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Core Statistics is a compact starter course on the theory, models, and computational tools needed to make informed use of powerful statistical methods.
Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the notation and basic results needed are presented in an initial chapter on probability, so prior knowledge of these topics is not essential. The presentation is designed to expose students to as many of the central ideas and topics in the discipline as possible, balancing various approaches to inference as well as exact, numerical, and large sample methods. Moving beyond more standard material, the book includes chapters introducing bootstrap methods, nonparametric regression, equivariant estimation, empirical Bayes, and sequential design and analysis. The book has a rich collection of exercises. Several of them illustrate how the theory developed in the book may be used in various applications. Solutions to many of the exercises are included in an appendix.
This Bayesian modeling book provides the perfect entry for gaining a practical understanding of Bayesian methodology. It focuses on standard statistical models and is backed up by discussed real datasets available from the book website.
This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design. Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets.
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics.
Core Concepts in Data Analysis: Summarization, Correlation and Visualization provides in-depth descriptions of those data analysis approaches that either summarize data (principal component analysis and clustering, including hierarchical and network clustering) or correlate different aspects of data (decision trees, linear rules, neuron networks, and Bayes rule). Boris Mirkin takes an unconventional approach and introduces the concept of multivariate data summarization as a counterpart to conventional machine learning prediction schemes, utilizing techniques from statistics, data analysis, data mining, machine learning, computational intelligence, and information retrieval. Innovations following from his in-depth analysis of the models underlying summarization techniques are introduced, and applied to challenging issues such as the number of clusters, mixed scale data standardization, interpretation of the solutions, as well as relations between seemingly unrelated concepts: goodness-of-fit functions for classification trees and data standardization, spectral clustering and additive clustering, correlation and visualization of contingency data. The mathematical detail is encapsulated in the so-called “formulation” parts, whereas most material is delivered through “presentation” parts that explain the methods by applying them to small real-world data sets; concise “computation” parts inform of the algorithmic and coding issues. Four layers of active learning and self-study exercises are provided: worked examples, case studies, projects and questions.
A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.
Core Statistical Concepts with Excel® connects statistical concepts to applications with Excel® using practical research examples. The text jointly promotes an understanding of Excel® and a deeper knowledge of core concepts through practice. Authors Gregory J. Privitera and Darryl Mayeaux provide students step-by-step instruction for using Excel® software as a useful tool not only to manage but also analyze data—all through the use of key themes, features, and pedagogy: an emphasis on student learning, a focus on current research, and integration of Excel® to introduce statistical concepts.
Provides an introduction to modern statistical theory for social and health scientists while invoking minimal modeling assumptions.
Written with as little technical language as possible, Dr. Angela Shirley (PhD, Northeastern University) unravels the foundational concepts of statistics, many of which can be quite difficult to grasp. To explain advanced topics she uses a practical, intuitive approach, gained from her many years of teaching statistics at the University of the West Indies, St Augustine, Trinidad. Starting with a brief review of prerequisite probability, the text develops the theory of classical statistics, from estimation, to confidence intervals, to hypothesis testing. Along the way, students are treated to brief vignettes describing the fascinating history of statistics and how its founding fathers developed the field in response to the needs of a world on the verge of a data revolution. With many worked examples, including exam-type questions, this book provides students with a solid foundation on which to build successful careers in statistics or statistics-related fields. Foundations of Classical Statistics: Advanced Core is a textbook especially designed for students at The University of the West Indies pursuing final-year undergraduate or graduate level courses in Inferential Statistics. As such, it can serve as a valuable resource for students worldwide. A first course in Probability, as well as some Calculus, is required.