Sampling consists of selection, acquisition, and quantification of a part of the population. While selection and acquisition apply to physical sampling units of the population, quantification pertains only to the variable of interest, which is a particular characteristic of the sampling units. A sampling procedure is expected to provide a sample that is representative with respect to some specified criteria. Composite sampling, under idealized conditions, incurs no loss of information for estimating the population means. But an important limitation to the method has been the loss of information on individual sample values, such as, the extremely large value. In many of the situations where individual sample values are of interest or concern, composite sampling methods can be suitably modified to retrieve the information on individual sample values that may be lost due to compositing. This book presents statistical solutions to issues that arise in the context of applications of composite sampling.

Containing a summary of several recent results on Markov-based input modeling in a coherent notation, this book introduces and compares algorithms for parameter fitting and gives an overview of available software tools in the area. Due to progress made in recent years with respect to new algorithms to generate PH distributions and Markovian arrival processes from measured data, the models outlined are useful alternatives to other distributions or stochastic processes used for input modeling. Graduate students and researchers in applied probability, operations research and computer science along with practitioners using simulation or analytical models for performance analysis and capacity planning will find the unified notation and up-to-date results presented useful. Input modeling is the key step in model based system analysis to adequately describe the load of a system using stochastic models.

The goal of input modeling is to find a stochastic model to describe a sequence ofmeasurements from a real system to model for example the inter-arrival times of packets in a computer network or failure times of components in a manufacturing plant. Typical application areas are performance and dependability analysis of computer systems, communication networks, logistics or manufacturing systems but also the analysis of biological or chemical reaction networks and similar problems. Often the measured values have a high variability and are correlated. It s been known for a long time that Markov based models like phase type distributions or Markovian arrival processes are very general and allow one to capture even complex behaviors. However, the parameterization of these models results often in a complex and non-linear optimization problem. Only recently, several new results about the modeling capabilities of Markov based models and algorithms to fit the parameters of those models have been published.

"

Separation of signal from noise is the most fundamental problem in data analysis, arising in such fields as: signal processing, econometrics, actuarial science, and geostatistics. This book introduces the local regression method in univariate and multivariate settings, with extensions to local likelihood and density estimation. Practical information is also included on how to implement these methods in the programs S-PLUS and LOCFIT.

Looking back at the years that have passed since the realization of the very first electronic, multi-purpose computers, one observes a tremendous growth in hardware and software performance. Today, researchers and engi neers have access to computing power and software that can solve numerical problems which are not fully understood in terms of existing mathemati cal theory. Thus, computational sciences must in many respects be viewed as experimental disciplines. As a consequence, there is a demand for high quality, flexible software that allows, and even encourages, experimentation with alternative numerical strategies and mathematical models. Extensibil ity is then a key issue; the software must provide an efficient environment for incorporation of new methods and models that will be required in fu ture problem scenarios. The development of such kind of flexible software is a challenging and expensive task. One way to achieve these goals is to in vest much work in the design and implementation of generic software tools which can be used in a wide range of application fields. In order to provide a forum where researchers could present and discuss their contributions to the described development, an International Work shop on Modern Software Tools for Scientific Computing was arranged in Oslo, Norway, September 16-18, 1996. This workshop, informally referred to as Sci Tools '96, was a collaboration between SINTEF Applied Mathe matics and the Departments of Informatics and Mathematics at the Uni versity of Oslo."

The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.

Developments in both computer hardware and Perhaps the greatest impact has been felt by the software over the decades have fundamentally education community. Today, it is nearly changed the way people solve problems. impossible to find a college or university that has Technical professionals have greatly benefited not introduced mathematical computation in from new tools and techniques that have allowed some form, into the curriculum. Students now them to be more efficient, accurate, and creative have regular access to the amount of in their work. computational power that were available to a very exclusive set of researchers five years ago. This Maple V and the new generation of mathematical has produced tremendous pedagogical computation systems have the potential of challenges and opportunities. having the same kind of revolutionary impact as high-level general purpose programming Comparisons to the calculator revolution of the languages (e.g. FORTRAN, BASIC, C), 70's are inescapable. Calculators have application software (e.g. spreadsheets, extended the average person's ability to solve Computer Aided Design - CAD), and even common problems more efficiently, and calculators have had. Maple V has amplified our arguably, in better ways. Today, one needs at mathematical abilities: we can solve more least a calculator to deal with standard problems problems more accurately, and more often. In in life -budgets, mortgages, gas mileage, etc. specific disciplines, this amplification has taken For business people or professionals, the excitingly different forms.

A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance. The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics. The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors' accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB (R) GUIs allows students to discover patterns and make conjectures.

This book presents the statistical analysis of compositional data sets, i.e., data in percentages, proportions, concentrations, etc. The subject is covered from its grounding principles to the practical use in descriptive exploratory analysis, robust linear models and advanced multivariate statistical methods, including zeros and missing values, and paying special attention to data visualization and model display issues. Many illustrated examples and code chunks guide the reader into their modeling and interpretation. And, though the book primarily serves as a reference guide for the R package "compositions," it is also a general introductory text on Compositional Data Analysis. Awareness of their special characteristics spread in the Geosciences in the early sixties, but a strategy for properly dealing with them was not available until the works of Aitchison in the eighties. Since then, research has expanded our understanding of their theoretical principles and the potentials and limitations of their interpretation. This is the first comprehensive textbook addressing these issues, as well as their practical implications with regard to software. The book is intended for scientists interested in statistically analyzing their compositional data. The subject enjoys relatively broad awareness in the geosciences and environmental sciences, but the spectrum of recent applications also covers areas like medicine, official statistics, and economics. Readers should be familiar with basic univariate and multivariate statistics. Knowledge of R is recommended but not required, as the book is self-contained.

Intended for both researchers and practitioners, this book will be a valuable resource for studying and applying recent robust statistical methods. It contains up-to-date research results in the theory of robust statistics

Treats computational aspects and algorithms and shows interesting and new applications.

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."

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.

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.

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.

Recent advances in the understanding of star formation and evolution have been impressive and aspects of that knowledge are explored in this volume. The black hole stellar endpoints are studied and geodesic motion is explored. The emission of gravitational waves is featured due to their very recent experimental discovery.The second aspect of the text is space exploration which began 62 years ago with the Sputnik Earth satellite followed by the landing on the Moon just 50 years ago. Since then Mars has been explored remotely as well as flybys of the outer planets and probes which have escaped the solar system. The text explores many aspects of rocket travel. Finally possibilities for interstellar travel are discussed.All these topics are treated in a unified way using the Matlab App to combine text, figures, formulae and numeric input and output. In this way the reader may vary parameters and see the results in real time. That experience aids in building up an intuitive feel for the many specific problems given in this text.

Accessible to a general audience with some background in statistics and computing Many examples and extended case studies Illustrations using R and Rstudio A true blend of statistics and computer science -- not just a grab bag of topics from each

Modelling Survival Data in Medical Research, Fourth Edition describes the analysis of survival data, illustrated using a wide range of examples from biomedical research. Written in a non-technical style, it concentrates on how the techniques are used in practice. Starting with standard methods for summarising survival data, Cox regression and parametric modelling, the book covers many more advanced techniques, including interval-censoring, frailty modelling, competing risks, analysis of multiple events, and dependent censoring. This new edition contains chapters on Bayesian survival analysis and use of the R software. Earlier chapters have been extensively revised and expanded to add new material on several topics. These include methods for assessing the predictive ability of a model, joint models for longitudinal and survival data, and modern methods for the analysis of interval-censored survival data. Features: Presents an accessible account of a wide range of statistical methods for analysing survival data Contains practical guidance on modelling survival data from the author's many years of experience in teaching and consultancy Shows how Bayesian methods can be used to analyse survival data Includes details on how R can be used to carry out all the methods described, with guidance on the interpretation of the resulting output Contains many real data examples and additional data sets that can be used for coursework All data sets used are available in electronic format from the publisher's website Modelling Survival Data in Medical Research, Fourth Edition is an invaluable resource for statisticians in the pharmaceutical industry and biomedical research centres, research scientists and clinicians who are analysing their own data, and students following undergraduate or postgraduate courses in survival analysis.

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.

"MATLAB for Neuroscientists" serves as the only complete study manual and teaching resource for MATLAB, the globally accepted standard for scientific computing, in the neurosciences and psychology. This unique introduction can be used to learn the entire empirical and experimental process (including stimulus generation, experimental control, data collection, data analysis, modeling, and more), and the 2nd Edition continues to ensure that a wide variety of computational problems can be addressed in a single programming environment.

This updated edition features additional material on the creation of visual stimuli, advanced psychophysics, analysis of LFP data, choice probabilities, synchrony, and advanced spectral analysis. Users at a variety of levels-advanced undergraduates, beginning graduate students, and researchers looking to modernize their skills-will learn to design and implement their own analytical tools, and gain the fluency required to meet the computational needs of neuroscience practitioners.
The first complete volume on MATLAB focusing on neuroscience and psychology applicationsProblem-based approach with many examples from neuroscience and cognitive psychology using real dataIllustrated in full color throughout Careful tutorial approach, by authors who are award-winning educators with strong teaching experience

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.

This is the first book to show the capabilities of Microsoft Excel to teach biological and life sciences statistics effectively. It is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical science problems. If understanding statistics isn't your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in science courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2007 for Biological and Life Sciences Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work. Each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand science problems. Practice problems are provided at the end of each chapter with their solutions in an appendix. Separately, there is a full Practice Test (with answers in an Appendix) that allows readers to test what they have learned.

The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. At the same time, it is now being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems.
In this extensively updated new edition there is more material on methods and examples including several new approaches for discrete variables, new results on risk measures in modeling and Monte Carlo sampling methods, a new chapter on relationships to other methods including approximate dynamic programming, robust optimization and online methods.

The book is highly illustrated with chapter summaries and many examples and exercises. Students, researchers and practitioners in operations research and the optimization area will find it particularly of interest.

Review of First Edition:

"The discussion on modeling issues, the large number of examples used to illustrate the material, and the breadth of the coverage make'Introduction to Stochastic Programming' an ideal textbook for the area." (Interfaces, 1998)

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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.

"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.

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."