Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.
A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems Numerous examples that use R software for all text data analyses More than 400 exercises for readers to practice and extend the theory, methods, and data analysis A supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.
Statistics Analysis of Geographical Data: An Introduction provides a comprehensive and accessible introduction to the theory and practice of statistical analysis in geography. It covers a wide range of topics including graphical and numerical description of datasets, probability, calculation of confidence intervals, hypothesis testing, collection and analysis of data using analysis of variance and linear regression. Taking a clear and logical approach, this book examines real problems with real data from the geographical literature in order to illustrate the important role that statistics play in geographical investigations. Presented in a clear and accessible manner the book includes recent, relevant examples, designed to enhance the reader’s understanding.
A comprehensive introduction to statistical methods for data mining and knowledge discovery. Applications of data mining and ‘big data’ increasingly take center stage in our modern, knowledge-driven society, supported by advances in computing power, automated data acquisition, social media development and interactive, linkable internet software. This book presents a coherent, technical introduction to modern statistical learning and analytics, starting from the core foundations of statistics and probability. It includes an overview of probability and statistical distributions, basics of data manipulation and visualization, and the central components of standard statistical inferences. The majority of the text extends beyond these introductory topics, however, to supervised learning in linear regression, generalized linear models, and classification analytics. Finally, unsupervised learning via dimension reduction, cluster analysis, and market basket analysis are introduced. Extensive examples using actual data (with sample R programming code) are provided, illustrating diverse informatic sources in genomics, biomedicine, ecological remote sensing, astronomy, socioeconomics, marketing, advertising and finance, among many others. Statistical Data Analytics: Focuses on methods critically used in data mining and statistical informatics. Coherently describes the methods at an introductory level, with extensions to selected intermediate and advanced techniques. Provides informative, technical details for the highlighted methods. Employs the open-source R language as the computational vehicle – along with its burgeoning collection of online packages – to illustrate many of the analyses contained in the book. Concludes each chapter with a range of interesting and challenging homework exercises using actual data from a variety of informatic application areas. This book will appeal as a classroom or training text to intermediate and advanced undergraduates, and to beginning graduate students, with sufficient background in calculus and matrix algebra. It will also serve as a source-book on the foundations of statistical informatics and data analytics to practitioners who regularly apply statistical learning to their modern data.
Solutions Manual to accompany Fundamentals of Matrix Analysis with Applications – an accessible and clear introduction to linear algebra with a focus on matrices and engineering applications
Modeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method. Based upon short courses delivered by the authors, it provides a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to improve understanding, as well as data and a solutions manual which is available on an accompanying website. Complementing Pawlowsky-Glahn’s earlier collective text that provides an overview of the state-of-the-art in this field, Modeling and Analysis of Compositional Data fills a gap in the literature for a much-needed manual for teaching, self learning or consulting.
An easily accessible introduction to log-linear modeling for non-statisticians Highlighting advances that have lent to the topic's distinct, coherent methodology over the past decade, Log-Linear Modeling: Concepts, Interpretation, and Application provides an essential, introductory treatment of the subject, featuring many new and advanced log-linear methods, models, and applications. The book begins with basic coverage of categorical data, and goes on to describe the basics of hierarchical log-linear models as well as decomposing effects in cross-classifications and goodness-of-fit tests. Additional topics include: The generalized linear model (GLM) along with popular methods of coding such as effect coding and dummy coding Parameter interpretation and how to ensure that the parameters reflect the hypotheses being studied Symmetry, rater agreement, homogeneity of association, logistic regression, and reduced designs models Throughout the book, real-world data illustrate the application of models and understanding of the related results. In addition, each chapter utilizes R, SYSTAT®, and §¤EM software, providing readers with an understanding of these programs in the context of hierarchical log-linear modeling. Log-Linear Modeling is an excellent book for courses on categorical data analysis at the upper-undergraduate and graduate levels. It also serves as an excellent reference for applied researchers in virtually any area of study, from medicine and statistics to the social sciences, who analyze empirical data in their everyday work.
A modern and practical guide to the essential concepts and ideas for analyzing data with missing observations in the field of biostatistics With an emphasis on hands-on applications, Applied Missing Data Analysis in the Health Sciences outlines the various modern statistical methods for the analysis of missing data. The authors acknowledge the limitations of established techniques and provide newly-developed methods with concrete applications in areas such as causal inference methods and the field of diagnostic medicine. Organized by types of data, chapter coverage begins with an overall introduction to the existence and limitations of missing data and continues into traditional techniques for missing data inference, including likelihood-based, weighted GEE, multiple imputation, and Bayesian methods. The book’s subsequently covers cross-sectional, longitudinal, hierarchical, survival data. In addition, Applied Missing Data Analysis in the Health Sciences features: Multiple data sets that can be replicated using the SAS®, Stata®, R, and WinBUGS software packages Numerous examples of case studies in the field of biostatistics to illustrate real-world scenarios and demonstrate applications of discussed methodologies Detailed appendices to guide readers through the use of the presented data in various software environments Applied Missing Data Analysis in the Health Sciences is an excellent textbook for upper-undergraduate and graduate-level biostatistics courses as well as an ideal resource for health science researchers and applied statisticians.
Time Series Analysis in Meteorology and Climatology provides an accessible overview of this notoriously difficult subject. Clearly structured throughout, the authors develop sufficient theoretical foundation to understand the basis for applying various analytical methods to a time series and show clearly how to interpret the results. Taking a unique approach to the subject, the authors use a combination of theory and application to real data sets to enhance student understanding throughout the book. This book is written for those students that have a data set in the form of a time series and are confronted with the problem of how to analyse this data. Each chapter covers the various methods that can be used to carry out this analysis with coverage of the necessary theory and its application. In the theoretical section topics covered include; the mathematical origin of spectrum windows, leakage of variance and understanding spectrum windows. The applications section includes real data sets for students to analyse. Scalar variables are used for ease of understanding for example air temperatures, wind speed and precipitation. Students are encouraged to write their own computer programmes and data sets are provided to enable them to recognize quickly whether their programme is working correctly- one data set is provided with artificial data and the other with real data where the students are required to physically interpret the results of their periodgram analysis. Based on the acclaimed and long standing course at the University of Oklahoma and part of the RMetS Advancing Weather and Climate Science Series, this book is distinct in its approach to the subject matter in that it is written specifically for readers in meteorology and climatology and uses a mix of theory and application to real data sets.
A comprehensive introduction to bootstrap methods in the R programming environment Bootstrap methods provide a powerful approach to statistical data analysis, as they have more general applications than standard parametric methods. An Introduction to Bootstrap Methods with Applications to R explores the practicality of this approach and successfully utilizes R to illustrate applications for the bootstrap and other resampling methods. This book provides a modern introduction to bootstrap methods for readers who do not have an extensive background in advanced mathematics. Emphasis throughout is on the use of bootstrap methods as an exploratory tool, including its value in variable selection and other modeling environments. The authors begin with a description of bootstrap methods and its relationship to other resampling methods, along with an overview of the wide variety of applications of the approach. Subsequent chapters offer coverage of improved confidence set estimation, estimation of error rates in discriminant analysis, and applications to a wide variety of hypothesis testing and estimation problems, including pharmaceutical, genomics, and economics. To inform readers on the limitations of the method, the book also exhibits counterexamples to the consistency of bootstrap methods. An introduction to R programming provides the needed preparation to work with the numerous exercises and applications presented throughout the book. A related website houses the book's R subroutines, and an extensive listing of references provides resources for further study. Discussing the topic at a remarkably practical and accessible level, An Introduction to Bootstrap Methods with Applications to R is an excellent book for introductory courses on bootstrap and resampling methods at the upper-undergraduate and graduate levels. It also serves as an insightful reference for practitioners working with data in engineering, medicine, and the social sciences who would like to acquire a basic understanding of bootstrap methods.
A step-by-step introduction to using SAS® statistical software as a foundational approach to data analysis and interpretation Presenting a straightforward introduction from the ground up, SAS® Essentials: Mastering SAS for Data Analytics, Second Edition illustrates SAS using hands-on learning techniques and numerous real-world examples. Keeping different experience levels in mind, the highly-qualified author team has developed the book over 20 years of teaching introductory SAS courses. Divided into two sections, the first part of the book provides an introduction to data manipulation, statistical techniques, and the SAS programming language. The second section is designed to introduce users to statistical analysis using SAS Procedures. Featuring self-contained chapters to enhance the learning process, the Second Edition also includes: Programming approaches for the most up-to-date version of the SAS platform including information on how to use the SAS University Edition Discussions to illustrate the concepts and highlight key fundamental computational skills that are utilized by business, government, and organizations alike New chapters on reporting results in tables and factor analysis Additional information on the DATA step for data management with an emphasis on importing data from other sources, combining data sets, and data cleaning Updated ANOVA and regression examples as well as other data analysis techniques A companion website with the discussed data sets, additional code, and related PowerPoint® slides SAS Essentials: Mastering SAS for Data Analytics, Second Edition is an ideal textbook for upper-undergraduate and graduate-level courses in statistics, data analytics, applied SAS programming, and statistical computer applications as well as an excellent supplement for statistical methodology courses. The book is an appropriate reference for researchers and academicians who require a basic introduction to SAS for statistical analysis and for preparation for the Basic SAS Certification Exam.
Guides readers through the quantitative data analysis process including contextualizing data within a research situation, connecting data to the appropriate statistical tests, and drawing valid conclusions Introduction to Quantitative Data Analysis in the Behavioral and Social Sciences presents a clear and accessible introduction to the basics of quantitative data analysis and focuses on how to use statistical tests as a key tool for analyzing research data. The book presents the entire data analysis process as a cyclical, multiphase process and addresses the processes of exploratory analysis, decision-making for performing parametric or nonparametric analysis, and practical significance determination. In addition, the author details how data analysis is used to reveal the underlying patterns and relationships between the variables and connects those trends to the data’s contextual situation. Filling the gap in quantitative data analysis literature, this book teaches the methods and thought processes behind data analysis, rather than how to perform the study itself or how to perform individual statistical tests. With a clear and conversational style, readers are provided with a better understanding of the overall structure and methodology behind performing a data analysis as well as the needed techniques to make informed, meaningful decisions during data analysis. The book features numerous data analysis examples in order to emphasize the decision and thought processes that are best followed, and self-contained sections throughout separate the statistical data analysis from the detailed discussion of the concepts allowing readers to reference a specific section of the book for immediate solutions to problems and/or applications. Introduction to Quantitative Data Analysis in the Behavioral and Social Sciences also features coverage of the following: • The overall methodology and research mind-set for how to approach quantitative data analysis and how to use statistics tests as part of research data analysis • A comprehensive understanding of the data, its connection to a research situation, and the most appropriate statistical tests for the data • Numerous data analysis problems and worked-out examples to illustrate the decision and thought processes that reveal underlying patterns and trends • Detailed examples of the main concepts to aid readers in gaining the needed skills to perform a full analysis of research problems • A conversational tone to effectively introduce readers to the basics of how to perform data analysis as well as make meaningful decisions during data analysis Introduction to Quantitative Data Analysis in the Behavioral and Social Sciences is an ideal textbook for upper-undergraduate and graduate-level research method courses in the behavioral and social sciences, statistics, and engineering. This book is also an appropriate reference for practitioners who require a review of quantitative research methods. Michael J. Albers, Ph.D., is Professor in the Department of English at East Carolina University. His research interests include information design with a focus on answering real-world questions, the presentation of complex information, and human–information interaction. Dr. Albers received his Ph.D. in Technical Communication and Rhetoric from Texas Tech University.
This book provides an introduction to spatial analyses concerning disaggregated (or micro) spatial data. Particular emphasis is put on spatial data compilation and the structuring of the connections between the observations. Descriptive analysis methods of spatial data are presented in order to identify and measure the spatial, global and local dependency. The authors then focus on autoregressive spatial models, to control the problem of spatial dependency between the residues of a basic linear statistical model, thereby contravening one of the basic hypotheses of the ordinary least squares approach. This book is a popularized reference for students looking to work with spatialized data, but who do not have the advanced statistical theoretical basics.
A research-based foundational overview of contemporary adult education Foundations of Adult and Continuing Education distills decades of scholarship in the field to provide students and practitioners with an up-to-date practical resource. Grounded in research and focused on the unique needs of adult learners, this book provides a foundational overview of adult education, and an introduction to the organizations and practices developed to support adult learning in a variety of contexts. The discussion also includes select understandings of international adult education, policy, and methods alongside theoretical frameworks, contemporary and historical contexts, and the guiding principles of adult education today. Coverage of emerging issues includes the aging society, social justice, and more, with expert insight from leading authorities in the field. Many adult educators begin practice through the context of their own experiences in the field. This book provides the broader research, theory, and practice needed for a deeper understanding of adult education and its place in society. Learn the key philosophical and theoretical frameworks of adult education Survey the landscape of the field through contemporary and historical foundations Examine key guiding understandings and practices targeted to adult learners Delve into newer concerns including technology, globalization, and more Foundations of Adult and Continuing Education provides an expertly-led overview of the field, and an essential introduction to real-world practice.
An invaluable tool in Bioinformatics, this unique volume provides both theoretical and experimental results, and describes basic principles of computational intelligence and pattern analysis while deepening the reader's understanding of the ways in which these principles can be used for analyzing biological data in an efficient manner. This book synthesizes current research in the integration of computational intelligence and pattern analysis techniques, either individually or in a hybridized manner. The purpose is to analyze biological data and enable extraction of more meaningful information and insight from it. Biological data for analysis include sequence data, secondary and tertiary structure data, and microarray data. These data types are complex and advanced methods are required, including the use of domain-specific knowledge for reducing search space, dealing with uncertainty, partial truth and imprecision, efficient linear and/or sub-linear scalability, incremental approaches to knowledge discovery, and increased level and intelligence of interactivity with human experts and decision makers Chapters authored by leading researchers in CI in biology informatics. Covers highly relevant topics: rational drug design; analysis of microRNAs and their involvement in human diseases. Supplementary material included: program code and relevant data sets correspond to chapters.