This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

This volume presents selected peer-reviewed contributions from The International Work-Conference on Time Series, ITISE 2015, held in Granada, Spain, July 1-3, 2015. It discusses topics in time series analysis and forecasting, advanced methods and online learning in time series, high-dimensional and complex/big data time series as well as forecasting in real problems. The International Work-Conferences on Time Series (ITISE) provide a forum for scientists, engineers, educators and students to discuss the latest ideas and implementations in the foundations, theory, models and applications in the field of time series analysis and forecasting. It focuses on interdisciplinary and multidisciplinary research encompassing the disciplines of computer science, mathematics, statistics and econometrics.

This book offers a collection of recent contributions and emerging ideas in the areas of robust statistics presented at the International Conference on Robust Statistics 2015 (ICORS 2015) held in Kolkata during 12-16 January, 2015. The book explores the applicability of robust methods in other non-traditional areas which includes the use of new techniques such as skew and mixture of skew distributions, scaled Bregman divergences, and multilevel functional data methods; application areas being circular data models and prediction of mortality and life expectancy. The contributions are of both theoretical as well as applied in nature. Robust statistics is a relatively young branch of statistical sciences that is rapidly emerging as the bedrock of statistical analysis in the 21st century due to its flexible nature and wide scope. Robust statistics supports the application of parametric and other inference techniques over a broader domain than the strictly interpreted model scenarios employed in classical statistical methods. The aim of the ICORS conference, which is being organized annually since 2001, is to bring together researchers interested in robust statistics, data analysis and related areas. The conference is meant for theoretical and applied statisticians, data analysts from other fields, leading experts, junior researchers and graduate students. The ICORS meetings offer a forum for discussing recent advances and emerging ideas in statistics with a focus on robustness, and encourage informal contacts and discussions among all the participants. They also play an important role in maintaining a cohesive group of international researchers interested in robust statistics and related topics, whose interactions transcend the meetings and endure year round.

This volume collects selected, peer-reviewed contributions from the 2nd Conference of the International Society for Nonparametric Statistics (ISNPS), held in Cadiz (Spain) between June 11-16 2014, and sponsored by the American Statistical Association, the Institute of Mathematical Statistics, the Bernoulli Society for Mathematical Statistics and Probability, the Journal of Nonparametric Statistics and Universidad Carlos III de Madrid. The 15 articles are a representative sample of the 336 contributed papers presented at the conference. They cover topics such as high-dimensional data modelling, inference for stochastic processes and for dependent data, nonparametric and goodness-of-fit testing, nonparametric curve estimation, object-oriented data analysis, and semiparametric inference. The aim of the ISNPS 2014 conference was to bring together recent advances and trends in several areas of nonparametric statistics in order to facilitate the exchange of research ideas, promote collaboration among researchers from around the globe, and contribute to the further development of the field.

This second edition is an intensively revised and updated version of the book MATLAB (R) and Design Recipes for Earth Sciences. It aims to introduce students to the typical course followed by a data analysis project in earth sciences. A project usually involves searching relevant literature, reviewing and ranking published books and journal articles, extracting relevant information from the literature in the form of text, data, or graphs, searching and processing the relevant original data using MATLAB, and compiling and presenting the results as posters, abstracts, and oral presentations using graphics design software. The text of this book includes numerous examples on the use of internet resources, on the visualization of data with MATLAB, and on preparing scientific presentations. As with the book MATLAB Recipes for Earth Sciences-4rd Edition (2015), which demonstrates the use of statistical and numerical methods on earth science data, this book uses state-of-the art software packages, including MATLAB and the Adobe Creative Suite, to process and present geoscientific information collected during the course of an earth science project. The book's supplementary electronic material (available online through the publisher's website) includes color versions of all figures, recipes with all the MATLAB commands featured in the book, the example data, exported MATLAB graphics, and screenshots of the most important steps involved in processing the graphics.

This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms. Another feature of the book is that it emphasizes what model underlies a procedure and what objective function is optimized for fitting the model to data. The author believes that the matrix-based learning of such models and objective functions is the fastest way to comprehend multivariate data analysis. The text is arranged so that readers can intuitively capture the purposes for which multivariate analysis procedures are utilized: plain explanations of the purposes with numerical examples precede mathematical descriptions in almost every chapter. This volume is appropriate for undergraduate students who already have studied introductory statistics. Graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis will also find the book useful, as it is based on modern matrix formulations with a special emphasis on singular value decomposition among theorems in matrix algebra. The book begins with an explanation of fundamental matrix operations and the matrix expressions of elementary statistics, followed by the introduction of popular multivariate procedures with advancing levels of matrix algebra chapter by chapter. This organization of the book allows readers without knowledge of matrices to deepen their understanding of multivariate data analysis.

The revised Fourth Edition of this popular textbook is redesigned with Excel 2016 to encourage business students to develop competitive advantages for use in their future careers as decision makers. Students learn to build models using logic and experience, produce statistics using Excel 2016 with shortcuts, and translate results into implications for decision makers. The textbook features new examples and assignments on global markets, including cases featuring Chipotle and Costco. A number of examples focus on business in emerging global markets with particular emphasis on emerging markets in Latin America, China, and India. Results are linked to implications for decision making with sensitivity analyses to illustrate how alternate scenarios can be compared. The author emphasises communicating results effectively in plain English and with screenshots and compelling graphics in the form of memos and PowerPoints. Chapters include screenshots to make it easy to conduct analyses in Excel 2016. PivotTables and PivotCharts, used frequently in business, are introduced from the start. The Fourth Edition features Monte Carlo simulation in four chapters, as a tool to illustrate the range of possible outcomes from decision makers' assumptions and underlying uncertainties. Model building with regression is presented as a process, adding levels of sophistication, with chapters on multicollinearity and remedies, forecasting and model validation, auto-correlation and remedies, indicator variables to represent segment differences, and seasonality, structural shifts or shocks in time series models. Special applications in market segmentation and portfolio analysis are offered, and an introduction to conjoint analysis is included. Nonlinear models are motivated with arguments of diminishing or increasing marginal response.

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

The goal of this guide and manual is to provide a practical and brief overview of the theory on computerized adaptive testing (CAT) and multistage testing (MST) and to illustrate the methodologies and applications using R open source language and several data examples. Implementation relies on the R packages catR and mstR that have been already or are being developed by the first author (with the team) and that include some of the newest research algorithms on the topic. The book covers many topics along with the R-code: the basics of R, theoretical overview of CAT and MST, CAT designs, CAT assembly methodologies, CAT simulations, catR package, CAT applications, MST designs, IRT-based MST methodologies, tree-based MST methodologies, mstR package, and MST applications. CAT has been used in many large-scale assessments over recent decades, and MST has become very popular in recent years. R open source language also has become one of the most useful tools for applications in almost all fields, including business and education. Though very useful and popular, R is a difficult language to learn, with a steep learning curve. Given the obvious need for but with the complex implementation of CAT and MST, it is very difficult for users to simulate or implement CAT and MST. Until this manual, there has been no book for users to design and use CAT and MST easily and without expense; i.e., by using the free R software. All examples and illustrations are generated using predefined scripts in R language, available for free download from the book's website.

This textbook provides an introduction to the free software 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. Working code and data for Python solutions for each test, together with easy-to-follow Python examples, can be reproduced by the reader and reinforce their immediate understanding of the topic. With recent advances in the Python ecosystem, Python has become a popular language for scientific computing, offering a powerful environment for statistical data analysis and an interesting alternative to R. The book is intended for master and PhD students, mainly from the life and medical sciences, with a basic knowledge of statistics. As it also provides some statistics background, the book can be used by anyone who wants to perform a statistical data analysis.

This book discusses examples in parametric inference with R. Combining basic theory with modern approaches, it presents the latest developments and trends in statistical inference for students who do not have an advanced mathematical and statistical background. The topics discussed in the book are fundamental and common to many fields of statistical inference and thus serve as a point of departure for in-depth study. The book is divided into eight chapters: Chapter 1 provides an overview of topics on sufficiency and completeness, while Chapter 2 briefly discusses unbiased estimation. Chapter 3 focuses on the study of moments and maximum likelihood estimators, and Chapter 4 presents bounds for the variance. In Chapter 5, topics on consistent estimator are discussed. Chapter 6 discusses Bayes, while Chapter 7 studies some more powerful tests. Lastly, Chapter 8 examines unbiased and other tests. Senior undergraduate and graduate students in statistics and mathematics, and those who have taken an introductory course in probability, will greatly benefit from this book. Students are expected to know matrix algebra, calculus, probability and distribution theory before beginning this course. Presenting a wealth of relevant solved and unsolved problems, the book offers an excellent tool for teachers and instructors who can assign homework problems from the exercises, and students will find the solved examples hugely beneficial in solving the exercise problems.

This book covers all the topics found in introductory descriptive statistics courses, including simple linear regression and time series analysis, the fundamentals of inferential statistics (probability theory, random sampling and estimation theory), and inferential statistics itself (confidence intervals, testing). Each chapter starts with the necessary theoretical background, which is followed by a variety of examples. The core examples are based on the content of the respective chapter, while the advanced examples, designed to deepen students' knowledge, also draw on information and material from previous chapters. The enhanced online version helps students grasp the complexity and the practical relevance of statistical analysis through interactive examples and is suitable for undergraduate and graduate students taking their first statistics courses, as well as for undergraduate students in non-mathematical fields, e.g. economics, the social sciences etc.

This book features research contributions from The Abel Symposium on Statistical Analysis for High Dimensional Data, held in Nyvagar, Lofoten, Norway, in May 2014. The focus of the symposium was on statistical and machine learning methodologies specifically developed for inference in "big data" situations, with particular reference to genomic applications. The contributors, who are among the most prominent researchers on the theory of statistics for high dimensional inference, present new theories and methods, as well as challenging applications and computational solutions. Specific themes include, among others, variable selection and screening, penalised regression, sparsity, thresholding, low dimensional structures, computational challenges, non-convex situations, learning graphical models, sparse covariance and precision matrices, semi- and non-parametric formulations, multiple testing, classification, factor models, clustering, and preselection. Highlighting cutting-edge research and casting light on future research directions, the contributions will benefit graduate students and researchers in computational biology, statistics and the machine learning community.

This book reviews the theoretical concepts, leading-edge techniques and practical tools involved in the latest multi-disciplinary approaches addressing the challenges of big data. Illuminating perspectives from both academia and industry are presented by an international selection of experts in big data science. Topics and features: describes the innovative advances in theoretical aspects of big data, predictive analytics and cloud-based architectures; examines the applications and implementations that utilize big data in cloud architectures; surveys the state of the art in architectural approaches to the provision of cloud-based big data analytics functions; identifies potential research directions and technologies to facilitate the realization of emerging business models through big data approaches; provides relevant theoretical frameworks, empirical research findings, and numerous case studies; discusses real-world applications of algorithms and techniques to address the challenges of big datasets.

This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.

These are the proceedings of the 22nd International Conference on Domain Decomposition Methods, which was held in Lugano, Switzerland. With 172 participants from over 24 countries, this conference continued a long-standing tradition of internationally oriented meetings on Domain Decomposition Methods. The book features a well-balanced mix of established and new topics, such as the manifold theory of Schwarz Methods, Isogeometric Analysis, Discontinuous Galerkin Methods, exploitation of modern HPC architectures and industrial applications. As the conference program reflects, the growing capabilities in terms of theory and available hardware allow increasingly complex non-linear and multi-physics simulations, confirming the tremendous potential and flexibility of the domain decomposition concept.

Numerical computation, knowledge discovery and statistical data analysis integrated with powerful 2D and 3D graphics for visualization are the key topics of this book. The Python code examples powered by the Java platform can easily be transformed to other programming languages, such as Java, Groovy, Ruby and BeanShell. This book equips the reader with a computational platform which, unlike other statistical programs, is not limited by a single programming language.The author focuses on practical programming aspects and covers a broad range of topics, from basic introduction to the Python language on the Java platform (Jython), to descriptive statistics, symbolic calculations, neural networks, non-linear regression analysis and many other data-mining topics. He discusses how to find regularities in real-world data, how to classify data, and how to process data for knowledge discoveries. The code snippets are so short that they easily fit into single pages. Numeric Computation and Statistical Data Analysis on the Java Platform is a great choice for those who want to learn how statistical data analysis can be done using popular programming languages, who want to integrate data analysis algorithms in full-scale applications, and deploy such calculations on the web pages or computational servers regardless of their operating system. It is an excellent reference for scientific computations to solve real-world problems using a comprehensive stack of open-source Java libraries included in the DataMelt (DMelt) project and will be appreciated by many data-analysis scientists, engineers and students.

Practical Numerical and Scientific Computing with MATLAB (R) and Python concentrates on the practical aspects of numerical analysis and linear and non-linear programming. It discusses the methods for solving different types of mathematical problems using MATLAB and Python. Although the book focuses on the approximation problem rather than on error analysis of mathematical problems, it provides practical ways to calculate errors. The book is divided into three parts, covering topics in numerical linear algebra, methods of interpolation, numerical differentiation and integration, solutions of differential equations, linear and non-linear programming problems, and optimal control problems. This book has the following advantages: It adopts the programming languages, MATLAB and Python, which are widely used among academics, scientists, and engineers, for ease of use and contain many libraries covering many scientific and engineering fields. It contains topics that are rarely found in other numerical analysis books, such as ill-conditioned linear systems and methods of regularization to stabilize their solutions, nonstandard finite differences methods for solutions of ordinary differential equations, and the computations of the optimal controls. It provides a practical explanation of how to apply these topics using MATLAB and Python. It discusses software libraries to solve mathematical problems, such as software Gekko, pulp, and pyomo. These libraries use Python for solutions to differential equations and static and dynamic optimization problems. Most programs in the book can be applied in versions prior to MATLAB 2017b and Python 3.7.4 without the need to modify these programs. This book is aimed at newcomers and middle-level students, as well as members of the scientific community who are interested in solving math problems using MATLAB or Python.

This easy-to-follow applied book on semiparametric regression methods using R is intended to close the gap between the available methodology and its use in practice. Semiparametric regression has a large literature but much of it is geared towards data analysts who have advanced knowledge of statistical methods. While R now has a great deal of semiparametric regression functionality, many of these developments have not trickled down to rank-and-file statistical analysts. The authors assemble a broad range of semiparametric regression R analyses and put them in a form that is useful for applied researchers. There are chapters devoted to penalized spines, generalized additive models, grouped data, bivariate extensions of penalized spines, and spatial semi-parametric regression models. Where feasible, the R code is provided in the text, however the book is also accompanied by an external website complete with datasets and R code. Because of its flexibility, semiparametric regression has proven to be of great value with many applications in fields as diverse as astronomy, biology, medicine, economics, and finance. This book is intended for applied statistical analysts who have some familiarity with R.

This volume conveys some of the surprises, puzzles and success stories in high-dimensional and complex data analysis and related fields. Its peer-reviewed contributions showcase recent advances in variable selection, estimation and prediction strategies for a host of useful models, as well as essential new developments in the field. The continued and rapid advancement of modern technology now allows scientists to collect data of increasingly unprecedented size and complexity. Examples include epigenomic data, genomic data, proteomic data, high-resolution image data, high-frequency financial data, functional and longitudinal data, and network data. Simultaneous variable selection and estimation is one of the key statistical problems involved in analyzing such big and complex data. The purpose of this book is to stimulate research and foster interaction between researchers in the area of high-dimensional data analysis. More concretely, its goals are to: 1) highlight and expand the breadth of existing methods in big data and high-dimensional data analysis and their potential for the advancement of both the mathematical and statistical sciences; 2) identify important directions for future research in the theory of regularization methods, in algorithmic development, and in methodologies for different application areas; and 3) facilitate collaboration between theoretical and subject-specific researchers.

This book presents a theoretical and practical overview of computational modeling in bioengineering, focusing on a range of applications including electrical stimulation of neural and cardiac tissue, implantable drug delivery, cancer therapy, biomechanics, cardiovascular dynamics, as well as fluid-structure interaction for modelling of organs, tissues, cells and devices. It covers the basic principles of modeling and simulation with ordinary and partial differential equations using MATLAB and COMSOL Multiphysics numerical software. The target audience primarily comprises postgraduate students and researchers, but the book may also be beneficial for practitioners in the medical device industry.

Get an introduction to functional data structures using R and write more effective code and gain performance for your programs. This book teaches you workarounds because data in functional languages is not mutable: for example you'll learn how to change variable-value bindings by modifying environments, which can be exploited to emulate pointers and implement traditional data structures. You'll also see how, by abandoning traditional data structures, you can manipulate structures by building new versions rather than modifying them. You'll discover how these so-called functional data structures are different from the traditional data structures you might know, but are worth understanding to do serious algorithmic programming in a functional language such as R. By the end of Functional Data Structures in R, you'll understand the choices to make in order to most effectively work with data structures when you cannot modify the data itself. These techniques are especially applicable for algorithmic development important in big data, finance, and other data science applications. What You'll Learn Carry out algorithmic programming in R Use abstract data structures Work with both immutable and persistent data Emulate pointers and implement traditional data structures in R Build new versions of traditional data structures that are known Who This Book Is For Experienced or advanced programmers with at least a comfort level with R. Some experience with data structures recommended.

This textbook presents the basic concepts and methods of fluid mechanics, including Lagrangian and Eulerian descriptions, tensors of stresses and strains, continuity, momentum, energy, thermodynamics laws, and similarity theory. The models and their solutions are presented within a context of the mechanics of multiphase media. The treatment fully utilizes the computer algebra and software system Mathematica (R) to both develop concepts and help the reader to master modern methods of solving problems in fluid mechanics. Topics and features: Glossary of over thirty Mathematica (R) computer programs Extensive, self-contained appendix of Mathematica (R) functions and their use Chapter coverage of mechanics of multiphase heterogeneous media Detailed coverage of theory of shock waves in gas dynamics Thorough discussion of aerohydrodynamics of ideal and viscous fluids an d gases Complete worked examples with detailed solutions Problem-solving approach Foundations of Fluid Mechanics with Applications is a complete and accessible text or reference for graduates and professionals in mechanics, applied mathematics, physical sciences, materials science, and engineering. It is an essential resource for the study and use of modern solution methods for problems in fluid mechanics and the underlying mathematical models. The present, softcover reprint is designed to make this classic textbook available to a wider audience.

This focuses on the developing field of building probability models with the power of symbolic algebra systems. The book combines the uses of symbolic algebra with probabilistic/stochastic application and highlights the applications in a variety of contexts. The research explored in each chapter is unified by the use of A Probability Programming Language (APPL) to achieve the modeling objectives. APPL, as a research tool, enables a probabilist or statistician the ability to explore new ideas, methods, and models. Furthermore, as an open-source language, it sets the foundation for future algorithms to augment the original code. Computational Probability Applications is comprised of fifteen chapters, each presenting a specific application of computational probability using the APPL modeling and computer language. The chapter topics include using inverse gamma as a survival distribution, linear approximations of probability density functions, and also moment-ratio diagrams for univariate distributions. These works highlight interesting examples, often done by undergraduate students and graduate students that can serve as templates for future work. In addition, this book should appeal to researchers and practitioners in a range of fields including probability, statistics, engineering, finance, neuroscience, and economics.

This book provides comprehensive coverage of the field of outlier analysis from a computer science point of view. It integrates methods from data mining, machine learning, and statistics within the computational framework and therefore appeals to multiple communities. The chapters of this book can be organized into three categories: Basic algorithms: Chapters 1 through 7 discuss the fundamental algorithms for outlier analysis, including probabilistic and statistical methods, linear methods, proximity-based methods, high-dimensional (subspace) methods, ensemble methods, and supervised methods. Domain-specific methods: Chapters 8 through 12 discuss outlier detection algorithms for various domains of data, such as text, categorical data, time-series data, discrete sequence data, spatial data, and network data. Applications: Chapter 13 is devoted to various applications of outlier analysis. Some guidance is also provided for the practitioner. The second edition of this book is more detailed and is written to appeal to both researchers and practitioners. Significant new material has been added on topics such as kernel methods, one-class support-vector machines, matrix factorization, neural networks, outlier ensembles, time-series methods, and subspace methods. It is written as a textbook and can be used for classroom teaching.