Statistics and Computing – serie

Now in its second edition, this textbook provides an introduction to Python and its use for statistical data analysis. It covers common statistical tests for continuous, discrete and categorical data, as well as linear regression analysis and topics from survival analysis and Bayesian statistics.For this new edition, the introductory chapters on Python, data input and visualization have been reworked and updated. The chapter on experimental design has been expanded, and programs for the determination of confidence intervals commonly used in quality control have been introduced. The book also features a new chapter on finding patterns in data, including time series. A new appendix describes useful programming tools, such as testing tools, code repositories, and GUIs.The provided working code for Python solutions, together with easy-to-follow examples, will reinforce the reader’s immediate understanding of the topic. Accompanying data sets and Python programs are also available online. With recent advances in the Python ecosystem, Python has become a popular language for scientific computing, offering a powerful environment for statistical data analysis.With examples drawn mainly from the life and medical sciences, this book is intended primarily for masters and PhD students. As it provides the required statistics background, the book can also be used by anyone who wants to perform a statistical data analysis.

This book provides an elementary-level introduction to R, targeting both non-statistician scientists in various fields and students of statistics. The main mode of presentation is via code examples with liberal commenting of the code and the output, from the computational as well as the statistical viewpoint. Brief sections introduce the statistical methods before they are used. A supplementary R package can be downloaded and contains the data sets. All examples are directly runnable and all graphics in the text are generated from the examples. 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. In addition, the last four chapters contain introductions to multiple linear regression analysis, linear models in general, logistic regression, and survival analysis.

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.

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. From the reviews:"This book should be read by all statisticians, engineers, and scientists who want to implement an algorithm as a computer program. The book is the best introduction to programming that I have ever read. I value it as one of my important reference books in my personal library." Melvin J. Hinich for Techonmetrics, November 2006"Overall, the book is well written and provides a reasonable introduction to the use of modern versions of Fortran for statistical computation. The real thrust of the book is building COM interfaces using Fortran, and it will no doubt be most useful to anyone who needs to build such interfaces." Journal of the American Statistical Association, June 2006"The book is well written and is divided into chapters and sections which are coherent...Overall the book seems like a good resource for someone that already knows some dialect of FORTRAN and wants to learn a bit about what is new in FORTRAN 95..." Robert Gentleman for the Journal of Statistical Software, December 2006

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. I was determined to produce a package that could draw every statistical graphic I had ever seen. The structure of the program was a collection of procedures named after the basic graph types they p- duced. The graphics code was roughly one and a half megabytes in size. In the early 1990’s, I redesigned the SYSTAT graphics package using - ject-based technology. I intended to produce a more comprehensive and - namic package. I accomplished this by embedding graphical elements in a tree structure. Rendering graphics was done by walking the tree and editing worked by adding and deleting nodes. The code size fell to under a megabyte. In the late 1990’s, I collaborated with Dan Rope at the Bureau of Labor Statistics and Dan Carr at George Mason University to produce a graphics p- duction library called GPL, this time in Java. Our goal was to develop graphics components. This book was nourished by that project. So far, the GPL code size is under half a megabyte.

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).

Thisisnowthefourtheditionof“TheBasicsofS-Plus”since1997.S-Plus saw a steady growth in popularity, and it established itself in many edu- tional and business places as a major data analysis tool.S-Plus is valued for its modern, interactive data analysis environment, whether it is the p- mary system or a complement to other standards like SAS (the latter is in particular true for the industry we work in, pharmaceuticals). We have followed the various releases with new editions of our book, introducing over time major changes like the incorporation of S Version 4 (the underlying language), Trellis graphs, a graphical user interface, in particular for the Windows operating system, and a chapter on R and its di?erencestoS-Plus(thatareminorforthematerialcoveredinthisbook). Thiseditionisanupdatefromedition3tocovernewfunctionsandfeatures ofS-Plus Version 7.0 (working from the beta release for MS Windows and Linux), adding more practical tips and examples, and correcting a few mistakes. We are very grateful to all our readers, in particular those sending us suggestions, comments, and any other kind of feedback. You will see some of these re?ected in the book.

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. 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.

This book describes an interactive statistical computing environment called 1 XploRe. As the name suggests, support for exploratory statistical analysis is given by a variety of computational tools. XploRe is a matrix-oriented statistical language with a comprehensive set of basic statistical operations that provides highly interactive graphics, as well as a programming environ­ ment for user-written macros; it offers hard-wired smoothing procedures for effective high-dimensional data analysis. Its highly dynamic graphic capa­ bilities make it possible to construct student-level front ends for teaching basic elements of statistics. Hot keys make it an easy-to-use computing environment for statistical analysis. The primary objective of this book is to show how the XploRe system can be used as an effective computing environment for a large number of statistical tasks. The computing tasks we consider range from basic data matrix manipulations to interactive customizing of graphs and dynamic fit­ ting of high-dimensional statistical models. The XploRe language is similar to other statistical languages and offers an interactive help system that can be extended to user-written algorithms. The language is intuitive and read­ ers with access to other systems can, without major difficulty, reproduce the examples presented here and use them as a basis for further investigation.

This book is concerned with the processing of signals that have been sam­ pled and digitized. The fundamental theory behind Digital Signal Process­ ing has been in existence for decades and has extensive applications to the fields of speech and data communications, biomedical engineering, acous­ tics, sonar, radar, seismology, oil exploration, instrumentation and audio signal processing to name but a few [87]. The term "Digital Signal Processing", in its broadest sense, could apply to any operation carried out on a finite set of measurements for whatever purpose. A book on signal processing would usually contain detailed de­ scriptions of the standard mathematical machinery often used to describe signals. It would also motivate an approach to real world problems based on concepts and results developed in linear systems theory, that make use of some rather interesting properties of the time and frequency domain representations of signals. While this book assumes some familiarity with traditional methods the emphasis is altogether quite different. The aim is to describe general methods for carrying out optimal signal processing.

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.

“Over 170 figures are included in the book. … the material covered in the book is self-contained … . The balanced mix of real data examples, modeling software, and theory makes this book a useful reference for practitioners who use, or intend to use, 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.” (E.M.Psyadlo, zbMATH 0953.62065, 2022)

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.

Stata is the most flexible and extensible data analysis package available from a commercial vendor. R is a similarly flexible free and open source package for data analysis, with over 3,000 add-on packages available. This book shows you how to extend the power of Stata through the use of R. It introduces R using Stata terminology with which you are already familiar. It steps through more than 30 programs written in both languages, comparing and contrasting the two packages' different approaches. 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. The table of contents and index allow you to find equivalent R functions by looking up Stata commands and vice versa. The example programs and practice datasets for both R and Stata are available for download.

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. I was determined to produce a package that could draw every statistical graphic I had ever seen. The structure of the program was a collection of procedures named after the basic graph types they p- duced. The graphics code was roughly one and a half megabytes in size. In the early 1990’s, I redesigned the SYSTAT graphics package using - ject-based technology. I intended to produce a more comprehensive and - namic package. I accomplished this by embedding graphical elements in a tree structure. Rendering graphics was done by walking the tree and editing worked by adding and deleting nodes. The code size fell to under a megabyte. In the late 1990’s, I collaborated with Dan Rope at the Bureau of Labor Statistics and Dan Carr at George Mason University to produce a graphics p- duction library called GPL, this time in Java. Our goal was to develop graphics components. This book was nourished by that project. So far, the GPL code size is under half a megabyte.

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.

Every advance in computer architecture and software tempts statisticians to tackle numerically harder problems. To do so intelligently requires a good working knowledge of numerical analysis. This book equips students to craft their own software and to understand the advantages and disadvantages of different numerical methods. 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.In this second edition, the material on optimization has been completely rewritten. There is now an entire chapter on the MM algorithm in addition to more comprehensive treatments of constrained optimization, penalty and barrier methods, and model selection via the lasso. There is also new material on the Cholesky decomposition, Gram-Schmidt orthogonalization, the QR decomposition, the singular value decomposition, and reproducing kernel Hilbert spaces. The discussions of the bootstrap, permutation testing, independent Monte Carlo, and hidden Markov chains are updated, and a new chapter on advanced MCMC topics introduces students to Markov random fields, reversible jump MCMC, and convergence analysis in Gibbssampling.Numerical Analysis for Statisticians can serve as a graduate text for a course surveying computational statistics. With a careful selection of topics and appropriate supplementation, it can be used at the undergraduate level. It contains enough material for a graduate course on optimization theory. Because many chapters are nearly self-contained, professional statisticians will also find the book useful as a reference.

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