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.
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.
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 timely update of the classic book on the theory and application of random data analysis First published in 1971, Random Data served as an authoritative book on the analysis of experimental physical data for engineering and scientific applications. This Fourth Edition features coverage of new developments in random data management and analysis procedures that are applicable to a broad range of applied fields, from the aerospace and automotive industries to oceanographic and biomedical research. This new edition continues to maintain a balance of classic theory and novel techniques. The authors expand on the treatment of random data analysis theory, including derivations of key relationships in probability and random process theory. The book remains unique in its practical treatment of nonstationary data analysis and nonlinear system analysis, presenting the latest techniques on modern data acquisition, storage, conversion, and qualification of random data prior to its digital analysis. The Fourth Edition also includes: A new chapter on frequency domain techniques to model and identify nonlinear systems from measured input/output random data New material on the analysis of multiple-input/single-output linear models The latest recommended methods for data acquisition and processing of random data Important mathematical formulas to design experiments and evaluate results of random data analysis and measurement procedures Answers to the problem in each chapter Comprehensive and self-contained, Random Data, Fourth Edition is an indispensible book for courses on random data analysis theory and applications at the upper-undergraduate and graduate level. It is also an insightful reference for engineers and scientists who use statistical methods to investigate and solve problems with dynamic data.
Foundations of Risk Analysis presents the issues core to risk analysis – understanding what risk means, expressing risk, building risk models, addressing uncertainty, and applying probability models to real problems. The author provides the readers with the knowledge and basic thinking they require to successfully manage risk and uncertainty to support decision making. This updated edition reflects recent developments on risk and uncertainty concepts, representations and treatment. New material in Foundations of Risk Analysis includes: An up to date presentation of how to understand, define and describe risk based on research carried out in recent years. A new definition of the concept of vulnerability consistent with the understanding of risk. Reflections on the need for seeing beyond probabilities to measure/describe uncertainties. A presentation and discussion of a method for assessing the importance of assumptions (uncertainty factors) in the background knowledge that the subjective probabilities are based on A brief introduction to approaches that produce interval (imprecise) probabilities instead of exact probabilities. In addition the new version provides a number of other improvements, for example, concerning the use of cost-benefit analyses and the As Low As Reasonably Practicable (ALARP) principle. Foundations of Risk Analysis provides a framework for understanding, conducting and using risk analysis suitable for advanced undergraduates, graduates, analysts and researchers from statistics, engineering, finance, medicine and the physical sciences, as well as for managers facing decision making problems involving risk and uncertainty.
An accessible introduction to the essential quantitative methods for making valuable business decisions Quantitative methods-research techniques used to analyze quantitative data-enable professionals to organize and understand numbers and, in turn, to make good decisions. Quantitative Methods: An Introduction for Business Management presents the application of quantitative mathematical modeling to decision making in a business management context and emphasizes not only the role of data in drawing conclusions, but also the pitfalls of undiscerning reliance of software packages that implement standard statistical procedures. With hands-on applications and explanations that are accessible to readers at various levels, the book successfully outlines the necessary tools to make smart and successful business decisions. Progressing from beginner to more advanced material at an easy-to-follow pace, the author utilizes motivating examples throughout to aid readers interested in decision making and also provides critical remarks, intuitive traps, and counterexamples when appropriate. The book begins with a discussion of motivations and foundations related to the topic, with introductory presentations of concepts from calculus to linear algebra. Next, the core ideas of quantitative methods are presented in chapters that explore introductory topics in probability, descriptive and inferential statistics, linear regression, and a discussion of time series that includes both classical topics and more challenging models. The author also discusses linear programming models and decision making under risk as well as less standard topics in the field such as game theory and Bayesian statistics. Finally, the book concludes with a focus on selected tools from multivariate statistics, including advanced regression models and data reduction methods such as principal component analysis, factor analysis, and cluster analysis. The book promotes the importance of an analytical approach, particularly when dealing with a complex system where multiple individuals are involved and have conflicting incentives. A related website features Microsoft Excel® workbooks and MATLAB® scripts to illustrate concepts as well as additional exercises with solutions. Quantitative Methods is an excellent book for courses on the topic at the graduate level. The book also serves as an authoritative reference and self-study guide for financial and business professionals, as well as readers looking to reinforce their analytical skills.
Praise for the Second Edition «A must-have book for anyone expecting to do research and/or applications in categorical data analysis.» —Statistics in Medicine «It is a total delight reading this book.» —Pharmaceutical Research «If you do any analysis of categorical data, this is an essential desktop reference.» —Technometrics The use of statistical methods for analyzing categorical data has increased dramatically, particularly in the biomedical, social sciences, and financial industries. Responding to new developments, this book offers a comprehensive treatment of the most important methods for categorical data analysis. Categorical Data Analysis, Third Edition summarizes the latest methods for univariate and correlated multivariate categorical responses. Readers will find a unified generalized linear models approach that connects logistic regression and Poisson and negative binomial loglinear models for discrete data with normal regression for continuous data. This edition also features: An emphasis on logistic and probit regression methods for binary, ordinal, and nominal responses for independent observations and for clustered data with marginal models and random effects models Two new chapters on alternative methods for binary response data, including smoothing and regularization methods, classification methods such as linear discriminant analysis and classification trees, and cluster analysis New sections introducing the Bayesian approach for methods in that chapter More than 100 analyses of data sets and over 600 exercises Notes at the end of each chapter that provide references to recent research and topics not covered in the text, linked to a bibliography of more than 1,200 sources A supplementary website showing how to use R and SAS; for all examples in the text, with information also about SPSS and Stata and with exercise solutions Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and methodologists, such as biostatisticians and researchers in the social and behavioral sciences, medicine and public health, marketing, education, finance, biological and agricultural sciences, and industrial quality control.
Business intelligence is a broad category of applications and technologies for gathering, providing access to, and analyzing data for the purpose of helping enterprise users make better business decisions. The term implies having a comprehensive knowledge of all factors that affect a business, such as customers, competitors, business partners, economic environment, and internal operations, therefore enabling optimal decisions to be made. Business Intelligence provides readers with an introduction and practical guide to the mathematical models and analysis methodologies vital to business intelligence. This book: Combines detailed coverage with a practical guide to the mathematical models and analysis methodologies of business intelligence. Covers all the hot topics such as data warehousing, data mining and its applications, machine learning, classification, supply optimization models, decision support systems, and analytical methods for performance evaluation. Is made accessible to readers through the careful definition and introduction of each concept, followed by the extensive use of examples and numerous real-life case studies. Explains how to utilise mathematical models and analysis models to make effective and good quality business decisions. This book is aimed at postgraduate students following data analysis and data mining courses. Researchers looking for a systematic and broad coverage of topics in operations research and mathematical models for decision-making will find this an invaluable guide.
This book provides an essential understanding of statistical concepts necessary for the analysis of genomic and proteomic data using computational techniques. The author presents both basic and advanced topics, focusing on those that are relevant to the computational analysis of large data sets in biology. Chapters begin with a description of a statistical concept and a current example from biomedical research, followed by more detailed presentation, discussion of limitations, and problems. The book starts with an introduction to probability and statistics for genome-wide data, and moves into topics such as clustering, classification, multi-dimensional visualization, experimental design, statistical resampling, and statistical network analysis. Clearly explains the use of bioinformatics tools in life sciences research without requiring an advanced background in math/statistics Enables biomedical and life sciences researchers to successfully evaluate the validity of their results and make inferences Enables statistical and quantitative researchers to rapidly learn novel statistical concepts and techniques appropriate for large biological data analysis Carefully revisits frequently used statistical approaches and highlights their limitations in large biological data analysis Offers programming examples and datasets Includes chapter problem sets, a glossary, a list of statistical notations, and appendices with references to background mathematical and technical material Features supplementary materials, including datasets, links, and a statistical package available online Statistical Bioinformatics is an ideal textbook for students in medicine, life sciences, and bioengineering, aimed at researchers who utilize computational tools for the analysis of genomic, proteomic, and many other emerging high-throughput molecular data. It may also serve as a rapid introduction to the bioinformatics science for statistical and computational students and audiences who have not experienced such analysis tasks before.
The field of data mining lies at the confluence of predictive analytics, statistical analysis, and business intelligence. Due to the ever-increasing complexity and size of data sets and the wide range of applications in computer science, business, and health care, the process of discovering knowledge in data is more relevant than ever before. This book provides the tools needed to thrive in today’s big data world. The author demonstrates how to leverage a company’s existing databases to increase profits and market share, and carefully explains the most current data science methods and techniques. The reader will “learn data mining by doing data mining”. By adding chapters on data modelling preparation, imputation of missing data, and multivariate statistical analysis, Discovering Knowledge in Data, Second Edition remains the eminent reference on data mining. The second edition of a highly praised, successful reference on data mining, with thorough coverage of big data applications, predictive analytics, and statistical analysis. Includes new chapters on Multivariate Statistics, Preparing to Model the Data, and Imputation of Missing Data, and an Appendix on Data Summarization and Visualization Offers extensive coverage of the R statistical programming language Contains 280 end-of-chapter exercises Includes a companion website for university instructors who adopt the book
A friendly and accessible approach to applying statistics in the real world With an emphasis on critical thinking, The Art of Data Analysis: How to Answer Almost Any Question Using Basic Statistics presents fun and unique examples, guides readers through the entire data collection and analysis process, and introduces basic statistical concepts along the way. Leaving proofs and complicated mathematics behind, the author portrays the more engaging side of statistics and emphasizes its role as a problem-solving tool. In addition, light-hearted case studies illustrate the application of statistics to real data analyses, highlighting the strengths and weaknesses of commonly used techniques. Written for the growing academic and industrial population that uses statistics in everyday life, The Art of Data Analysis: How to Answer Almost Any Question Using Basic Statistics highlights important issues that often arise when collecting and sifting through data. Featured concepts include: • Descriptive statistics • Analysis of variance • Probability and sample distributions • Confidence intervals • Hypothesis tests • Regression • Statistical correlation • Data collection • Statistical analysis with graphs Fun and inviting from beginning to end, The Art of Data Analysis is an ideal book for students as well as managers and researchers in industry, medicine, or government who face statistical questions and are in need of an intuitive understanding of basic statistical reasoning.
Praise for the First Edition “…a well-written book on data analysis and data mining that provides an excellent foundation…” —CHOICE “This is a must-read book for learning practical statistics and data analysis…” —Computing Reviews.com A proven go-to guide for data analysis, Making Sense of Data I: A Practical Guide to Exploratory Data Analysis and Data Mining, Second Edition focuses on basic data analysis approaches that are necessary to make timely and accurate decisions in a diverse range of projects. Based on the authors’ practical experience in implementing data analysis and data mining, the new edition provides clear explanations that guide readers from almost every field of study. In order to facilitate the needed steps when handling a data analysis or data mining project, a step-by-step approach aids professionals in carefully analyzing data and implementing results, leading to the development of smarter business decisions. The tools to summarize and interpret data in order to master data analysis are integrated throughout, and the Second Edition also features: Updated exercises for both manual and computer-aided implementation with accompanying worked examples New appendices with coverage on the freely available Traceis™ software, including tutorials using data from a variety of disciplines such as the social sciences, engineering, and finance New topical coverage on multiple linear regression and logistic regression to provide a range of widely used and transparent approaches Additional real-world examples of data preparation to establish a practical background for making decisions from data Making Sense of Data I: A Practical Guide to Exploratory Data Analysis and Data Mining, Second Edition is an excellent reference for researchers and professionals who need to achieve effective decision making from data. The Second Edition is also an ideal textbook for undergraduate and graduate-level courses in data analysis and data mining and is appropriate for cross-disciplinary courses found within computer science and engineering departments.
It is difficult to imagine that the statistical analysis of compositional data has been a major issue of concern for more than 100 years. It is even more difficult to realize that so many statisticians and users of statistics are unaware of the particular problems affecting compositional data, as well as their solutions. The issue of ``spurious correlation'', as the situation was phrased by Karl Pearson back in 1897, affects all data that measures parts of some whole, such as percentages, proportions, ppm and ppb. Such measurements are present in all fields of science, ranging from geology, biology, environmental sciences, forensic sciences, medicine and hydrology. This book presents the history and development of compositional data analysis along with Aitchison's log-ratio approach. Compositional Data Analysis describes the state of the art both in theoretical fields as well as applications in the different fields of science. Key Features: Reflects the state-of-the-art in compositional data analysis. Gives an overview of the historical development of compositional data analysis, as well as basic concepts and procedures. Looks at advances in algebra and calculus on the simplex. Presents applications in different fields of science, including, genomics, ecology, biology, geochemistry, planetology, chemistry and economics. Explores connections to correspondence analysis and the Dirichlet distribution. Presents a summary of three available software packages for compositional data analysis. Supported by an accompanying website featuring R code. Applied scientists working on compositional data analysis in any field of science, both in academia and professionals will benefit from this book, along with graduate students in any field of science working with compositional data.
A modern, comprehensive treatment of latent class and latent transition analysis for categorical data On a daily basis, researchers in the social, behavioral, and health sciences collect information and fit statistical models to the gathered empirical data with the goal of making significant advances in these fields. In many cases, it can be useful to identify latent, or unobserved, subgroups in a population, where individuals' subgroup membership is inferred from their responses on a set of observed variables. Latent Class and Latent Transition Analysis provides a comprehensive and unified introduction to this topic through one-of-a-kind, step-by-step presentations and coverage of theoretical, technical, and practical issues in categorical latent variable modeling for both cross-sectional and longitudinal data. The book begins with an introduction to latent class and latent transition analysis for categorical data. Subsequent chapters delve into more in-depth material, featuring: A complete treatment of longitudinal latent class models Focused coverage of the conceptual underpinnings of interpretation and evaluationof a latent class solution Use of parameter restrictions and detection of identification problems Advanced topics such as multi-group analysis and the modeling and interpretation of interactions between covariates The authors present the topic in a style that is accessible yet rigorous. Each method is presented with both a theoretical background and the practical information that is useful for any data analyst. Empirical examples showcase the real-world applications of the discussed concepts and models, and each chapter concludes with a «Points to Remember» section that contains a brief summary of key ideas. All of the analyses in the book are performed using Proc LCA and Proc LTA, the authors' own software packages that can be run within the SAS® environment. A related Web site houses information on these freely available programs and the book's data sets, encouraging readers to reproduce the analyses and also try their own variations. Latent Class and Latent Transition Analysis is an excellent book for courses on categorical data analysis and latent variable models at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners in the social, behavioral, and health sciences who conduct latent class and latent transition analysis in their everyday work.
The bestselling guide to qualitative research, updated and expanded Qualitative Research is the essential guide to understanding, designing, conducting, and presenting a qualitative research study. This fourth edition features new material covering mixed methods, action research, arts-based research, online data sources, and the latest in data analysis, including data analysis software packages as well as narrative and poetic analysis strategies. A new section offers multiple ways of presenting qualitative research findings. The reader-friendly, jargon-free style makes this book accessible to both novice and experienced researchers, emphasizing the role of a theoretical framework in designing a study while providing practical guidance. Qualitative research reaches beyond the what, where, and when of quantitative analysis to investigate the why and how behind human behavior and the reasons that govern such behavior, but this presents a number of significant challenges. This guide is an invaluable reference for students and practitioners alike, providing the deep understanding that this sometimes difficult area of research requires to produce accurate results. The book contains a step-by-step guide to analyzing qualitative data and an addendum for graduate students with a template for a thesis, dissertation, or grant application. Build a strong foundation in qualitative research theory and application Design and implement effective qualitative research studies Communicate findings more successfully with clear presentation Explore data sources, data analysis tools, and the different types of research