Математика

Различные книги в жанре Математика

Advances in DEA Theory and Applications. With Extensions to Forecasting Models

Kaoru Tone

A key resource and framework for assessing the performance of competing entities, including forecasting models Advances in DEA Theory and Applications provides a much-needed framework for assessing the performance of competing entities with special emphasis on forecasting models. It helps readers to determine the most appropriate methodology in order to make the most accurate decisions for implementation. Written by a noted expert in the field, this text provides a review of the latest advances in DEA theory and applications to the field of forecasting. Designed for use by anyone involved in research in the field of forecasting or in another application area where forecasting drives decision making, this text can be applied to a wide range of contexts, including education, health care, banking, armed forces, auditing, market research, retail outlets, organizational effectiveness, transportation, public housing, and manufacturing. This vital resource: Explores the latest developments in DEA frameworks for the performance evaluation of entities such as public or private organizational branches or departments, economic sectors, technologies, and stocks Presents a novel area of application for DEA; namely, the performance evaluation of forecasting models Promotes the use of DEA to assess the performance of forecasting models in a wide area of applications Provides rich, detailed examples and case studies Advances in DEA Theory and Applications includes information on a balanced benchmarking tool that is designed to help organizations examine their assumptions about their productivity and performance.

An Introduction to SAGE Programming. With Applications to SAGE Interacts for Numerical Methods

Razvan Mezei A.

Features a simplified presentation of numerical methods by introducing and implementing SAGE programs An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods emphasizes how to implement numerical methods using SAGE Math and SAGE Interacts and also addresses the fundamentals of computer programming, including if statements, loops, functions, and interacts. The book also provides a unique introduction to SAGE and its computer algebra system capabilities; discusses second and higher order equations and estimate limits; and determines derivatives, integrals, and summations. Providing critical resources for developing successful interactive SAGE numerical computations, the book is accessible without delving into the mathematical rigor of numerical methods. The author illustrates the benefits of utilizing the SAGE language for calculus and the numerical analysis of various methods such as bisection methods, numerical integration, Taylor’s expansions, and Newton’s iterations. Providing an introduction to the terminology and concepts involved, An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods also features: An introduction to computer programming using SAGE Many practical examples throughout to illustrate the application of SAGE Interacts for various numerical methods Discussions on how to use SAGE Interacts and SAGE Cloud in order to create mathematical demonstrations Numerous homework problems and exercises that allow readers to practice their programming skillset A companion website that includes related SAGE programming code and select solutions to the homework problems and exercises An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods is an ideal reference for applied mathematicians who need to employ SAGE for the study of numerical methods and analysis. The book is also an appropriate supplemental textbook for upper-undergraduate and graduate-level courses in numerical methods.

Spline Collocation Methods for Partial Differential Equations. With Applications in R

William Schiesser E.

A comprehensive approach to numerical partial differential equations Spline Collocation Methods for Partial Differential Equations combines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive method for numerical integration of PDEs when it is used with the MOL in which spatial (boundary value) derivatives are approximated with splines, including the boundary conditions. R, an open-source scientific programming system, is used throughout for programming the PDEs and numerical algorithms, and each section of code is clearly explained. As a result, readers gain a complete picture of the model and its computer implementation without having to fill in the details of the numerical analysis, algorithms, or programming. The presentation is not heavily mathematical, and in place of theorems and proofs, detailed example applications are provided. Appropriate for scientists, engineers, and applied mathematicians, Spline Collocation Methods for Partial Differential Equations: Introduces numerical methods by first presenting basic examples followed by more complicated applications Employs R to illustrate accurate and efficient solutions of the PDE models Presents spline collocation as a comprehensive approach to the numerical integration of PDEs and an effective alternative to other, well established methods Discusses how to reproduce and extend the presented numerical solutions Identifies the use of selected algorithms, such as the solution of nonlinear equations and banded or sparse matrix processing Features a companion website that provides the related R routines Spline Collocation Methods for Partial Differential Equations is a valuable reference and/or self-study guide for academics, researchers, and practitioners in applied mathematics and engineering, as well as for advanced undergraduates and graduate-level students.

Mathematical and Computational Modeling. With Applications in Natural and Social Sciences, Engineering, and the Arts

Roderick Melnik

Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-the-art achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts also features: Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, industrial, and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.

Banking Systems Simulation. Theory, Practice, and Application of Modeling Shocks, Losses, and Contagion

Stefano Zedda

Presents information sources and methodologies for modeling and simulating banking system stability Combining both academic and institutional knowledge and experience, Banking Systems Simulation: Theory, Practice, and Application of Modeling Shocks, Losses, and Contagion presents banking system risk modeling clearly within a theoretical framework. Written from the global financial perspective, the book explores single bank risk, common bank exposures, and contagion, and how these apply on a systemic level. Zedda approaches these simulation methods logically by providing the basic building blocks of modeling and simulation, and then delving further into the individual techniques that make up a systems model. In addition, the author provides clear and detailed explanations of the foundational research into the mathematical and legal concepts used to analyze banking risk problems, measures and data for representing the main banking risk sources, and the major problems researchers are likely to encounter. There are numerous software descriptions throughout, with references and tools to help readers gain a proper understanding of the presented techniques and possibly develop new applications and research. The book concludes with an appendix that features real-world datasets and models. In addition, this book: • Provides a comprehensive overview of methods for analyzing models and simulating risk for banking and financial systems • Provides a clear presentation of the technical and legal concepts used in banking regulation • Presents unique insights from an expert’s perspective, with specific coverage of assessing risks and developing what-if analyses at the systems level • Concludes with a discussion of applications, including banking systems regulation what-if tests, cost-benefit analysis, evaluations of banking systems stability effects on public finances, dimensioning, and risk-based contributions for Deposit Guarantee Schemes (DGS) and Resolution Funds Banking Systems Simulation: Theory, Practice, and Application of Modeling Shocks, Losses, and Contagion is ideal for banking researchers focusing on computational methods of analysis as well as an appropriate reference for graduate-level students in banking, finance, and computational methods. Stefano Zedda is Researcher in Financial Mathematics at the University of Cagliari in Italy and qualified as associate professor in banking and corporate finance. His research is mainly focused on quantitative analyses for banking and finance, with a particular focus on banking systems modeling and simulation. In 2008, Zedda developed the mathematical modeling and software implementation of the Systemic Model for Banking Originated Losses (SYMBOL), further developed during his activity at the European Commission. The Commission subsequently adopted it as a standard tool for testing banking regulation proposals. Stefano Zedda’s research interests include banking, financial mathematics, and statistics, specifically simulation of banking and financial systems stability, banking regulation impact assessment, and interactive agent simulation.

Mixed Models. Theory and Applications with R

Eugene Demidenko

Praise for the First Edition “This book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one’s personal library.” —Journal of the American Statistical Association Mixed modeling is a crucial area of statistics, enabling the analysis of clustered and longitudinal data. Mixed Models: Theory and Applications with R, Second Edition fills a gap in existing literature between mathematical and applied statistical books by presenting a powerful examination of mixed model theory and application with special attention given to the implementation in R. The new edition provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as nontraditional applications, such as regrowth curves, shapes, and images. The book features the latest topics in statistics including modeling of complex clustered or longitudinal data, modeling data with multiple sources of variation, modeling biological variety and heterogeneity, Healthy Akaike Information Criterion (HAIC), parameter multidimensionality, and statistics of image processing. Mixed Models: Theory and Applications with R, Second Edition features unique applications of mixed model methodology, as well as: Comprehensive theoretical discussions illustrated by examples and figures Over 300 exercises, end-of-section problems, updated data sets, and R subroutines Problems and extended projects requiring simulations in R intended to reinforce material Summaries of major results and general points of discussion at the end of each chapter Open problems in mixed modeling methodology, which can be used as the basis for research or PhD dissertations Ideal for graduate-level courses in mixed statistical modeling, the book is also an excellent reference for professionals in a range of fields, including cancer research, computer science, and engineering.

The Data Industry. The Business and Economics of Information and Big Data

Chunlei Tang

Provides an introduction of the data industry to the field of economics This book bridges the gap between economics and data science to help data scientists understand the economics of big data, and enable economists to analyze the data industry. It begins by explaining data resources and introduces the data asset. This book defines a data industry chain, enumerates data enterprises’ business models versus operating models, and proposes a mode of industrial development for the data industry. The author describes five types of enterprise agglomerations, and multiple industrial cluster effects. A discussion on the establishment and development of data industry related laws and regulations is provided. In addition, this book discusses several scenarios on how to convert data driving forces into productivity that can then serve society. This book is designed to serve as a reference and training guide for ata scientists, data-oriented managers and executives, entrepreneurs, scholars, and government employees. Defines and develops the concept of a “Data Industry,” and explains the economics of data to data scientists and statisticians Includes numerous case studies and examples from a variety of industries and disciplines Serves as a useful guide for practitioners and entrepreneurs in the business of data technology The Data Industry: The Business and Economics of Information and Big Data is a resource for practitioners in the data science industry, government, and students in economics, business, and statistics. CHUNLEI TANG, Ph.D., is a research fellow at Harvard University. She is the co-founder of Fudan’s Institute for Data Industry and proposed the concept of the “data industry”. She received a Ph.D. in Computer and Software Theory in 2012 and a Master of Software Engineering in 2006 from Fudan University, Shanghai, China.

Nonlinear Parameter Optimization Using R Tools

John Nash C.

Nonlinear Parameter Optimization Using R John C. Nash, Telfer School of Management, University of Ottawa, Canada A systematic and comprehensive treatment of optimization software using R In recent decades, optimization techniques have been streamlined by computational and artificial intelligence methods to analyze more variables, especially under non–linear, multivariable conditions, more quickly than ever before. Optimization is an important tool for decision science and for the analysis of physical systems used in engineering. Nonlinear Parameter Optimization with R explores the principal tools available in R for function minimization, optimization, and nonlinear parameter determination and features numerous examples throughout. Nonlinear Parameter Optimization with R: Provides a comprehensive treatment of optimization techniques Examines optimization problems that arise in statistics and how to solve them using R Enables researchers and practitioners to solve parameter determination problems Presents traditional methods as well as recent developments in R Is supported by an accompanying website featuring R code, examples and datasets Researchers and practitioners who have to solve parameter determination problems who are users of R but are novices in the field optimization or function minimization will benefit from this book. It will also be useful for scientists building and estimating nonlinear models in various fields such as hydrology, sports forecasting, ecology, chemical engineering, pharmaco-kinetics, agriculture, economics and statistics.

Beyond Basic Statistics. Tips, Tricks, and Techniques Every Data Analyst Should Know

Kristin Jarman H.

Features basic statistical concepts as a tool for thinking critically, wading through large quantities of information, and answering practical, everyday questions Written in an engaging and inviting manner, Beyond Basic Statistics: Tips, Tricks, and Techniques Every Data Analyst Should Know presents the more subjective side of statistics—the art of data analytics. Each chapter explores a different question using fun, common sense examples that illustrate the concepts, methods, and applications of statistical techniques. Without going into the specifics of theorems, propositions, or formulas, the book effectively demonstrates statistics as a useful problem-solving tool. In addition, the author demonstrates how statistics is a tool for thinking critically, wading through large volumes of information, and answering life’s important questions. Beyond Basic Statistics: Tips, Tricks, and Techniques Every Data Analyst Should Know also features: Plentiful examples throughout aimed to strengthen readers’ understanding of the statistical concepts and methods A step-by-step approach to elementary statistical topics such as sampling, hypothesis tests, outlier detection, normality tests, robust statistics, and multiple regression A case study in each chapter that illustrates the use of the presented techniques Highlights of well-known shortcomings that can lead to false conclusions An introduction to advanced techniques such as validation and bootstrapping Featuring examples that are engaging and non-application specific, the book appeals to a broad audience of students and professionals alike, specifically students of undergraduate statistics, managers, medical professionals, and anyone who has to make decisions based on raw data or compiled results.

Introduction to Probability and Statistics for Ecosystem Managers. Simulation and Resampling

Timothy Haas C.

Explores computer-intensive probability and statistics for ecosystem management decision making Simulation is an accessible way to explain probability and stochastic model behavior to beginners. This book introduces probability and statistics to future and practicing ecosystem managers by providing a comprehensive treatment of these two areas. The author presents a self-contained introduction for individuals involved in monitoring, assessing, and managing ecosystems and features intuitive, simulation-based explanations of probabilistic and statistical concepts. Mathematical programming details are provided for estimating ecosystem model parameters with Minimum Distance, a robust and computer-intensive method. The majority of examples illustrate how probability and statistics can be applied to ecosystem management challenges. There are over 50 exercises – making this book suitable for a lecture course in a natural resource and/or wildlife management department, or as the main text in a program of self-study. Key features: Reviews different approaches to wildlife and ecosystem management and inference. Uses simulation as an accessible way to explain probability and stochastic model behavior to beginners. Covers material from basic probability through to hierarchical Bayesian models and spatial/ spatio-temporal statistical inference. Provides detailed instructions for using R, along with complete R programs to recreate the output of the many examples presented. Provides an introduction to Geographic Information Systems (GIS) along with examples from Quantum GIS, a free GIS software package. A companion website featuring all R code and data used throughout the book. Solutions to all exercises are presented along with an online intelligent tutoring system that supports readers who are using the book for self-study.