Statistics and Computing – serie

Now in its second edition, this textbook provides an introduction to Python and its use for statistical data analysis.

The statistical methodology covered includes statistical standard distributions, one- and two-sample tests with continuous data, regression analysis, one- and two-way analysis of variance, regression analysis, analysis of tabular data, and sample size calculations.

Monte Carlo simulation has become one of the most important tools in all fields of science. Simulation methodology relies on a good source of numbers that appear to be random. These "pseudorandom" numbers must pass statistical tests just as random samples would. Methods for producing pseudorandom numbers and transforming those numbers to simulate samples from various distributions are among the most important topics in statistical computing. This book surveys techniques of random number generation and the use of random numbers in Monte Carlo simulation. The book covers basic principles, as well as newer methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. The best methods for generating random variates from the standard distributions are presented, but also general techniques useful in more complicated models and in novel settings are described. The emphasis throughout the book is on practical methods that work well in current computing environments. The book includes exercises and can be used as a test or supplementary text for various courses in modern statistics.It could serve as the primary test for a specialized course in statistical computing, or as a supplementary text for a course in computational statistics and other areas of modern statistics that rely on simulation. The book, which covers recent developments in the field, could also serve as a useful reference for practitioners. Although some familiarity with probability and statistics is assumed, the book is accessible to a broad audience. The second edition is approximately 50 per cent longer than the first edition. It includes advances in methods for parallel random number generation, universal methods for generation of nonuniform variates, perfect sampling, and software for random number generation.

Many books teach computational statistics. Until now, however, none has shown how to write a good program. This book gives statisticians, biostatisticians and methodologically-oriented researchers the tools they need to develop high-quality statistical software. Topics include how to:Program in Fortran 95 using a pseudo object-oriented style Write accurate and efficient computational procedures Create console applications Build dynamic-link libraries (DLLs) and Windows-based software components Develop graphical user interfaces (GUIs)Through detailed examples, readers are shown how to call Fortran procedures from packages including Excel, SAS, SPSS, S-PLUS, R, and MATLAB. They are even given a tutorial on creating GUIs for Fortran computational code using Visual Basic. NET. This book is for those who want to learn how to create statistical applications quickly and effectively. Prior experience with a programming language such as Basic, Fortran or C is helpful but not required. More experienced programmers will learn new strategies to harness the power of modern Fortran and the object-oriented paradigm.This may serve as a supplementary text for a graduate course on statistical computing.

This book was written for statisticians, computer scientists, geographers, researchers, and others interested in visualizing data. It presents a unique foundation for producing almost every quantitative graphic found in scientific journals, newspapers, statistical packages, and data visualization systems. While the tangible results of this work have been several visualization software libraries, this book focuses on the deep structures involved in producing quantitative graphics from data. What are the rules that underlie the production of pie charts, bar charts, scatterplots, function plots, maps, mosaics, and radar charts? Those less interested in the theoretical and mathematical foundations can still get a sense of the richness and structure of the system by examining the numerous and often unique color graphics it can produce. The second edition is almost twice the size of the original, with six new chapters and substantial revision. Much of the added material makes this book suitable for survey courses in visualization and statistical graphics.

This monograph focuses on the application of the solution strategy known as branch-and-bound to problems of combinatorial data analysis. Combinatorial data analysis problems typically require either the sel- tion of a subset of objects from a larger (master) set, the grouping of a collection of objects into mutually exclusive and exhaustive subsets, or the sequencing of objects. To obtain verifiably optimal solutions for this class of problems, we must evaluate (either explicitly or implicitly) all feasible solutions. Unfortunately, the number of feasible solutions for problems of combinatorial data analysis grows exponentially with pr- lem size. For this reason, the explicit enumeration and evaluation of all solutions is computationally infeasible for all but the smallest problems. The branch-and-bound solution method is one type of partial enume- tion solution strategy that enables some combinatorial data analysis pr- lems to be solved optimally without explicitly enumerating all feasible solutions. To understand the operation of a branch-and-bound algorithm, we d- tinguish complete solutions from partial solutions. A complete solution is one for which a feasible solution to the optimization problem has been produced (e. g. , all objects are assigned to a group, or all objects are - signed a sequence position). A partial solution is an incomplete solution (e. g. , some objects are not assigned to a group, or some objects are not assigned a sequence position).

This book explains the basics of S-PLUS in a clear style at a level suitable for people with little computing or statistical knowledge. Unlike the manuals, it is not comprehensive, but instead introduces the most important ideas of S-PLUS and R, its companion in implementing the S language.The authors take the reader on a journey into the world of interactive computing, data exploration, and statistical analysis. They explain how to approach data sets and teach the corresponding S-PLUS commands.A collection of exercises summarizes the main ideas of each chapter. The exercises are accompanied by solutions that are worked out in full detail, and the code is ready to use and to be modified.The volume is rounded off with practical hints on how efficient work can be performed in S-PLUS, for example by pointing out how to set up a good working environment and how to integrate S-PLUS with office products.The book is well suited for self-study and as a textbook. It serves as an introduction to S-PLUS as well as R. A separate chapter points out the major differences between R and S-PLUS.Over the last editions, the book has been updated to cover important changes like the inclusion of S Language Version 4, Trellis graphics, a graphical user interface, and many useful tips and tricks.The fourth edition is based on S-PLUS Version 7.0 for Windows and UNIX and has been updated and revised accordingly.

Graphics are great for exploring data, but how can they be used for looking at the large datasets that are commonplace to-day? This book shows how to look at ways of visualizing large datasets, whether large in numbers of cases or large in numbers of variables or large in both. Data visualization is useful for data cleaning, exploring data, identifying trends and clusters, spotting local patterns, evaluating modeling output, and presenting results. It is essential for exploratory data analysis and data mining. Data analysts, statisticians, computer scientists-indeed anyone who has to explore a large dataset of their own-should benefit from reading this book.New approaches to graphics are needed to visualize the information in large datasets and most of the innovations described in this book are developments of standard graphics. There are considerable advantages in extending displays which are well-known and well-tried, both in understanding how best to make use of them in your work and in presenting results to others. It should also make the book readily accessible for readers who already have a little experience of drawing statistical graphics. All ideas are illustrated with displays from analyses of real datasets and the authors emphasize the importance of interpreting displays effectively. Graphics should be drawn to convey information and the book includes many insightful examples.From the reviews:"Anyone interested in modern techniques for visualizing data will be well rewarded by reading this book. There is a wealth of important plotting types and techniques." Paul Murrell for the Journal of Statistical Software, December 2006"This fascinating book looks at the question of visualizing large datasets from many different perspectives. Different authors are responsible for different chapters and this approach works well in giving the reader alternative viewpoints of the same problem. Interestingly the authors havecleverly chosen a definition of 'large dataset'. Essentially they focus on datasets with the order of a million cases. As the authors point out there are now many examples of much larger datasets but by limiting to ones that can be loaded in their entirety in standard statistical software they end up with a book that has great utility to the practitioner rather than just the theorist. Another very attractive feature of the book is the many colour plates, showing clearly what can now routinely be seen on the computer screen. The interactive nature of data analysis with large datasets is hard to reproduce in a book but the authors make an excellent attempt to do just this." P. Marriott for the Short Book Reviews of the ISI

John Chambers has been the principal designer of the S language since its beginning, and in 1999 received the ACM System Software award for S, the only statistical software to receive this award.

This book describes the statistical computing environment called XploRe which is a widely available package (details on how to obtain it are provided in the book). As its name suggests, XploRe provides a highly interactive graphics interface for exploratory statistical analysis and provides for user-written macros and smoothing procedures for effective high-dimensional data analysis. The main aim of the book is to show how XploRe can be used for a wide variety of statistical tasks ranging from basic data manipulation to interactive customizing of graphs and dynamic fitting of high-dimensional statistical models. As a result, it may be used as the basis of a course in model building, computational statistics, applied multivariate analysis, and econometrics.

This book is concerned with the processing of signals that have been sampled and digitized. The authors present algorithms for the optimization, random simulation, and numerical integration of probability densities for applications of Bayesian inference to signal processing. In particular, methods are developed for the computation of marginal densities and evidence, and are applied to previously intractable problems either involving large numbers of parameters or where the signal model is of a complex form. The emphasis is on the applications of these methods notably to the restoration of digital audio recordings and biomedical data. After a chapter which sets out the main principles of Bayesian inference applied to signal processing, subsequent chapters cover numerical approaches to these techniques, the use of Markov chain Monte Carlo methods, the identification of abrupt changes in data using the Bayesian piecewise linear model, and identifying missing samples in digital audio signals.

S is a powerful environment for the statistical and graphical analysis of data. It provides the tools to implement many statistical ideas that have been made possible by the widespread availability of workstations having good graphics and computational capabilities. This book is a guide to using S environments to perform statistical analyses and provides both an introduction to the use of S and a course in modern statistical methods. Implementations of S are available commercially in S-PLUS(R) workstations and as the Open Source R for a wide range of computer systems. The aim of this book is to show how to use S as a powerful and graphical data analysis system. Readers are assumed to have a basic grounding in statistics, and so the book is intended for would-be users of S-PLUS or R and both students and researchers using statistics. Throughout, the emphasis is on presenting practical problems and full analyses of real data sets. Many of the methods discussed are state of the art approaches to topics such as linear, nonlinear and smooth regression models, tree-based methods, multivariate analysis, pattern recognition, survival analysis, time series and spatial statistics.Throughout modern techniques such as robust methods, non-parametric smoothing and bootstrapping are used where appropriate. This fourth edition is intended for users of S-PLUS 6.0 or R 1.5.0 or later. A substantial change from the third edition is updating for the current versions of S-PLUS and adding coverage of R. The introductory material has been rewritten to emphasis the import, export and manipulation of data. Increased computational power allows even more computer-intensive methods to be used, and methods such as GLMMs.

In recent years developments in statistics have to a great extent gone hand in hand with developments in computing. Indeed, many of the recent advances in statistics have been dependent on advances in computer science and techn- ogy. Many of the currently interesting statistical methods are computationally intensive, eitherbecausetheyrequireverylargenumbersofnumericalcompu- tions or because they depend on visualization of many projections of the data. The class of statistical methods characterized by computational intensity and the supporting theory for such methods constitute a discipline called “com- tational statistics”. (Here, I am following Wegman, 1988, and distinguishing “computationalstatistics”from“statisticalcomputing”, whichwetaketomean “computational methods, including numerical analysis, for statisticians”.) The computationally-intensive methods of modern statistics rely heavily on the developments in statistical computing and numerical analysis generally. Computational statistics shares two hallmarks with other “computational” sciences, such as computational physics, computational biology, and so on. One is a characteristic of the methodology: it is computationally intensive. The other is the nature of the tools of discovery. Tools of the scienti?c method have generally been logical deduction (theory) and observation (experimentation). The computer, used to explore large numbers of scenarios, constitutes a new type of tool. Use of the computer to simulate alternatives and to present the research worker with information about these alternatives is a characteristic of thecomputationalsciences. Insomewaysthisusageisakintoexperimentation. The observations, however, are generated from an assumed model, and those simulated data are used toevaluate and study the model.

Computational inference has taken its place alongside asymptotic inference and exact techniques in the standard collection of statistical methods. Computational inference is based on an approach to statistical methods that uses modern computational power to simulate distributional properties of estimators and test statistics. This book describes computationally-intensive statistical methods in a unified presentation, emphasizing techniques, such as the PDF decomposition, that arise in a wide range of methods.The book assumes an intermediate background in mathematics, computing, and applied and theoretical statistics. The first part of the book, consisting of a single long chapter, reviews this background material while introducing computationally-intensive exploratory data analysis and computational inference.The six chapters in the second part of the book are on statistical computing. This part describes arithmetic in digital computers and how the nature of digital computations affects algorithms used in statistical methods. Building on the first chapters on numerical computations and algorithm design, the following chapters cover the main areas of statistical numerical analysis, that is, approximation of functions, numerical quadrature, numerical linear algebra, solution of nonlinear equations, optimization, and random number generation.The third and fourth parts of the book cover methods of computational statistics, including Monte Carlo methods, randomization and cross validation, the bootstrap, probability density estimation, and statistical learning.The book includes a large number of exercises with some solutions provided in an appendix.

Numerical linear algebra is one of the most important subjects in the field of statistical computing. Statistical methods in many areas of application require computations with vectors and matrices. This book describes accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. An understanding of numerical linear algebra requires basic knowledge both of linear algebra and of how numerical data are stored and manipulated in the computer. The book begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, matrix factorizations, matrix and vector norms, and other topics in linear algebra; hence, the book is essentially self- contained. The topics addressed in this bookconstitute the most important material for an introductory course in statistical computing, and should be covered in every such course. The book includes exercises and can be used as a text for a first course in statistical computing or as supplementary text for various courses that emphasize computations. James Gentle is University Professor of Computational Statistics at George Mason University. During a thirteen-year hiatus from academic work before joining George Mason, he was director of research and design at the world's largest independent producer of Fortran and C general-purpose scientific software libraries. These libraries implement many algorithms for numerical linear algebra. He is a Fellow of the American Statistical Association and member of the International Statistical Institute. He has held several national

Separation of signal from noise is the most fundamental problem in data analysis, and arises in many fields, for example, signal processing, econometrics, acturial science, and geostatistics. This book introduces the local regression method in univariate and multivariate settings, and extensions to local likelihood and density estimation. Basic theoretical results and diagnostic tools such as cross validation are introduced along the way. Examples illustrate the implementation of the methods using the LOCFIT software.

This book provides an overview of the theory and application of linearand nonlinear mixed-effects models in the analysis of grouped data,such as longitudinal data, repeated measures, and multilevel data. Aunified model-building strategy for both linear and nonlinear modelsis presented and applied to the analysis of over 20 real datasets froma wide variety of areas, including pharmacokinetics, agriculture, andmanufacturing. A strong emphasis is placed on the use of graphicaldisplays at the various phases of the model-building process, startingwith exploratory plots of the data and concluding with diagnosticplots to assess the adequacy of a fitted model. Over 170 figures areincluded in the book.The NLME library for analyzing mixed-effects models in S andS-PLUS, developed by the authors, provides the underlyingsoftware for implementing the methods presented in the text, beingdescribed and illustrated in detail throughout the book.The balanced mix of real data examples, modeling software, and theorymakes this book a useful reference for practitioners using mixed-effects models in their data analyses.It can also be used as a text for a one-semester graduate-level applied course in mixed-effects models. Researchers in statistical computing will also find this book appealing for its presentation of novel andefficient computational methods for fitting linear and nonlinearmixed-effects models.Jose C. Pinheiro has been a member of the technical staff instatistics research at Bell Laboratories since 1996. He received hisPh.D. in Statistics from and worked for two years in the Department of Biostatistics at the University of Wisconsin-Madison. The author of several articles in mixed-effects models, he is a member of the American Statistical Association and the Biometric Society. Douglas M. Bates is Professor of Statistics at the University of Wisconsin-Madison. He is the author, with Donald G. Watts, of Nonlinear Regression Analysis and Its Applications, aFellow of the American Statistical Association, and a former chair ofits Statistical Computing Section.

S is a high-level language for manipulating, analysing and displayingdata. It forms the basis of two highly acclaimed and widely used dataanalysis software systems, the commercial S-PLUS and the OpenSource R. This book provides an in-depth guide to writing software inthe S language under either or both of those systems. It is intendedfor readers who have some acquaintance with the S language and want toknow how to use it more effectively, for example to build re-usabletools for streamlining routine data analysis or to implement newstatistical methods.One of the outstanding strengths of the S language is the ease withwhich it can be extended by users. S is a functional language, andfunctions written by users are first-class objects treated in the sameway as functions provided by the system. S code is eminently readableand so a good way to document precisely what algorithms were used, andas much of the implementations are themselves written in S, they can bestudied as models and to understand their subtleties. The currentimplementations also provide easy ways for S functions to callcompiled code written in C, Fortran and similar languages; this isdocumented here in depth.Increasingly S is being used for statistical or graphical analysiswithin larger software systems or for whole vertical-marketapplications.The interface facilities are most developed onWindows and these are covered with worked examples.The authors have written the widely used Modern Applied Statisticswith S-PLUS, now in its third edition, and several software librariesthat enhance S-PLUS and R; these and the examples used in both booksare available on the Internet.Dr. W.N. Venables is a senior Statistician with the CSIRO/CMISEnvironmetrics Project in Australia, having been at the Department ofStatistics, University of Adelaide for many years previously.Professor B.D. Ripley holds the Chair of Applied Statistics at theUniversity of Oxford, and is the author of four other books on spatialstatistics, simulation, pattern recognition and neural networks. Bothauthors are known and respected throughout the international S and Rcommunities, for their books, workshops, short courses, freelyavailable software and through their extensive contributions to theS-news and R mailing lists.

When finished, you will be able to use R in conjunction with Stata, or separately, to import data, manage and transform it, create publication quality graphics, and perform basic statistical analyses.A glossary defines over 50 R terms using Stata jargon and again using more formal R terminology.

Monte Carlo simulation has become one of the most important tools in all fields of science. Simulation methodology relies on a good source of numbers that appear to be random. These "pseudorandom" numbers must pass statistical tests just as random samples would. Methods for producing pseudorandom numbers and transforming those numbers to simulate samples from various distributions are among the most important topics in statistical computing. This book surveys techniques of random number generation and the use of random numbers in Monte Carlo simulation. The book covers basic principles, as well as newer methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. The best methods for generating random variates from the standard distributions are presented, but also general techniques useful in more complicated models and in novel settings are described. The emphasis throughout the book is on practical methods that work well in current computing environments. The book includes exercises and can be used as a test or supplementary text for various courses in modern statistics. It could serve as the primary test for a specialized course in statistical computing, or as a supplementary text for a course in computational statistics and other areas of modern statistics that rely on simulation. The book, which covers recent developments in the field, could also serve as a useful reference for practitioners. Although some familiarity with probability and statistics is assumed, the book is accessible to a broad audience. The second edition is approximately 50% longer than the first edition. It includes advances in methods for parallel random number generation, universal methods for generation of nonuniform variates, perfect sampling, and software for random number generation.

Preface to First Edition Before writing the graphics for SYSTAT in the 1980’s, I began by teaching a seminar in statistical graphics and collecting as many different quantitative graphics as I could find.

This monograph focuses on the application of the solution strategy known as branch-and-bound to problems of combinatorial data analysis. Combinatorial data analysis problems typically require either the sel- tion of a subset of objects from a larger (master) set, the grouping of a collection of objects into mutually exclusive and exhaustive subsets, or the sequencing of objects. To obtain verifiably optimal solutions for this class of problems, we must evaluate (either explicitly or implicitly) all feasible solutions. Unfortunately, the number of feasible solutions for problems of combinatorial data analysis grows exponentially with pr- lem size. For this reason, the explicit enumeration and evaluation of all solutions is computationally infeasible for all but the smallest problems. The branch-and-bound solution method is one type of partial enume- tion solution strategy that enables some combinatorial data analysis pr- lems to be solved optimally without explicitly enumerating all feasible solutions. To understand the operation of a branch-and-bound algorithm, we d- tinguish complete solutions from partial solutions. A complete solution is one for which a feasible solution to the optimization problem has been produced (e. g. , all objects are assigned to a group, or all objects are - signed a sequence position). A partial solution is an incomplete solution (e. g. , some objects are not assigned to a group, or some objects are not assigned a sequence position).

John Chambers has been the principal designer of the S language since its beginning, and in 1999 received the ACM System Software award for S, the only statistical software to receive this award. He is author or coauthor of the landmark books on S.Now he turns to R, the enormously successful open-source system based on the S language. R's international support and the thousands of packages and other contributions have made it the standard for statistical computing in research and teaching.This book guides the reader through programming with R, beginning with simple interactive use and progressing by gradual stages, starting with simple functions. More advanced programming techniques can be added as needed, allowing users to grow into software contributors, benefiting their careers and the community. R packages provide a powerful mechanism for contributions to be organized and communicated.The techniques covered include such modern programming enhancements as classes and methods, namespaces, and interfaces to spreadsheets or data bases, as well as computations for data visualization, numerical methods, and the use of text data.

S is a powerful environment for the statistical and graphical analysis of data. It provides the tools to implement many statistical ideas that have been made possible by the widespread availability of workstations having good graphics and computational capabilities. This book is a guide to using S environments to perform statistical analyses and provides both an introduction to the use of S and a course in modern statistical methods. Implementations of S are available commercially in S-PLUS(R) workstations and as the Open Source R for a wide range of computer systems. The aim of this book is to show how to use S as a powerful and graphical data analysis system. Readers are assumed to have a basic grounding in statistics, and so the book is intended for would-be users of S-PLUS or R and both students and researchers using statistics. Throughout, the emphasis is on presenting practical problems and full analyses of real data sets. Many of the methods discussed are state of the art approaches to topics such as linear, nonlinear and smooth regression models, tree-based methods, multivariate analysis, pattern recognition, survival analysis, time series and spatial statistics. Throughout modern techniques such as robust methods, non-parametric smoothing and bootstrapping are used where appropriate. This fourth edition is intended for users of S-PLUS 6.0 or R 1.5.0 or later. A substantial change from the third edition is updating for the current versions of S-PLUS and adding coverage of R. The introductory material has been rewritten to emphasis the import, export and manipulation of data. Increased computational power allows even more computer-intensive methods to be used, and methods such as GLMMs,

In recent years developments in statistics have to a great extent gone hand in hand with developments in computing. Indeed, many of the recent advances in statistics have been dependent on advances in computer science and techn- ogy. Many of the currently interesting statistical methods are computationally intensive, eitherbecausetheyrequireverylargenumbersofnumericalcompu- tions or because they depend on visualization of many projections of the data. The class of statistical methods characterized by computational intensity and the supporting theory for such methods constitute a discipline called “com- tational statistics”. (Here, I am following Wegman, 1988, and distinguishing “computationalstatistics”from“statisticalcomputing”, whichwetaketomean “computational methods, including numerical analysis, for statisticians”.) The computationally-intensive methods of modern statistics rely heavily on the developments in statistical computing and numerical analysis generally. Computational statistics shares two hallmarks with other “computational” sciences, such as computational physics, computational biology, and so on. One is a characteristic of the methodology: it is computationally intensive. The other is the nature of the tools of discovery. Tools of the scienti?c method have generally been logical deduction (theory) and observation (experimentation). The computer, used to explore large numbers of scenarios, constitutes a new type of tool. Use of the computer to simulate alternatives and to present the research worker with information about these alternatives is a characteristic of thecomputationalsciences. Insomewaysthisusageisakintoexperimentation. The observations, however, are generated from an assumed model, and those simulated data are used toevaluate and study the model.

S is a high-level language for manipulating, analysing and displayingdata. It forms the basis of two highly acclaimed and widely used dataanalysis software systems, the commercial S-PLUS® and the OpenSource R. This book provides an in-depth guide to writing software inthe S language under either or both of those systems. It is intendedfor readers who have some acquaintance with the S language and want toknow how to use it more effectively, for example to build re-usabletools for streamlining routine data analysis or to implement newstatistical methods.One of the outstanding strengths of the S language is the ease withwhich it can be extended by users. S is a functional language, andfunctions written by users are first-class objects treated in the sameway as functions provided by the system. S code is eminently readableand so a good way to document precisely what algorithms were used, andas much of the implementations are themselves written in S, they can bestudied as models and to understand their subtleties. The currentimplementations also provide easy ways for S functions to callcompiled code written in C, Fortran and similar languages; this isdocumented here in depth.Increasingly S is being used for statistical or graphical analysiswithin larger software systems or for whole vertical-marketapplications. The interface facilities are most developed onWindows® and these are covered with worked examples.The authors have written the widely used Modern Applied Statisticswith S-PLUS, now in its third edition, and several software librariesthat enhance S-PLUS and R; these and the examples used in both booksare available on the Internet.Dr. W.N. Venables is a senior Statistician with theCSIRO/CMISEnvironmetrics Project in Australia, having been at the Department ofStatistics, University of Adelaide for many years previously.Professor B.D. Ripley holds the Chair of Applied Statistics at theUniversity of Oxford, and is the author of four other books on spatialstatistics, simulation, pattern recognition and neural networks. Bothauthors are known and respected throughout the international S and Rcommunities, for their books, workshops, short courses, freelyavailable software and through their extensive contributions to theS-news and R mailing lists.

Linear models courses are often presented as either theoretical or applied. Consequently, students may find themselves either proving theorems or using high-level procedures like PROC GLM to analyze data. There exists a gap between the derivation of formulas and analyses that hide these formulas behind attractive user interfaces. This book bridges that gap, demonstrating theory put into practice.Concepts presented in a theoretical linear models course are often trivialized in applied linear models courses by the facility of high-level SAS procedures like PROC MIXED and PROC REG that require the user to provide a few options and statements and in return produce vast amounts of output. This book uses PROC IML to show how analytic linear models formulas can be typed directly into PROC IML, as they were presented in the linear models course, and solved using data. This helps students see the link between theory and application. This also assists researchers in developing new methodologies in the area of linear models.The book contains complete examples of SAS code for many of the computations relevant to a linear models course. However, the SAS code in these examples automates the analytic formulas. The code for high-level procedures like PROC MIXED is also included for side-by-side comparison. The book computes basic descriptive statistics, matrix algebra, matrix decomposition, likelihood maximization, non-linear optimization, etc. in a format conducive to a linear models or a special topics course.Also included in the book is an example of a basic analysis of a linear mixed model using restricted maximum likelihood estimation (REML). The example demonstrates tests for fixed effects, estimates of linear functions, and contrasts. The example starts by showing the steps for analyzing the data using PROC IML and then provides the analysis using PROC MIXED. This allows students to follow the process that lead to the output.

Issues of numerical stability, accurate approximation, computational complexity, and mathematical modeling share the limelight in a broad yet rigorous overview of those parts of numerical analysis most relevant to statisticians.

Numerical linear algebra is one of the most important subjects in the field of statistical computing. Statistical methods in many areas of application require computations with vectors and matrices. This book describes accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. An understanding of numerical linear algebra requires basic knowledge both of linear algebra and of how numerical data are stored and manipulated in the computer. The book begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, matrix factorizations, matrix and vector norms, and other topics in linear algebra; hence, the book is essentially self- contained. The topics addressed in this bookconstitute the most important material for an introductory course in statistical computing, and should be covered in every such course. The book includes exercises and can be used as a text for a first course in statistical computing or as supplementary text for various courses that emphasize computations. James Gentle is University Professor of Computational Statistics at George Mason University. During a thirteen-year hiatus from academic work before joining George Mason, he was director of research and design at the world's largest independent producer of Fortran and C general-purpose scientific software libraries. These libraries implement many algorithms for numerical linear algebra. He is a Fellow of the American Statistical Association and member of the International Statistical Institute. He has held several national