Bayes Linear Statistics

The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.

A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.

Presents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function This book addresses mathematical statistics for upper-undergraduates and first year graduate students, tying chapters on estimation, confidence intervals, hypothesis testing, and statistical models together to present a unifying focus on the likelihood function. It also emphasizes the important ideas in statistical modeling, such as sufficiency, exponential family distributions, and large sample properties. Mathematical Statistics: An Introduction to Likelihood Based Inference makes advanced topics accessible and understandable and covers many topics in more depth than typical mathematical statistics textbooks. It includes numerous examples, case studies, a large number of exercises ranging from drill and skill to extremely difficult problems, and many of the important theorems of mathematical statistics along with their proofs. In addition to the connected chapters mentioned above, Mathematical Statistics covers likelihood-based estimation, with emphasis on multidimensional parameter spaces and range dependent support. It also includes a chapter on confidence intervals, which contains examples of exact confidence intervals along with the standard large sample confidence intervals based on the MLE's and bootstrap confidence intervals. There’s also a chapter on parametric statistical models featuring sections on non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. Prepares students with the tools needed to be successful in their future work in statistics data science Includes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage Emphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties Includes sections on Bayesian estimation and credible intervals Features examples, problems, and solutions Mathematical Statistics: An Introduction to Likelihood Based Inference is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and/or statistical inference.

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processeswith Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I Richard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups andAssociative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel & Fred S. Wood Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume II Morris H. DeGroot Optimal Statistical Decisions W. Edwards Deming Sample Design in Business Research Amos de Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume 1—Nuclear Structure Harold F. Dodge & Harry G. Romig Sampling Inspection Tables: Single and Double Sampling J. L. Doob Stochastic Processes

A comprehensive examination of high-dimensional analysis of multivariate methods and their real-world applications Multivariate Statistics: High-Dimensional and Large-Sample Approximations is the first book of its kind to explore how classical multivariate methods can be revised and used in place of conventional statistical tools. Written by prominent researchers in the field, the book focuses on high-dimensional and large-scale approximations and details the many basic multivariate methods used to achieve high levels of accuracy. The authors begin with a fundamental presentation of the basic tools and exact distributional results of multivariate statistics, and, in addition, the derivations of most distributional results are provided. Statistical methods for high-dimensional data, such as curve data, spectra, images, and DNA microarrays, are discussed. Bootstrap approximations from a methodological point of view, theoretical accuracies in MANOVA tests, and model selection criteria are also presented. Subsequent chapters feature additional topical coverage including: High-dimensional approximations of various statistics High-dimensional statistical methods Approximations with computable error bound Selection of variables based on model selection approach Statistics with error bounds and their appearance in discriminant analysis, growth curve models, generalized linear models, profile analysis, and multiple comparison Each chapter provides real-world applications and thorough analyses of the real data. In addition, approximation formulas found throughout the book are a useful tool for both practical and theoretical statisticians, and basic results on exact distributions in multivariate analysis are included in a comprehensive, yet accessible, format. Multivariate Statistics is an excellent book for courses on probability theory in statistics at the graduate level. It is also an essential reference for both practical and theoretical statisticians who are interested in multivariate analysis and who would benefit from learning the applications of analytical probabilistic methods in statistics.

Presents new and up-dated material on both the underlying theory and the practical methodology of directional statistics, helping the reader to utilise and develop the techniques appropriate to their work. The book is divided into three parts. The first part concentrates on statistics on the circle. Topics covered include tests of uniformity, tests of good-of-fit, inference on von Mises distributions and non-parametric methods. The second part considers statistics on spheres of arbitrary dimension, and includes a detailed account of inference on the main distributions on spheres. Recent material on correlation, regression time series, robust techniques, bootstrap methods, density estimation and curve fitting is presented. The third part considers statistics on more general sample spaces, in particular rotation groups, Stiefel manifolds, Grassmann manifolds and complex projective spaces. Shape analysis is considered from the perspective of directional statistics. Written by leading authors in the field, this text will be invaluable not only to researchers in probability and statistics interested in the latest developments in directional statistics, but also to practitioners and researchers in many scientific fields, including astronomy, biology, computer vision, earth sciences and image analysis.

A visually intuitive approach to statistical data analysis Visual Statistics brings the most complex and advanced statistical methods within reach of those with little statistical training by using animated graphics of the data. Using ViSta: The Visual Statistics System-developed by Forrest Young and Pedro Valero-Mora and available free of charge on the Internet-students can easily create fully interactive visualizations from relevant mathematical statistics, promoting perceptual and cognitive understanding of the data's story. An emphasis is placed on a paradigm for understanding data that is visual, intuitive, geometric, and active, rather than one that relies on convoluted logic, heavy mathematics, systems of algebraic equations, or passive acceptance of results. A companion Web site complements the book by further demonstrating the concept of creating interactive and dynamic graphics. The book provides users with the opportunity to view the graphics in a dynamic way by illustrating how to analyze statistical data and explore the concepts of visual statistics. Visual Statistics addresses and features the following topics: * Why use dynamic graphics? * A history of statistical graphics * Visual statistics and the graphical user interface * Visual statistics and the scientific method * Character-based statistical interface objects * Graphics-based statistical interfaces * Visualization for exploring univariate data This is an excellent textbook for undergraduate courses in data analysis and regression, for students majoring or minoring in statistics, mathematics, science, engineering, and computer science, as well as for graduate-level courses in mathematics. The book is also ideal as a reference/self-study guide for engineers, scientists, and mathematicians. With contributions by highly regarded professionals in the field, Visual Statistics not only improves a student's understanding of statistics, but also builds confidence to overcome problems that may have previously been intimidating.

A completely revised and expanded edition of a classic resource In the over twenty years since the publication of the Second Edition of Order Statistics, the theories and applications of this dynamic field have changed markedly. Meeting the challenges and demands of today’s students and research community, authors H. A. David and H. N. Nagaraja return with a completely revised and updated Order Statistics, Third Edition. Chapters two through nine of this comprehensive volume deal with finite-sample theory, with individual topics grouped under distribution theory (chapters two through six) and statistical inference (chapters seven through nine). Chapters ten and eleven cover asymptotic theory for central, intermediate, and extreme order statistics, representing twice the coverage of this subject than the previous edition. New sections include: Stochastic orderings Characterizations Distribution-free prediction intervals Bootstrap estimations Moving order statistics Studentized range Ranked-set sampling Estimators of tail index The authors further explain application procedures for many data-analysis techniques and quality control. An appendix provides a guide to related tables and computer algorithms. Extensive exercise sets have been updated since the last edition. In spite of many eliminations, the total number of references has increased from 1,000 to 1,500. Expanded coverage of shortcut methods, robust estimation, life testing, reliability, L-statistics, and extreme-value theory complete this one-of-a-kind resource. Students and researchers of order statistics will appreciate this updated and thorough edition.

A new edition of the classic, groundbreaking book on robust statistics Over twenty-five years after the publication of its predecessor, Robust Statistics, Second Edition continues to provide an authoritative and systematic treatment of the topic. This new edition has been thoroughly updated and expanded to reflect the latest advances in the field while also outlining the established theory and applications for building a solid foundation in robust statistics for both the theoretical and the applied statistician. A comprehensive introduction and discussion on the formal mathematical background behind qualitative and quantitative robustness is provided, and subsequent chapters delve into basic types of scale estimates, asymptotic minimax theory, regression, robust covariance, and robust design. In addition to an extended treatment of robust regression, the Second Edition features four new chapters covering: Robust Tests Small Sample Asymptotics Breakdown Point Bayesian Robustness An expanded treatment of robust regression and pseudo-values is also featured, and concepts, rather than mathematical completeness, are stressed in every discussion. Selected numerical algorithms for computing robust estimates and convergence proofs are provided throughout the book, along with quantitative robustness information for a variety of estimates. A General Remarks section appears at the beginning of each chapter and provides readers with ample motivation for working with the presented methods and techniques. Robust Statistics, Second Edition is an ideal book for graduate-level courses on the topic. It also serves as a valuable reference for researchers and practitioners who wish to study the statistical research associated with robust statistics.

Environmental statistics is a rapidly growing discipline that is important not only as a division of professional and academic statistics, but also in the accumulation of data on environmental effects and in the formulation of environmental policy by government agencies. This book features contributions from policy makers, scientists actively involved in collection of data, and professional, academic and government statisticians. These explore the interfaces between the different areas of application of environmental statistics and consider the future applications of methods arising from this discipline. Some of the chapters deal specifically with environmental models and methods. Here, the contributors explain specialized statistical techniques that have been developed for analysing environmental data and mathematical models that have been applied to the problem of integrating large amounts of environmental data into a coherent picture of particular environmental systems. Several of the contributions deal specifically with the problems involved in co-ordinating data collection over large geographical areas and over many dimensions of measurement. Finally, the book discusses the problems of formulating specific environmental policies given the nature of the information that has been made available using environmental statistical methods.