Dealing with methods for sampling from posterior distributions and how to compute posterior quantities of interest using Markov chain Monte Carlo (MCMC) samples, this book addresses such topics as improving simulation accuracy, marginal posterior density estimation, estimation of normalizing constants, constrained parameter problems, highest posterior density interval calculations, computation of posterior modes, and posterior computations for proportional hazards models and Dirichlet process models. The authors also discuss model comparisons, including both nested and non-nested models, marginal likelihood methods, ratios of normalizing constants, Bayes factors, the Savage-Dickey density ratio, Stochastic Search Variable Selection, Bayesian Model Averaging, the reverse jump algorithm, and model adequacy using predictive and latent residual approaches. The book presents an equal mixture of theory and applications involving real data, and is intended as a graduate textbook or a reference book for a one-semester course at the advanced masters or Ph.D. level. It will also serve as a useful reference for applied or theoretical researchers as well as practitioners.

The intensive use of automatic data acquisition system and the use of cloud computing for process monitoring have led to an increased occurrence of industrial processes that utilize statistical process control and capability analysis. These analyses are performed almost exclusively with multivariate methodologies. The aim of this Brief is to present the most important MSQC techniques developed in R language. The book is divided into two parts. The first part contains the basic R elements, an introduction to statistical procedures, and the main aspects related to Statistical Quality Control (SQC). The second part covers the construction of multivariate control charts, the calculation of Multivariate Capability Indices.

This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.

Automatic Graph Drawing is concerned with the layout of relational structures as they occur in Computer Science (Data Base Design, Data Mining, Web Mining), Bioinformatics (Metabolic Networks), Businessinformatics (Organization Diagrams, Event Driven Process Chains), or the Social Sciences (Social Networks).

In mathematical terms, such relational structures are modeled as graphs or more general objects such as hypergraphs, clustered graphs, or compound graphs. A variety of layout algorithms that are based on graph theoretical foundations have been developed in the last two decades and implemented in software systems.

After an introduction to the subject area and a concise treatment of the technical foundations for the subsequent chapters, this book features 14 chapters on state-of-the-art graph drawing software systems, ranging from general "tool boxes'' to customized software for various applications. These chapters are written by leading experts, they follow a uniform scheme and can be read independently from each other.

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 Gibbs sampling. 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.

Biological and biomedical studies have entered a new era over the past two decades thanks to the wide use of mathematical models and computational approaches. A booming of computational biology, which sheerly was a theoretician's fantasy twenty years ago, has become a reality. Obsession with computational biology and theoretical approaches is evidenced in articles hailing the arrival of what are va- ously called quantitative biology, bioinformatics, theoretical biology, and systems biology. New technologies and data resources in genetics, such as the International HapMap project, enable large-scale studies, such as genome-wide association st- ies, which could potentially identify most common genetic variants as well as rare variants of the human DNA that may alter individual's susceptibility to disease and the response to medical treatment. Meanwhile the multi-electrode recording from behaving animals makes it feasible to control the animal mental activity, which could potentially lead to the development of useful brain-machine interfaces. - bracing the sheer volume of genetic, genomic, and other type of data, an essential approach is, ?rst of all, to avoid drowning the true signal in the data. It has been witnessed that theoretical approach to biology has emerged as a powerful and st- ulating research paradigm in biological studies, which in turn leads to a new - search paradigm in mathematics, physics, and computer science and moves forward with the interplays among experimental studies and outcomes, simulation studies, and theoretical investigations.

Molchanov, S.: Lectures on random media.- Zeitouni, Ofer: Random walks in random environment.-den Hollander, Frank: Random polymers "

Rcpp is the glue that binds the power and versatility of R with the speed and efficiency of C++. With Rcpp, the transfer of data between R and C++ is nearly seamless, and high-performance statistical computing is finally accessible to most R users. Rcpp should be part of every statistician's toolbox. -- Michael Braun, MIT Sloan School of Management

"Seamless R and C++ integration with Rcpp" is simply a wonderful book. For anyone who uses C/C++ and R, it is an indispensable resource. The writing is outstanding. A huge bonus is the section on applications. This section covers the matrix packages Armadillo and Eigen and the GNU Scientific Library as well as RInside which enables you to use R inside C++. These applications are what most of us need to know to really do scientific programming with R and C++. I love this book. -- Robert McCulloch, University of Chicago Booth School of Business

Rcpp is now considered an essential package for anybody doing serious computational research using R. Dirk's book is an excellent companion and takes the reader from a gentle introduction to more advanced applications via numerous examples and efficiency enhancing gems. The book is packed with all you might have ever wanted to know about Rcpp, its cousins (RcppArmadillo, RcppEigen .etc.), modules, package development and sugar. Overall, this book is a must-have on your shelf. -- Sanjog Misra, UCLA Anderson School of Management

The Rcpp package represents a major leap forward for scientific computations with R. With very few lines of C++ code, one has R's data structures readily at hand for further computations in C++. Hence, high-level numerical programming can be made in C++ almost as easily as in R, but often with a substantial speed gain. Dirk is a crucial person in these developments, and his book takes the reader from the first fragile steps on to using the full Rcpp machinery. A very recommended book -- Soren Hojsgaard," "Department of Mathematical Sciences, Aalborg University, Denmark

"Seamless R and C ++ Integration with Rcpp" provides the first comprehensive introduction to Rcpp. Rcpp has become the most widely-used language extension for R, and is deployed by over one-hundred different CRAN and BioConductor packages. Rcpp permits users to pass scalars, vectors, matrices, list or entire R objects back and forth between R and C++ with ease. This brings the depth of the R analysis framework together with the power, speed, and efficiency of C++.

Dirk Eddelbuettel has been a contributor to CRAN for over a decade and maintains around twenty packages. He is the Debian/Ubuntu maintainer for R and other quantitative software, edits the CRAN Task Views for Finance and High-Performance Computing, is a co-founder of the annual R/Finance conference, and an editor of the Journal of Statistical Software. He holds a Ph.D. in Mathematical Economics from EHESS (Paris), and works in Chicago as a Senior Quantitative Analyst.

"

Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.

Many of the commonly used methods for modeling and fitting psychophysical data are special cases of statistical procedures of great power and generality, notably the Generalized Linear Model (GLM). This book illustrates how to fit data from a variety of psychophysical paradigms using modern statistical methods and the statistical language R.The paradigms include signal detection theory, psychometric function fitting, classification images and more. In two chapters, recently developed methods for scaling appearance, maximum likelihood difference scaling and maximum likelihood conjoint measurement are examined.The authors also consider the applicationof mixed-effects models to psychophysical data.

R is an open-source programming language that is widely used by statisticians and is seeing enormous growth in its application to data in all fields. It is interactive, containing many powerful facilities for optimization, model evaluation, model selection, and graphical display of data. The reader who fits data in R can readily make use of these methods. The researcher who uses R to fit and model his data has access to most recently developed statistical methods.

This book does not assume that the reader is familiar with R, and a little experience with any programming language is all that is needed to appreciate this book. There are large numbers of examples of R in the text and the source code for all examples is available in an R package MPDiR available through R.
Kenneth Knoblauch is a researcher in the Department of Integrative Neurosciences in Inserm Unit 846, The Stem Cell and Brain Research Institute and associated with the University Claude Bernard, Lyon 1, in France.

Laurence T. Maloney is Professor of Psychology and Neural Science at New York University. His research focusses on applications of mathematical models to perception, motor control and decision making."

Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.

Bayesian Networks in R with Applications in Systems Biology is unique as it introduces the reader to the essential concepts in Bayesian network modeling and inference in conjunction with examples in the open-source statistical environment R. The level of sophistication is also gradually increased across the chapters with exercises and solutions for enhanced understanding for hands-on experimentation of the theory and concepts. The application focuses on systems biology with emphasis on modeling pathways and signaling mechanisms from high-throughput molecular data. Bayesian networks have proven to be especially useful abstractions in this regard. Their usefulness is especially exemplified by their ability to discover new associations in addition to validating known ones across the molecules of interest. It is also expected that the prevalence of publicly available high-throughput biological data sets may encourage the audience to explore investigating novel paradigms using the approaches presented in the book.

An overview of the theory and application of linear and nonlinear mixed-effects models in the analysis of grouped data, such as longitudinal data, repeated measures, and multilevel data. The authors present a unified model-building strategy for both models and apply this to the analysis of over 20 real datasets from a wide variety of areas, including pharmacokinetics, agriculture, and manufacturing. Much emphasis is placed on the use of graphical displays at the various phases of the model-building process, starting with exploratory plots of the data and concluding with diagnostic plots to assess the adequacy of a fitted model. The NLME library for analyzing mixed-effects models in S and S-PLUS, developed by the authors, provides the underlying software for implementing the methods presented. This balanced mix of real data examples, modeling software, and theory makes the 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.

Financial Risk Modelling and Portfolio Optimization with R, 2nd Edition Bernhard Pfaff, Invesco Global Asset Allocation, Germany A must have text for risk modelling and portfolio optimization using R. This book introduces the latest techniques advocated for measuring financial market risk and portfolio optimization, and provides a plethora of R code examples that enable the reader to replicate the results featured throughout the book. This edition has been extensively revised to include new topics on risk surfaces and probabilistic utility optimization as well as an extended introduction to R language. Financial Risk Modelling and Portfolio Optimization with R: * Demonstrates techniques in modelling financial risks and applying portfolio optimization techniques as well as recent advances in the field. * Introduces stylized facts, loss function and risk measures, conditional and unconditional modelling of risk; extreme value theory, generalized hyperbolic distribution, volatility modelling and concepts for capturing dependencies. * Explores portfolio risk concepts and optimization with risk constraints. * Is accompanied by a supporting website featuring examples and case studies in R. * Includes updated list of R packages for enabling the reader to replicate the results in the book. Graduate and postgraduate students in finance, economics, risk management as well as practitioners in finance and portfolio optimization will find this book beneficial. It also serves well as an accompanying text in computer-lab classes and is therefore suitable for self-study.

Today, certain computer software systems exist which surpass the computational ability of researchers when their mathematical techniques are applied to many areas of science and engineering. These computer systems can perform a large portion of the calculations seen in mathematical analysis. Despite this massive power, thousands of people use these systems as a routine resource for everyday calculations. These software programs are commonly called "Computer Algebra" systems. They have names such as MACSYMA, MAPLE, muMATH, REDUCE and SMP. They are receiving credit as a computational aid with in creasing regularity in articles in the scientific and engineering literature. When most people think about computers and scientific research these days, they imagine a machine grinding away, processing numbers arithmetically. It is not generally realized that, for a number of years, computers have been performing non-numeric computations. This means, for example, that one inputs an equa tion and obtains a closed form analytic answer. It is these Computer Algebra systems, their capabilities, and applications which are the subject of the papers in this volume."

This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail.

A t the terminal seated, the answering tone: pond and temple bell. ODAY as in the past, statistical method is profoundly affected by T resources for numerical calculation and visual display. The main line of development of statistical methodology during the first half of this century was conditioned by, and attuned to, the mechanical desk calculator. Now statisticians may use electronic computers of various kinds in various modes, and the character of statistical science has changed accordingly. Some, but not all, modes of modern computation have a flexibility and immediacy reminiscent of the desk calculator. They preserve the virtues of the desk calculator, while immensely exceeding its scope. Prominent among these is the computer language and conversational computing system known by the initials APL. This book is addressed to statisticians. Its first aim is to interest them in using APL in their work-for statistical analysis of data, for numerical support of theoretical studies, for simulation of random processes. In Part A the language is described and illustrated with short examples of statistical calculations. Part B, presenting some more extended examples of statistical analysis of data, has also the further aim of suggesting the interplay of computing and theory that must surely henceforth be typical of the develop ment of statistical science."

S is a high-level language for manipulating, analysing and displaying

data. It forms the basis of two highly acclaimed and widely used data

analysis software systems, the commercial S-PLUS(r) and the Open

Source R. This book provides an in-depth guide to writing software in

the S language under either or both of those systems. It is intended

for readers who have some acquaintance with the S language and want to

know how to use it more effectively, for example to build re-usable

tools for streamlining routine data analysis or to implement new

statistical methods.

One of the outstanding strengths of the S language is the ease with

which it can be extended by users. S is a functional language, and

functions written by users are first-class objects treated in the same

way as functions provided by the system. S code is eminently readable

and so a good way to document precisely what algorithms were used, and

as much of the implementations are themselves written in S, they can be

studied as models and to understand their subtleties. The current

implementations also provide easy ways for S functions to call

compiled code written in C, Fortran and similar languages; this is

documented here in depth.

Increasingly S is being used for statistical or graphical analysis

within larger software systems or for whole vertical-market

applications. The interface facilities are most developed on

Windows(r) and these are covered with worked examples.

The authors have written the widely used Modern Applied Statistics

with S-PLUS, now in its third edition, and several software libraries

that enhance S-PLUS and R; these and the examples used in both books

are available on the Internet.

Dr. W.N. Venables is a senior Statistician with the CSIRO/CMIS

Environmetrics Project in Australia, having been at the Department of

Statistics, University of Adelaide for many years previously.

Professor B.D. Ripley holds the Chair of Applied Statistics at the

University of Oxford, and is the author of four other books on spatial

statistics, simulation, pattern recognition and neural networks. Both

authors are known and respected throughout the international S and R

communities, for their books, workshops, short courses, freely

available software and through their extensive contributions to the

S-news and R mailing lists.

Keith M. Ponting Speech Research Unit, DERA Malvern St. Andrew's Road, Great Malvern, Worcs. WR14 3PS, UK email: ponting

"Fast Compact Algorithms and Software for Spline Smoothing" investigates algorithmic alternatives for computing cubic smoothing splines when the amount of smoothing is determined automatically by minimizing the generalized cross-validation score. These algorithms are based on Cholesky factorization, QR factorization, or the fast Fourier transform. All algorithms are implemented in MATLAB and are compared based on speed, memory use, and accuracy. An overall best algorithm is identified, which allows very large data sets to be processed quickly on a personal computer.

Grimmett, Geoffrey: Percolation and disordered systems.- Kesten, Harry: Aspects of first passage percolation. "

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.

Accompanying the book, as with all TELOS sponsored publications, is an electronic component. In this case it is a DOS-Diskette produced by one of the coauthors, Paul Wellin. This diskette consists of "Mathematica "notebooks and packages which contain the codes for all examples and exercises in the book, as well as additional materials intended to extend many ideas covered in the text. It is of great value to teachers, students, and others using this book to learn how to effectively program with "Mathematica" .

Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.

This book helps readers understand the mathematics of machine learning, and apply them in different situations. It is divided into two basic parts, the first of which introduces readers to the theory of linear algebra, probability, and data distributions and it's applications to machine learning. It also includes a detailed introduction to the concepts and constraints of machine learning and what is involved in designing a learning algorithm. This part helps readers understand the mathematical and statistical aspects of machine learning. In turn, the second part discusses the algorithms used in supervised and unsupervised learning. It works out each learning algorithm mathematically and encodes it in R to produce customized learning applications. In the process, it touches upon the specifics of each algorithm and the science behind its formulation. The book includes a wealth of worked-out examples along with R codes. It explains the code for each algorithm, and readers can modify the code to suit their own needs. The book will be of interest to all researchers who intend to use R for machine learning, and those who are interested in the practical aspects of implementing learning algorithms for data analysis. Further, it will be particularly useful and informative for anyone who has struggled to relate the concepts of mathematics and statistics to machine learning.