory.

Bayesian Data Analysis, Second Edition

Bayesian Data Analysis, Second Edition
Author: Andrew Gelman
Publisher: CRC Press
Total Pages: 717
Release: 2003-07-29
Genre: Mathematics
ISBN: 1420057294

Incorporating new and updated information, this second edition of THE bestselling text in Bayesian data analysis continues to emphasize practice over theory, describing how to conceptualize, perform, and critique statistical analyses from a Bayesian perspective. Its world-class authors provide guidance on all aspects of Bayesian data analysis and include examples of real statistical analyses, based on their own research, that demonstrate how to solve complicated problems. Changes in the new edition include: Stronger focus on MCMC Revision of the computational advice in Part III New chapters on nonlinear models and decision analysis Several additional applied examples from the authors' recent research Additional chapters on current models for Bayesian data analysis such as nonlinear models, generalized linear mixed models, and more Reorganization of chapters 6 and 7 on model checking and data collection Bayesian computation is currently at a stage where there are many reasonable ways to compute any given posterior distribution. However, the best approach is not always clear ahead of time. Reflecting this, the new edition offers a more pluralistic presentation, giving advice on performing computations from many perspectives while making clear the importance of being aware that there are different ways to implement any given iterative simulation computation. The new approach, additional examples, and updated information make Bayesian Data Analysis an excellent introductory text and a reference that working scientists will use throughout their professional life.

Normal Approximations with Malliavin Calculus

Normal Approximations with Malliavin Calculus
Author: Ivan Nourdin
Publisher: Cambridge University Press
Total Pages: 255
Release: 2012-05-10
Genre: Mathematics
ISBN: 1107017777

This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.

Biostatistics

Biostatistics
Author: Ronald N. Forthofer
Publisher: Elsevier
Total Pages: 521
Release: 2006-12-14
Genre: Mathematics
ISBN: 0080467725

Biostatistics, Second Edition, is a user-friendly guide on biostatistics, which focuses on the proper use and interpretation of statistical methods. This textbook does not require extensive background in mathematics, making it user-friendly for all students in the public health sciences field. Instead of highlighting derivations of formulas, the authors provide rationales for the formulas, allowing students to grasp a better understanding of the link between biology and statistics. The material on life tables and survival analysis allows students to better understand the recent literature in the health field, particularly in the study of chronic disease treatment. This updated edition contains over 40% new material with modern real-life examples, exercises, and references, including new chapters on Logistic Regression, Analysis of Survey Data, and Study Designs. The book is recommended for students in the health sciences, public health professionals, and practitioners. - Over 40% new material with modern real-life examples, exercises and references - New chapters on Logistic Regression; Analysis of Survey Data; and Study Designs - Introduces strategies for analyzing complex sample survey data - Written in a conversational style more accessible to students with real data

Introduction to Statistics and Econometrics

Introduction to Statistics and Econometrics
Author: Takeshi Amemiya
Publisher: Harvard University Press
Total Pages: 392
Release: 1994
Genre: Econometrics
ISBN: 9780674462250

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