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Basics of Matrix Algebra for Statistics with R

Basics of Matrix Algebra for Statistics with R

A Thorough Guide to Elementary Matrix Algebra and Implementation in RBasics 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.

GBP 44.99
1

Matrix Theory From Generalized Inverses to Jordan Form

Matrix Theory From Generalized Inverses to Jordan Form

In 1990 the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class. Tailoring the material to advanced undergraduate and beginning graduate students the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization derives Sylvester's rank formula introduces full-rank factorization and describes generalized inverses. After discussions on norms QR factorization and orthogonality the authors prove the important spectral theorem. They also highlight the primary decomposition theorem Schur's triangularization theorem singular value decomposition and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra. With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra. | Matrix Theory From Generalized Inverses to Jordan Form

GBP 59.99
1

Linear Models and the Relevant Distributions and Matrix Algebra A Unified Approach Volume 2

Linear Models and the Relevant Distributions and Matrix Algebra A Unified Approach Volume 2

Linear Models and the Relevant Distributions and Matrix Algebra: A Unified Approach Volume 2 covers several important topics that were not included in the first volume. The second volume complements the first providing detailed solutions to the exercises in both volumes thereby greatly enhancing its appeal for use in advanced statistics programs. This volume can serve as a valuable reference. It can also serve as a resource in a mathematical statistics course for use in illustrating various theoretical concepts in the context of a relatively complex setting of great practical importance. Together with the first volume this volume provides a largely self-contained treatment of an important area of statistics and should prove highly useful to graduate students and others. Key Features: Includes solutions to the exercises from both the first and second volumes Includes coverage of several topics not covered in the first volume Highly valuable as a reference book for graduate students and researchers | Linear Models and the Relevant Distributions and Matrix Algebra A Unified Approach Volume 2

GBP 89.99
1

Basic Matrix Algebra with Algorithms and Applications

Basic Matrix Algebra with Algorithms and Applications

Clear prose tight organization and a wealth of examples and computational techniques make Basic Matrix Algebra with Algorithms and Applications an outstanding introduction to linear algebra. The author designed this treatment specifically for freshman majors in mathematical subjects and upper-level students in natural resources the social sciences business or any discipline that eventually requires an understanding of linear models. With extreme pedagogical clarity that avoids abstraction wherever possible the author emphasizes minimal polynomials and their computation using a Krylov algorithm. The presentation is highly visual and relies heavily on work with a graphing calculator to allow readers to focus on concepts and techniques rather than on tedious arithmetic. Supporting materials including test preparation Maple worksheets are available for download from the Internet. This unassuming but insightful and remarkably original treatment is organized into bite-sized clearly stated objectives. It goes well beyond the LACSG recommendations for a first course while still implementing their philosophy and core material. Classroom tested with great success it prepares readers well for the more advanced studies their fields ultimately will require.

GBP 175.00
1

Summability Theory and Its Applications

Summability Theory and Its Applications

Summability Theory and Its Applications explains various aspects of summability and demonstrates its applications in a rigorous and coherent manner. The content can readily serve as a reference or as a useful series of lecture notes on the subject. This substantially revised new edition includes brand new material across several chapters as well as several corrections including: the addition of the domain of Cesaro matrix C(m) of order m in the classical sequence spaces to Chapter 4; and introducing the domain of four-dimensional binomial matrix in the spaces of bounded convergent in the Pringsheim's sense both convergent in the Pringsheim's sense and bounded and regularly convergent double sequences in Chapter 7. Features Investigates different types of summable spaces and computes their dual Suitable for graduate students and researchers with a (special) interest in spaces of single and double sequences matrix transformations and domains of triangle matrices Can serve as a reference or as supplementary reading in a computational physics course or as a key text for special Analysis seminars.

GBP 130.00
1

A Modern Introduction to Linear Algebra

A Modern Introduction to Linear Algebra

Useful Concepts and Results at the Heart of Linear AlgebraA one- or two-semester course for a wide variety of students at the sophomore/junior undergraduate levelA Modern Introduction to Linear Algebra provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of linear algebra. Concrete easy-to-understand examples motivate the theory. The book first discusses vectors Gaussian elimination and reduced row echelon forms. It then offers a thorough introduction to matrix algebra including defining the determinant naturally from the PA=LU factorization of a matrix. The author goes on to cover finite-dimensional real vector spaces infinite-dimensional spaces linear transformations and complex vector spaces. The final chapter presents Hermitian and normal matrices as well as quadratic forms. Taking a computational algebraic and geometric approach to the subject this book provides the foundation for later courses in higher mathematics. It also shows how linear algebra can be used in various areas of application. Although written in a pencil and paper manner the text offers ample opportunities to enhance learning with calculators or computer usage. Solutions manual available for qualifying instructors

GBP 59.99
1

Linear and Nonlinear Programming with Maple An Interactive Applications-Based Approach

Linear and Nonlinear Programming with Maple An Interactive Applications-Based Approach

Helps Students Understand Mathematical Programming Principles and Solve Real-World ApplicationsSupplies enough mathematical rigor yet accessible enough for undergraduatesIntegrating a hands-on learning approach a strong linear algebra focus Maple™ software and real-world applications Linear and Nonlinear Programming with Maple™: An Interactive Applications-Based Approach introduces undergraduate students to the mathematical concepts and principles underlying linear and nonlinear programming. This text fills the gap between management science books lacking mathematical detail and rigor and graduate-level books on mathematical programming. Essential linear algebra toolsThroughout the text topics from a first linear algebra course such as the invertible matrix theorem linear independence transpose properties and eigenvalues play a prominent role in the discussion. The book emphasizes partitioned matrices and uses them to describe the simplex algorithm in terms of matrix multiplication. This perspective leads to streamlined approaches for constructing the revised simplex method developing duality theory and approaching the process of sensitivity analysis. The book also discusses some intermediate linear algebra topics including the spectral theorem and matrix norms. Maple enhances conceptual understanding and helps tackle problemsAssuming no prior experience with Maple the author provides a sufficient amount of instruction for students unfamiliar with the software. He also includes a summary of Maple commands as well as Maple worksheets in the text and online. By using Maple’s symbolic computing components numeric capabilities graphical versatility and intuitive programming structures students will acquire a deep conceptual understanding of major mathematical programming principles along with the ability to solve moderately sized rea | Linear and Nonlinear Programming with Maple An Interactive Applications-Based Approach

GBP 59.99
1

Concise Introduction to Linear Algebra

Concise Introduction to Linear Algebra

Concise Introduction to Linear Algebra deals with the subject of linear algebra covering vectors and linear systems vector spaces orthogonality determinants eigenvalues and eigenvectors singular value decomposition. It adopts an efficient approach to lead students from vectors matrices quickly into more advanced topics including LU decomposition orthogonal decomposition Least squares solutions Gram-Schmidt process eigenvalues and eigenvectors diagonalizability spectral decomposition positive definite matrix quadratic forms singular value decompositions and principal component analysis. This book is designed for onesemester teaching to undergraduate students.

GBP 44.99
1

Sequence Space Theory with Applications

Sequence Space Theory with Applications

The book features original chapters on sequence spaces involving the idea of ideal convergence modulus function multiplier sequences Riesz mean Fibonacci difference matrix etc. and illustrate their involvement in various applications. The preliminaries have been presented in the beginning of each chapter and then the advanced discussion takes place so it is useful for both expert and nonexpert on aforesaid topics. The book consists of original thirteen research chapters contributed by the well-recognized researchers in the field of sequence spaces with associated applications. Features Discusses the Fibonacci and vector valued difference sequence spaces Presents the solution of Volterra integral equation in Banach algebra Discusses some sequence spaces involving invariant mean and related to the domain of Jordan totient matrix Presents the Tauberian theorems of double sequences Discusses the paranormed Riesz difference sequence space of fractional order Includes a technique for studying the existence of solutions of infinite system of functional integro-differential equations in Banach sequence spaces The subject of book is an active area of research of present time internationally and would serve as a good source for researcher and educators involved with the topic of sequence spaces. | Sequence Space Theory with Applications

GBP 150.00
1

Bounds for Determinants of Linear Operators and their Applications

Bounds for Determinants of Linear Operators and their Applications

This book deals with the determinants of linear operators in Euclidean Hilbert and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators enable us to describe the spectra to evaluate the multiplicities of eigenvalues etc. We derive upper and lower bounds and perturbation results for determinants and discuss applications of our theoretical results to spectrum perturbations matrix equations two parameter eigenvalue problems as well as to differential difference and functional-differential equations. | Bounds for Determinants of Linear Operators and their Applications

GBP 150.00
1

Big Data in Multimodal Medical Imaging

Big Data in Multimodal Medical Imaging

There is an urgent need to develop and integrate new statistical mathematical visualization and computational models with the ability to analyze Big Data in order to retrieve useful information to aid clinicians in accurately diagnosing and treating patients. The main focus of this book is to review and summarize state-of-the-art big data and deep learning approaches to analyze and integrate multiple data types for the creation of a decision matrix to aid clinicians in the early diagnosis and identification of high risk patients for human diseases and disorders. Leading researchers will contribute original research book chapters analyzing efforts to solve these important problems. | Big Data in Multimodal Medical Imaging

GBP 44.99
1

Linear Algebra

Linear Algebra

Linear Algebra is intended primarily as an undergraduate textbook but is written in such a way that it can also be a valuable resource for independent learning. The narrative of the book takes a matrix approach: the exposition is intertwined with matrices either as the main subject or as tools to explore the theory. Each chapter contains a description of its aims a summary at the end of the chapter exercises and solutions. The reader is carefully guided through the theory and techniques presented which are outlined throughout in How to… text boxes. Common mistakes and pitfalls are also pointed out as one goes along. Features Written to be self-contained Ideal as a primary textbook for an undergraduate course in linear algebra Applications of the general theory which are of interest to disciplines outside of mathematics such as engineering

GBP 52.99
1

An Introduction to Nonparametric Statistics

An Introduction to Nonparametric Statistics

An Introduction to Nonparametric Statistics presents techniques for statistical analysis in the absence of strong assumptions about the distributions generating the data. Rank-based and resampling techniques are heavily represented but robust techniques are considered as well. These techniques include one-sample testing and estimation multi-sample testing and estimation and regression. Attention is paid to the intellectual development of the field with a thorough review of bibliographical references. Computational tools in R and SAS are developed and illustrated via examples. Exercises designed to reinforce examples are included. Features Rank-based techniques including sign Kruskal-Wallis Friedman Mann-Whitney and Wilcoxon tests are presented Tests are inverted to produce estimates and confidence intervals Multivariate tests are explored Techniques reflecting the dependence of a response variable on explanatory variables are presented Density estimation is explored The bootstrap and jackknife are discussed This text is intended for a graduate student in applied statistics. The course is best taken after an introductory course in statistical methodology elementary probability and regression. Mathematical prerequisites include calculus through multivariate differentiation and integration and ideally a course in matrix algebra.

GBP 84.99
1

Probability and Statistics for Data Science Math + R + Data

Probability and Statistics for Data Science Math + R + Data

Probability and Statistics for Data Science: Math + R + Data covers math stat—distributions expected value estimation etc. —but takes the phrase Data Science in the title quite seriously: * Real datasets are used extensively. * All data analysis is supported by R coding. * Includes many Data Science applications such as PCA mixture distributions random graph models Hidden Markov models linear and logistic regression and neural networks. * Leads the student to think critically about the how and why of statistics and to see the big picture. * Not theorem/proof-oriented but concepts and models are stated in a mathematically precise manner. Prerequisites are calculus some matrix algebra and some experience in programming. Norman Matloff is a professor of computer science at the University of California Davis and was formerly a statistics professor there. He is on the editorial boards of the Journal of Statistical Software and The R Journal. His book Statistical Regression and Classification: From Linear Models to Machine Learning was the recipient of the Ziegel Award for the best book reviewed in Technometrics in 2017. He is a recipient of his university's Distinguished Teaching Award. | Probability and Statistics for Data Science Math + R + Data

GBP 56.99
1

Signal Processing A Mathematical Approach Second Edition

Signal Processing A Mathematical Approach Second Edition

Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and employ signal processing techniques in an applied environment. Assuming an advanced undergraduate- or graduate-level understanding of mathematics—including familiarity with Fourier series matrices probability and statistics—this Second Edition: Contains new chapters on convolution and the vector DFT plane-wave propagation and the BLUE and Kalman filtersExpands the material on Fourier analysis to three new chapters to provide additional background informationPresents real-world examples of applications that demonstrate how mathematics is used in remote sensingFeaturing problems for use in the classroom or practice Signal Processing: A Mathematical Approach Second Edition covers topics such as Fourier series and transforms in one and several variables; applications to acoustic and electro-magnetic propagation models transmission and emission tomography and image reconstruction; sampling and the limited data problem; matrix methods singular value decomposition and data compression; optimization techniques in signal and image reconstruction from projections; autocorrelations and power spectra; high-resolution methods; detection and optimal filtering; and eigenvector-based methods for array processing and statistical filtering time-frequency analysis and wavelets. | Signal Processing A Mathematical Approach Second Edition

GBP 44.99
1

Computational Framework for the Finite Element Method in MATLAB and Python

Computational Framework for the Finite Element Method in MATLAB and Python

Computational Framework for the Finite Element Method in MATLAB® and Python aims to provide a programming framework for coding linear FEM using matrix-based MATLAB® language and Python scripting language. It describes FEM algorithm implementation in the most generic formulation so that it is possible to apply this algorithm to as many application problems as possible. Readers can follow the step-by-step process of developing algorithms with clear explanations of its underlying mathematics and how to put it into MATLAB and Python code. The content is focused on aspects of numerical methods and coding FEM rather than FEM mathematical analysis. However basic mathematical formulations for numerical techniques which are needed to implement FEM are provided. Particular attention is paid to an efficient programming style using sparse matrices. Features Contains ready-to-use coding recipes allowing fast prototyping and solving of mathematical problems using FEM Suitable for upper-level undergraduates and graduates in applied mathematics science or engineering Both MATLAB and Python programming codes are provided to give readers more flexibility in the practical framework implementation | Computational Framework for the Finite Element Method in MATLAB® and Python

GBP 99.99
1

Design of Experiments for Generalized Linear Models

Design of Experiments for Generalized Linear Models

Generalized Linear Models (GLMs) allow many statistical analyses to be extended to important statistical distributions other than the Normal distribution. While numerous books exist on how to analyse data using a GLM little information is available on how to collect the data that are to be analysed in this way. This is the first book focusing specifically on the design of experiments for GLMs. Much of the research literature on this topic is at a high mathematical level and without any information on computation. This book explains the motivation behind various techniques reduces the difficulty of the mathematics or moves it to one side if it cannot be avoided and gives examples of how to write and run computer programs using R. FeaturesThe generalisation of the linear model to GLMsBackground mathematics and the use of constrained optimisation in RCoverage of the theory behind the optimality of a designIndividual chapters on designs for data that have Binomial or Poisson distributionsBayesian experimental designAn online resource contains R programs used in the bookThis book is aimed at readers who have done elementary differentiation and understand minimal matrix algebra and have familiarity with R. It equips professional statisticians to read the research literature. Nonstatisticians will be able to design their own experiments by following the examples and using the programs provided. | Design of Experiments for Generalized Linear Models

GBP 38.99
1

A Kalman Filter Primer

A Kalman Filter Primer

System state estimation in the presence of noise is critical for control systems signal processing and many other applications in a variety of fields. Developed decades ago the Kalman filter remains an important powerful tool for estimating the variables in a system in the presence of noise. However when inundated with theory and vast notations learning just how the Kalman filter works can be a daunting task. With its mathematically rigorous “no frills” approach to the basic discrete-time Kalman filter A Kalman Filter Primer builds a thorough understanding of the inner workings and basic concepts of Kalman filter recursions from first principles. Instead of the typical Bayesian perspective the author develops the topic via least-squares and classical matrix methods using the Cholesky decomposition to distill the essence of the Kalman filter and reveal the motivations behind the choice of the initializing state vector. He supplies pseudo-code algorithms for the various recursions enabling code development to implement the filter in practice. The book thoroughly studies the development of modern smoothing algorithms and methods for determining initial states along with a comprehensive development of the “diffuse” Kalman filter. Using a tiered presentation that builds on simple discussions to more complex and thorough treatments A Kalman Filter Primer is the perfect introduction to quickly and effectively using the Kalman filter in practice.

GBP 59.99
1

Foundations of Predictive Analytics

Foundations of Predictive Analytics

Drawing on the authors’ two decades of experience in applied modeling and data mining Foundations of Predictive Analytics presents the fundamental background required for analyzing data and building models for many practical applications such as consumer behavior modeling risk and marketing analytics and other areas. It also discusses a variety of practical topics that are frequently missing from similar texts. The book begins with the statistical and linear algebra/matrix foundation of modeling methods from distributions to cumulant and copula functions to Cornish–Fisher expansion and other useful but hard-to-find statistical techniques. It then describes common and unusual linear methods as well as popular nonlinear modeling approaches including additive models trees support vector machine fuzzy systems clustering naïve Bayes and neural nets. The authors go on to cover methodologies used in time series and forecasting such as ARIMA GARCH and survival analysis. They also present a range of optimization techniques and explore several special topics such as Dempster–Shafer theory. An in-depth collection of the most important fundamental material on predictive analytics this self-contained book provides the necessary information for understanding various techniques for exploratory data analysis and modeling. It explains the algorithmic details behind each technique (including underlying assumptions and mathematical formulations) and shows how to prepare and encode data select variables use model goodness measures normalize odds and perform reject inference. Web ResourceThe book’s website at www. DataMinerXL. com offers the DataMinerXL software for building predictive models. The site also includes more examples and information on modeling.

GBP 59.99
1

Banach Limit and Applications

Banach Limit and Applications

Banach Limit and Applications provides all the results in the area of Banach Limit its extensions generalizations and applications to various fields in one go (as far as possible). All the results in this field after Banach introduced this concept in 1932 were scattered till now. Sublinear functionals generating and dominating Banach Limit unique Banach Limit (almost convergence) invariant means and invariant limits absolute and strong almost convergence applications to ergodicity law of large numbers Fourier series uniform distribution of sequences uniform density core theorems and functional Banach limits are discussed in this book. The discovery of functional analysis such as the Hahn-Banach Theorem and the Banach-Steinhaus Theorem helped the researchers to develop a modern rich and unified theory of sequence spaces by encompassing classical summability theory via matrix transformations and the topics related to sequence spaces which arose from the concept of Banach limits all of which are presented in this book. The unique features of this book are as follows: All the results in this area which were scattered till now are in one place. The book is the first of its kind in the sense that there is no other competitive book. The contents of this monograph did not appear in any book form before. The audience of this book are the researchers in this area and Ph. D. and advanced master’s students. The book is suitable for one- or two-semester course work for Ph. D. students M. S. students in North America and Europe and M. Phil. and master’s students in India.

GBP 130.00
1

Mixed Effects Models for Complex Data

Mixed Effects Models for Complex Data

Although standard mixed effects models are useful in a range of studies other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts missing data measurement errors censoring and outliers. For each class of mixed effects model the author reviews the corresponding class of regression model for cross-sectional data. An overview of general models and methods along with motivating examples After presenting real data examples and outlining general approaches to the analysis of longitudinal/clustered data and incomplete data the book introduces linear mixed effects (LME) models generalized linear mixed models (GLMMs) nonlinear mixed effects (NLME) models and semiparametric and nonparametric mixed effects models. It also includes general approaches for the analysis of complex data with missing values measurement errors censoring and outliers. Self-contained coverage of specific topicsSubsequent chapters delve more deeply into missing data problems covariate measurement errors and censored responses in mixed effects models. Focusing on incomplete data the book also covers survival and frailty models joint models of survival and longitudinal data robust methods for mixed effects models marginal generalized estimating equation (GEE) models for longitudinal or clustered data and Bayesian methods for mixed effects models. Background materialIn the appendix the author provides background information such as likelihood theory the Gibbs sampler rejection and importance sampling methods numerical integration methods optimization methods bootstrap and matrix algebra. Failure to properly address missing data measurement errors and other issues in statistical analyses can lead

GBP 59.99
1

Business Financial Planning with Microsoft Excel

Business Financial Planning with Microsoft Excel

Business Finance Planning with Microsoft® Excel® shows how to visualize plan and put into motion an idea for creating a start-up company. Microsoft Excel is a tool that makes it easier to build a business financial planning process for a new business venture. With an easy-to follow structure the book flows as a six-step process: Presenting a case study of a business start-up Creating goals and objectives Determining expenses from those goals and objectives Estimating potential sales revenue based on what competitors charge their customers Predicting marketing costs Finalizing the financial analysis with a of financial statements. Written around an IT startup case study the book presents a host of Excel worksheets describing the case study along with accompanying blank forms. Readers can use these forms in their own businesses so they can build parts of their own business plans as they go. This is intended to be a practical guide that teaches and demonstrates by example in the end presenting a usable financial model to build and tweak a financial plan with a set of customizable Excel worksheets. The book uses practical techniques to help with the planning processing. These include applying a SWOT (strengths weaknesses opportunities and threats) matrix to evaluate a business idea and SMART (Specific Measurable Achievable Relevant and Time-Bound) objectives to link together goals. As the book concludes readers will be able to develop their own income statement balance sheet and the cash-flow statement for a full analysis of their new business ideas. Worksheets are available to download from: https://oracletroubleshooter. com/business-finance-planning/app/ | Business Financial Planning with Microsoft Excel

GBP 34.99
1

Secret History The Story of Cryptology

Secret History The Story of Cryptology

The first edition of this award-winning book attracted a wide audience. This second edition is both a joy to read and a useful classroom tool. Unlike traditional textbooks it requires no mathematical prerequisites and can be read around the mathematics presented. If used as a textbook the mathematics can be prioritized with a book both students and instructors will enjoy reading. Secret History: The Story of Cryptology Second Edition incorporates new material concerning various eras in the long history of cryptology. Much has happened concerning the political aspects of cryptology since the first edition appeared. The still unfolding story is updated here. The first edition of this book contained chapters devoted to the cracking of German and Japanese systems during World War II. Now the other side of this cipher war is also told that is how the United States was able to come up with systems that were never broken. The text is in two parts. Part I presents classic cryptology from ancient times through World War II. Part II examines modern computer cryptology. With numerous real-world examples and extensive references the author skillfully balances the history with mathematical details providing readers with a sound foundation in this dynamic field. FEATURES Presents a chronological development of key concepts Includes the Vigenère cipher the one-time pad transposition ciphers Jefferson’s wheel cipher Playfair cipher ADFGX matrix encryption Enigma Purple and other classic methods Looks at the work of Claude Shannon the origin of the National Security Agency elliptic curve cryptography the Data Encryption Standard the Advanced Encryption Standard public-key cryptography and many other topics New chapters detail SIGABA and SIGSALY successful systems used during World War II for text and speech respectively Includes quantum cryptography and the impact of quantum computers | Secret History The Story of Cryptology

GBP 74.99
1

Statistical Machine Learning A Unified Framework

Statistical Machine Learning A Unified Framework

The recent rapid growth in the variety and complexity of new machine learning architectures requires the development of improved methods for designing analyzing evaluating and communicating machine learning technologies. Statistical Machine Learning: A Unified Framework provides students engineers and scientists with tools from mathematical statistics and nonlinear optimization theory to become experts in the field of machine learning. In particular the material in this text directly supports the mathematical analysis and design of old new and not-yet-invented nonlinear high-dimensional machine learning algorithms. Features: Unified empirical risk minimization framework supports rigorous mathematical analyses of widely used supervised unsupervised and reinforcement machine learning algorithms Matrix calculus methods for supporting machine learning analysis and design applications Explicit conditions for ensuring convergence of adaptive batch minibatch MCEM and MCMC learning algorithms that minimize both unimodal and multimodal objective functions Explicit conditions for characterizing asymptotic properties of M-estimators and model selection criteria such as AIC and BIC in the presence of possible model misspecification This advanced text is suitable for graduate students or highly motivated undergraduate students in statistics computer science electrical engineering and applied mathematics. The text is self-contained and only assumes knowledge of lower-division linear algebra and upper-division probability theory. Students professional engineers and multidisciplinary scientists possessing these minimal prerequisites will find this text challenging yet accessible. About the Author: Richard M. Golden (Ph. D. M. S. E. E. B. S. E. E. ) is Professor of Cognitive Science and Participating Faculty Member in Electrical Engineering at the University of Texas at Dallas. Dr. Golden has published articles and given talks at scientific conferences on a wide range of topics in the fields of both statistics and machine learning over the past three decades. His long-term research interests include identifying conditions for the convergence of deterministic and stochastic machine learning algorithms and investigating estimation and inference in the presence of possibly misspecified probability models. | Statistical Machine Learning A Unified Framework

GBP 99.99
1

Theory of Statistical Inference

Theory of Statistical Inference

Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of the foundational ideas of modern statistical inference and would be suitable for a core course in a graduate program in statistics or biostatistics. The emphasis is on the application of mathematical theory to the problem of inference leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data. The book shows how a small number of key concepts such as sufficiency invariance stochastic ordering decision theory and vector space algebra play a recurring and unifying role. The volume can be divided into four sections. Part I provides a review of the required distribution theory. Part II introduces the problem of statistical inference. This includes the definitions of the exponential family invariant and Bayesian models. Basic concepts of estimation confidence intervals and hypothesis testing are introduced here. Part III constitutes the core of the volume presenting a formal theory of statistical inference. Beginning with decision theory this section then covers uniformly minimum variance unbiased (UMVU) estimation minimum risk equivariant (MRE) estimation and the Neyman-Pearson test. Finally Part IV introduces large sample theory. This section begins with stochastic limit theorems the δ-method the Bahadur representation theorem for sample quantiles large sample U-estimation the Cramér-Rao lower bound and asymptotic efficiency. A separate chapter is then devoted to estimating equation methods. The volume ends with a detailed development of large sample hypothesis testing based on the likelihood ratio test (LRT) Rao score test and the Wald test. Features This volume includes treatment of linear and nonlinear regression models ANOVA models generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk admissibility classification Bayes and minimax decision rules) is presented. The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text. Problems involving R programming are included. Appendices summarize the necessary background in analysis matrix algebra and group theory.

GBP 99.99
1