Author: Hrishikesh D. Vinod
Publisher: World Scientific
ISBN: 9814313688
Category : Mathematics
Languages : en
Pages : 348
Book Description
Teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. This book provides an overview of matrix theory without being bogged down in proofs or tedium.
Hands-on Matrix Algebra Using R: Active And Motivated Learning With Applications
Author: Hrishikesh D Vinod
Publisher: World Scientific Publishing Company
ISBN: 981310080X
Category : Mathematics
Languages : en
Pages : 348
Book Description
This is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a calculator, R is a vastly more powerful free software and graphics system.The book provides a comprehensive overview of matrix theory without being bogged down in proofs or tedium. The reader can check each matrix result with numerical examples of exactly what they mean and understand their implications. The book does not shy away from advanced topics, especially the ones with practical applications.
Publisher: World Scientific Publishing Company
ISBN: 981310080X
Category : Mathematics
Languages : en
Pages : 348
Book Description
This is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a calculator, R is a vastly more powerful free software and graphics system.The book provides a comprehensive overview of matrix theory without being bogged down in proofs or tedium. The reader can check each matrix result with numerical examples of exactly what they mean and understand their implications. The book does not shy away from advanced topics, especially the ones with practical applications.
Basics of Matrix Algebra for Statistics with R
Author: Nick Fieller
Publisher: CRC Press
ISBN: 1315360055
Category : Mathematics
Languages : en
Pages : 208
Book Description
A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.
Publisher: CRC Press
ISBN: 1315360055
Category : Mathematics
Languages : en
Pages : 208
Book Description
A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.
Data Science and Predictive Analytics
Author: Ivo D. Dinov
Publisher: Springer
ISBN: 3319723472
Category : Computers
Languages : en
Pages : 851
Book Description
Over the past decade, Big Data have become ubiquitous in all economic sectors, scientific disciplines, and human activities. They have led to striking technological advances, affecting all human experiences. Our ability to manage, understand, interrogate, and interpret such extremely large, multisource, heterogeneous, incomplete, multiscale, and incongruent data has not kept pace with the rapid increase of the volume, complexity and proliferation of the deluge of digital information. There are three reasons for this shortfall. First, the volume of data is increasing much faster than the corresponding rise of our computational processing power (Kryder’s law > Moore’s law). Second, traditional discipline-bounds inhibit expeditious progress. Third, our education and training activities have fallen behind the accelerated trend of scientific, information, and communication advances. There are very few rigorous instructional resources, interactive learning materials, and dynamic training environments that support active data science learning. The textbook balances the mathematical foundations with dexterous demonstrations and examples of data, tools, modules and workflows that serve as pillars for the urgently needed bridge to close that supply and demand predictive analytic skills gap. Exposing the enormous opportunities presented by the tsunami of Big data, this textbook aims to identify specific knowledge gaps, educational barriers, and workforce readiness deficiencies. Specifically, it focuses on the development of a transdisciplinary curriculum integrating modern computational methods, advanced data science techniques, innovative biomedical applications, and impactful health analytics. The content of this graduate-level textbook fills a substantial gap in integrating modern engineering concepts, computational algorithms, mathematical optimization, statistical computing and biomedical inference. Big data analytic techniques and predictive scientific methods demand broad transdisciplinary knowledge, appeal to an extremely wide spectrum of readers/learners, and provide incredible opportunities for engagement throughout the academy, industry, regulatory and funding agencies. The two examples below demonstrate the powerful need for scientific knowledge, computational abilities, interdisciplinary expertise, and modern technologies necessary to achieve desired outcomes (improving human health and optimizing future return on investment). This can only be achieved by appropriately trained teams of researchers who can develop robust decision support systems using modern techniques and effective end-to-end protocols, like the ones described in this textbook. • A geriatric neurologist is examining a patient complaining of gait imbalance and posture instability. To determine if the patient may suffer from Parkinson’s disease, the physician acquires clinical, cognitive, phenotypic, imaging, and genetics data (Big Data). Most clinics and healthcare centers are not equipped with skilled data analytic teams that can wrangle, harmonize and interpret such complex datasets. A learner that completes a course of study using this textbook will have the competency and ability to manage the data, generate a protocol for deriving biomarkers, and provide an actionable decision support system. The results of this protocol will help the physician understand the entire patient dataset and assist in making a holistic evidence-based, data-driven, clinical diagnosis. • To improve the return on investment for their shareholders, a healthcare manufacturer needs to forecast the demand for their product subject to environmental, demographic, economic, and bio-social sentiment data (Big Data). The organization’s data-analytics team is tasked with developing a protocol that identifies, aggregates, harmonizes, models and analyzes these heterogeneous data elements to generate a trend forecast. This system needs to provide an automated, adaptive, scalable, and reliable prediction of the optimal investment, e.g., R&D allocation, that maximizes the company’s bottom line. A reader that complete a course of study using this textbook will be able to ingest the observed structured and unstructured data, mathematically represent the data as a computable object, apply appropriate model-based and model-free prediction techniques. The results of these techniques may be used to forecast the expected relation between the company’s investment, product supply, general demand of healthcare (providers and patients), and estimate the return on initial investments.
Publisher: Springer
ISBN: 3319723472
Category : Computers
Languages : en
Pages : 851
Book Description
Over the past decade, Big Data have become ubiquitous in all economic sectors, scientific disciplines, and human activities. They have led to striking technological advances, affecting all human experiences. Our ability to manage, understand, interrogate, and interpret such extremely large, multisource, heterogeneous, incomplete, multiscale, and incongruent data has not kept pace with the rapid increase of the volume, complexity and proliferation of the deluge of digital information. There are three reasons for this shortfall. First, the volume of data is increasing much faster than the corresponding rise of our computational processing power (Kryder’s law > Moore’s law). Second, traditional discipline-bounds inhibit expeditious progress. Third, our education and training activities have fallen behind the accelerated trend of scientific, information, and communication advances. There are very few rigorous instructional resources, interactive learning materials, and dynamic training environments that support active data science learning. The textbook balances the mathematical foundations with dexterous demonstrations and examples of data, tools, modules and workflows that serve as pillars for the urgently needed bridge to close that supply and demand predictive analytic skills gap. Exposing the enormous opportunities presented by the tsunami of Big data, this textbook aims to identify specific knowledge gaps, educational barriers, and workforce readiness deficiencies. Specifically, it focuses on the development of a transdisciplinary curriculum integrating modern computational methods, advanced data science techniques, innovative biomedical applications, and impactful health analytics. The content of this graduate-level textbook fills a substantial gap in integrating modern engineering concepts, computational algorithms, mathematical optimization, statistical computing and biomedical inference. Big data analytic techniques and predictive scientific methods demand broad transdisciplinary knowledge, appeal to an extremely wide spectrum of readers/learners, and provide incredible opportunities for engagement throughout the academy, industry, regulatory and funding agencies. The two examples below demonstrate the powerful need for scientific knowledge, computational abilities, interdisciplinary expertise, and modern technologies necessary to achieve desired outcomes (improving human health and optimizing future return on investment). This can only be achieved by appropriately trained teams of researchers who can develop robust decision support systems using modern techniques and effective end-to-end protocols, like the ones described in this textbook. • A geriatric neurologist is examining a patient complaining of gait imbalance and posture instability. To determine if the patient may suffer from Parkinson’s disease, the physician acquires clinical, cognitive, phenotypic, imaging, and genetics data (Big Data). Most clinics and healthcare centers are not equipped with skilled data analytic teams that can wrangle, harmonize and interpret such complex datasets. A learner that completes a course of study using this textbook will have the competency and ability to manage the data, generate a protocol for deriving biomarkers, and provide an actionable decision support system. The results of this protocol will help the physician understand the entire patient dataset and assist in making a holistic evidence-based, data-driven, clinical diagnosis. • To improve the return on investment for their shareholders, a healthcare manufacturer needs to forecast the demand for their product subject to environmental, demographic, economic, and bio-social sentiment data (Big Data). The organization’s data-analytics team is tasked with developing a protocol that identifies, aggregates, harmonizes, models and analyzes these heterogeneous data elements to generate a trend forecast. This system needs to provide an automated, adaptive, scalable, and reliable prediction of the optimal investment, e.g., R&D allocation, that maximizes the company’s bottom line. A reader that complete a course of study using this textbook will be able to ingest the observed structured and unstructured data, mathematically represent the data as a computable object, apply appropriate model-based and model-free prediction techniques. The results of these techniques may be used to forecast the expected relation between the company’s investment, product supply, general demand of healthcare (providers and patients), and estimate the return on initial investments.
Statistical Regression and Classification
Author: Norman Matloff
Publisher: CRC Press
ISBN: 1351645897
Category : Business & Economics
Languages : en
Pages : 439
Book Description
Statistical Regression and Classification: From Linear Models to Machine Learning takes an innovative look at the traditional statistical regression course, presenting a contemporary treatment in line with today's applications and users. The text takes a modern look at regression: * A thorough treatment of classical linear and generalized linear models, supplemented with introductory material on machine learning methods. * Since classification is the focus of many contemporary applications, the book covers this topic in detail, especially the multiclass case. * In view of the voluminous nature of many modern datasets, there is a chapter on Big Data. * Has special Mathematical and Computational Complements sections at ends of chapters, and exercises are partitioned into Data, Math and Complements problems. * Instructors can tailor coverage for specific audiences such as majors in Statistics, Computer Science, or Economics. * More than 75 examples using real data. The book treats classical regression methods in an innovative, contemporary manner. Though some statistical learning methods are introduced, the primary methodology used is linear and generalized linear parametric models, covering both the Description and Prediction goals of regression methods. The author is just as interested in Description applications of regression, such as measuring the gender wage gap in Silicon Valley, as in forecasting tomorrow's demand for bike rentals. An entire chapter is devoted to measuring such effects, including discussion of Simpson's Paradox, multiple inference, and causation issues. Similarly, there is an entire chapter of parametric model fit, making use of both residual analysis and assessment via nonparametric analysis. Norman Matloff is a professor of computer science at the University of California, Davis, and was a founder of the Statistics Department at that institution. His current research focus is on recommender systems, and applications of regression methods to small area estimation and bias reduction in observational studies. He is on the editorial boards of the Journal of Statistical Computation and the R Journal. An award-winning teacher, he is the author of The Art of R Programming and Parallel Computation in Data Science: With Examples in R, C++ and CUDA.
Publisher: CRC Press
ISBN: 1351645897
Category : Business & Economics
Languages : en
Pages : 439
Book Description
Statistical Regression and Classification: From Linear Models to Machine Learning takes an innovative look at the traditional statistical regression course, presenting a contemporary treatment in line with today's applications and users. The text takes a modern look at regression: * A thorough treatment of classical linear and generalized linear models, supplemented with introductory material on machine learning methods. * Since classification is the focus of many contemporary applications, the book covers this topic in detail, especially the multiclass case. * In view of the voluminous nature of many modern datasets, there is a chapter on Big Data. * Has special Mathematical and Computational Complements sections at ends of chapters, and exercises are partitioned into Data, Math and Complements problems. * Instructors can tailor coverage for specific audiences such as majors in Statistics, Computer Science, or Economics. * More than 75 examples using real data. The book treats classical regression methods in an innovative, contemporary manner. Though some statistical learning methods are introduced, the primary methodology used is linear and generalized linear parametric models, covering both the Description and Prediction goals of regression methods. The author is just as interested in Description applications of regression, such as measuring the gender wage gap in Silicon Valley, as in forecasting tomorrow's demand for bike rentals. An entire chapter is devoted to measuring such effects, including discussion of Simpson's Paradox, multiple inference, and causation issues. Similarly, there is an entire chapter of parametric model fit, making use of both residual analysis and assessment via nonparametric analysis. Norman Matloff is a professor of computer science at the University of California, Davis, and was a founder of the Statistics Department at that institution. His current research focus is on recommender systems, and applications of regression methods to small area estimation and bias reduction in observational studies. He is on the editorial boards of the Journal of Statistical Computation and the R Journal. An award-winning teacher, he is the author of The Art of R Programming and Parallel Computation in Data Science: With Examples in R, C++ and CUDA.
Numerical Ecology
Author: P. Legendre
Publisher: Elsevier
ISBN: 0444538682
Category : Mathematics
Languages : en
Pages : 1008
Book Description
This volume describes and discusses the numerical methods which are successfully being used for analysing ecological data. These methods are derived from the fields of mathematical physics, parametric and nonparametric statistics, information theory, numerical taxonomy, archaeology, psychometry, sociometry, and others.
Publisher: Elsevier
ISBN: 0444538682
Category : Mathematics
Languages : en
Pages : 1008
Book Description
This volume describes and discusses the numerical methods which are successfully being used for analysing ecological data. These methods are derived from the fields of mathematical physics, parametric and nonparametric statistics, information theory, numerical taxonomy, archaeology, psychometry, sociometry, and others.
Thirty-three Miniatures
Author: Jiří Matoušek
Publisher: American Mathematical Soc.
ISBN: 0821849778
Category : Mathematics
Languages : en
Pages : 196
Book Description
This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53)
Publisher: American Mathematical Soc.
ISBN: 0821849778
Category : Mathematics
Languages : en
Pages : 196
Book Description
This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53)
The R Student Companion
Author: Brian Dennis
Publisher: CRC Press
ISBN: 1439875413
Category : Mathematics
Languages : en
Pages : 351
Book Description
This student-oriented manual describes how to use R in college science and mathematics courses. The manual features fully developed exercises based around the main precalculus analysis skills needed in the standard college general education courses in science and math. The exercises illustrate a wide variety of applications and subjects. The author presents applications drawn from all sciences and social sciences and includes the most often used features of R on a reference card in the back of the book. In addition, each chapter provides a set of computational challenges: exercises in R calculations that are designed to be performed alone or in groups.
Publisher: CRC Press
ISBN: 1439875413
Category : Mathematics
Languages : en
Pages : 351
Book Description
This student-oriented manual describes how to use R in college science and mathematics courses. The manual features fully developed exercises based around the main precalculus analysis skills needed in the standard college general education courses in science and math. The exercises illustrate a wide variety of applications and subjects. The author presents applications drawn from all sciences and social sciences and includes the most often used features of R on a reference card in the back of the book. In addition, each chapter provides a set of computational challenges: exercises in R calculations that are designed to be performed alone or in groups.
Matrix Algebra Useful for Statistics
Author: Shayle R. Searle
Publisher: John Wiley & Sons
ISBN: 1118935144
Category : Mathematics
Languages : en
Pages : 517
Book Description
A thoroughly updated guide to matrix algebra and it uses in statistical analysis and features SAS®, MATLAB®, and R throughout This Second Edition addresses matrix algebra that is useful in the statistical analysis of data as well as within statistics as a whole. The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained. Featuring numerous applied illustrations, numerical examples, and exercises, the book has been updated to include the use of SAS, MATLAB, and R for the execution of matrix computations. In addition, André I. Khuri, who has extensive research and teaching experience in the field, joins this new edition as co-author. The Second Edition also: Contains new coverage on vector spaces and linear transformations and discusses computational aspects of matrices Covers the analysis of balanced linear models using direct products of matrices Analyzes multiresponse linear models where several responses can be of interest Includes extensive use of SAS, MATLAB, and R throughout Contains over 400 examples and exercises to reinforce understanding along with select solutions Includes plentiful new illustrations depicting the importance of geometry as well as historical interludes Matrix Algebra Useful for Statistics, Second Edition is an ideal textbook for advanced undergraduate and first-year graduate level courses in statistics and other related disciplines. The book is also appropriate as a reference for independent readers who use statistics and wish to improve their knowledge of matrix algebra. THE LATE SHAYLE R. SEARLE, PHD, was professor emeritus of biometry at Cornell University. He was the author of Linear Models for Unbalanced Data and Linear Models and co-author of Generalized, Linear, and Mixed Models, Second Edition, Matrix Algebra for Applied Economics, and Variance Components, all published by Wiley. Dr. Searle received the Alexander von Humboldt Senior Scientist Award, and he was an honorary fellow of the Royal Society of New Zealand. ANDRÉ I. KHURI, PHD, is Professor Emeritus of Statistics at the University of Florida. He is the author of Advanced Calculus with Applications in Statistics, Second Edition and co-author of Statistical Tests for Mixed Linear Models, all published by Wiley. Dr. Khuri is a member of numerous academic associations, among them the American Statistical Association and the Institute of Mathematical Statistics.
Publisher: John Wiley & Sons
ISBN: 1118935144
Category : Mathematics
Languages : en
Pages : 517
Book Description
A thoroughly updated guide to matrix algebra and it uses in statistical analysis and features SAS®, MATLAB®, and R throughout This Second Edition addresses matrix algebra that is useful in the statistical analysis of data as well as within statistics as a whole. The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained. Featuring numerous applied illustrations, numerical examples, and exercises, the book has been updated to include the use of SAS, MATLAB, and R for the execution of matrix computations. In addition, André I. Khuri, who has extensive research and teaching experience in the field, joins this new edition as co-author. The Second Edition also: Contains new coverage on vector spaces and linear transformations and discusses computational aspects of matrices Covers the analysis of balanced linear models using direct products of matrices Analyzes multiresponse linear models where several responses can be of interest Includes extensive use of SAS, MATLAB, and R throughout Contains over 400 examples and exercises to reinforce understanding along with select solutions Includes plentiful new illustrations depicting the importance of geometry as well as historical interludes Matrix Algebra Useful for Statistics, Second Edition is an ideal textbook for advanced undergraduate and first-year graduate level courses in statistics and other related disciplines. The book is also appropriate as a reference for independent readers who use statistics and wish to improve their knowledge of matrix algebra. THE LATE SHAYLE R. SEARLE, PHD, was professor emeritus of biometry at Cornell University. He was the author of Linear Models for Unbalanced Data and Linear Models and co-author of Generalized, Linear, and Mixed Models, Second Edition, Matrix Algebra for Applied Economics, and Variance Components, all published by Wiley. Dr. Searle received the Alexander von Humboldt Senior Scientist Award, and he was an honorary fellow of the Royal Society of New Zealand. ANDRÉ I. KHURI, PHD, is Professor Emeritus of Statistics at the University of Florida. He is the author of Advanced Calculus with Applications in Statistics, Second Edition and co-author of Statistical Tests for Mixed Linear Models, all published by Wiley. Dr. Khuri is a member of numerous academic associations, among them the American Statistical Association and the Institute of Mathematical Statistics.