Basic algebraic concepts. Useful for any student in pre-algebra and beyond as a reference tool.  Read more

This book is written for high school and college students learning about probability for the first time. It will appeal to the reader who has a healthy level of enthusiasm for understanding how and why the various results of probability come about. All of the standard introductory topics in probability are covered: combinatorics, the rules of probability, Bayes’ theorem, expectation value, variance, probability density, common distributions, the law of large numbers, the central limit theorem, correlation, and regression. Calculus is not a prerequisite, although a few of the problems do involve calculus. These are marked clearly.The book features 150 worked-out problems in the form of examples in the text and solved problems at the end of each chapter. These problems, along with the discussions in the text, will be a valuable resource in any introductory probability course, either as the main text or as a helpful supplement. Read more

Here is a practical and mathematically rigorous introduction to the field of asymptotic statistics. In addition to most of the standard topics of an asymptotics course--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, one of the book's unifying themes that mainly entails the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Read more

Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout. Author resource page: http://www.stat.columbia.edu/~gelman/arm/ Read more

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This classic textbook builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and natural extensions, and consequences, of previous concepts. It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation.FeaturesThe classic graduate-level textbook on statistical inferenceDevelops elements of statistical theory from first principles of probabilityWritten in a lucid style accessible to anyone with some background in calculusCovers all key topics of a standard course in inferenceHundreds of examples throughout to aid understandingEach chapter includes an extensive set of graduated exercisesStatistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background. It also stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less focused on formal optimality considerations.This is a reprint of the second edition originally published by Cengage Learning, Inc. in 2001. Read more

“This is a fine textbook on probability theory based on measure theory. The parts of measure theory that are needed are developed within the book and a teacher of measure theory could find them quite useful. The construction of the Lebesgue measure (extension theorem) is unusual and interesting.” Mathematical Reviews “This short, lucid and excellent textbook should be a required course for all graduate students of mathematics and statistics as well as for interested graduate / PhD students in engineering, computer sciences, economics, and management who lack exposure to measure theoretic applications in probability theory.” Professor B K Sahu Indian Institute of Technology, India Solutions Manual for Free Download This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail. Read more

A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included. Read more

"Get the tools you need to use SAS® in clinical trial design! Unique and multifaceted, Modern Approaches to Clinical Trials Using SAS: Classical, Adaptive, and Bayesian Methods, edited by Sandeep M. Menon and Richard C. Zink, thoroughly covers several domains of modern clinical trial design: classical, group sequential, adaptive, and Bayesian methods that are applicable to and widely used in various phases of pharmaceutical development. Written for biostatisticians, pharmacometricians, clinical developers, and statistical programmers involved in the design, analysis, and interpretation of clinical trials, as well as students in graduate and postgraduate programs in statistics or biostatistics, the book touches on a wide variety of topics, including dose-response and dose-escalation designs; sequential methods to stop trials early for overwhelming efficacy, safety, or futility; Bayesian designs that incorporate historical data; adaptive sample size re-estimation; adaptive randomization to allocate subjects to more effective treatments; and population enrichment designs. Methods are illustrated using clinical trials from diverse therapeutic areas, including dermatology, endocrinology, infectious disease, neurology, oncology, and rheumatology. Individual chapters are authored by renowned contributors, experts, and key opinion leaders from the pharmaceutical/medical device industry or academia. Numerous real-world examples and sample SAS code enable users to readily apply novel clinical trial design and analysis methodologies in practice." Read more

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High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression. Read more

The past decade has witnessed an explosion of interest in research and education in causal inference, due to its wide applications in biomedical research, social sciences, artificial intelligence etc. This textbook, based on the author's course on causal inference at UC Berkeley taught over the past seven years, only requires basic knowledge of probability theory, statistical inference, and linear and logistic regressions. It assumes minimal knowledge of causal inference, and reviews basic probability and statistics in the appendix. It covers causal inference from a statistical perspective and includes examples and applications from biostatistics and econometrics.Key Features:All R code and data sets available at Harvard Dataverse.Solutions manual available for instructors.Includes over 100 exercises.This book is suitable for an advanced undergraduate or graduate-level course on causal inference, or postgraduate and PhD-level course in statistics and biostatistics departments. Read more

There has been considerable attention to making the methodologies of structural equation modeling available to researchers, practitioners, and students along with commonly used software. Structural Equation Modelling Using R/SAS aims to bring it all together to provide a concise point-of-reference for the most commonly used structural equation modeling from the fundamental level to the advanced level. This book is intended to contribute to the rapid development in structural equation modeling and its applications to real-world data. Straightforward explanations of the statistical theory and models related to structural equation models are provided, using a compilation of a variety of publicly available data, to provide an illustration of data analytics in a step-by-step fashion using commonly used statistical software of R and SAS. This book is appropriate for anyone who is interested in learning and practicing structural equation modeling, especially in using R and SAS. It is useful for applied statisticians, data scientists and practitioners, applied statistical analysts and scientists in public health, and academic researchers and graduate students in statistics, whilst also being of use to R&D professionals/practitioners in industry and governmental agencies.Key Features: Extensive compilation of commonly used structural equation models and methods from fundamental to advanced levelsStraightforward explanations of the theory related to the structural equation modelsCompilation of a variety of publicly available dataStep-by-step illustrations of data analysis using commonly used statistical software R and SASData and computer programs are available for readers to replicate and implement the new methods to better understand the book contents and for future applicationsHandbook for applied statisticians and practitioners Read more

"Overall, this textbook is a perfect guide for interested researchers and students who wish to understand the rationale and methods of causal inference. Each chapter provides an R implementation of the introduced causal concepts and models and concludes with appropriate exercises."-An-Shun Tai & Sheng-Hsuan Lin, in BiometricsOne of the primary motivations for clinical trials and observational studies of humans is to infer cause and effect. Disentangling causation from confounding is of utmost importance. Fundamentals of Causal Inference explains and relates different methods of confounding adjustment in terms of potential outcomes and graphical models, including standardization, difference-in-differences estimation, the front-door method, instrumental variables estimation, and propensity score methods. It also covers effect-measure modification, precision variables, mediation analyses, and time-dependent confounding. Several real data examples, simulation studies, and analyses using R motivate the methods throughout. The book assumes familiarity with basic statistics and probability, regression, and R and is suitable for seniors or graduate students in statistics, biostatistics, and data science as well as PhD students in a wide variety of other disciplines, including epidemiology, pharmacy, the health sciences, education, and the social, economic, and behavioral sciences.Beginning with a brief history and a review of essential elements of probability and statistics, a unique feature of the book is its focus on real and simulated datasets with all binary variables to reduce complex methods down to their fundamentals. Calculus is not required, but a willingness to tackle mathematical notation, difficult concepts, and intricate logical arguments is essential. While many real data examples are included, the book also features the Double What-If Study, based on simulated data with known causal mechanisms, in the belief that the methods are best understood in circumstances where they are known to either succeed or fail. Datasets, R code, and solutions to odd-numbered exercises are available on the book's website at www.routledge.com/9780367705053. Instructors can also find slides based on the book, and a full solutions manual under 'Instructor Resources'. Read more

Design and Analysis of Experiments provides a rigorous introduction to product and process design improvement through quality and performance optimization. Clear demonstration of widely practiced techniques and procedures allows readers to master fundamental concepts, develop design and analysis skills, and use experimental models and results in real-world applications. Detailed coverage of factorial and fractional factorial design, response surface techniques, regression analysis, biochemistry and biotechnology, single factor experiments, and other critical topics offer highly-relevant guidance through the complexities of the field.Stressing the importance of both conceptual knowledge and practical skills, this text adopts a balanced approach to theory and application. Extensive discussion of modern software tools integrate data from real-world studies, while examples illustrate the efficacy of designed experiments across industry lines, from service and transactional organizations to heavy industry and biotechnology. Broad in scope yet deep in detail, this text is both an essential student resource and an invaluable reference for professionals in engineering, science, manufacturing, statistics, and business management. Read more

Winner of the 2016 De Groot Prize from the International Society for Bayesian AnalysisNow in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors―all leaders in the statistics community―introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice.New to the Third EditionFour new chapters on nonparametric modelingCoverage of weakly informative priors and boundary-avoiding priorsUpdated discussion of cross-validation and predictive information criteriaImproved convergence monitoring and effective sample size calculations for iterative simulationPresentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagationNew and revised software codeThe book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page. Read more

Wouldn't it be great if there were a statistics book that made histograms, probability distributions, and chi square analysis more enjoyable than going to the dentist? Head First Statistics brings this typically dry subject to life, teaching you everything you want and need to know about statistics through engaging, interactive, and thought-provoking material, full of puzzles, stories, quizzes, visual aids, and real-world examples. Whether you're a student, a professional, or just curious about statistical analysis, Head First's brain-friendly formula helps you get a firm grasp of statistics so you can understand key points and actually use them. Learn to present data visually with charts and plots; discover the difference between taking the average with mean, median, and mode, and why it's important; learn how to calculate probability and expectation; and much more. Head First Statistics is ideal for high school and college students taking statistics and satisfies the requirements for passing the College Board's Advanced Placement (AP) Statistics Exam. With this book, you'll: Study the full range of topics covered in first-year statisticsTackle tough statistical concepts using Head First's dynamic, visually rich format proven to stimulate learning and help you retain knowledge Explore real-world scenarios, ranging from casino gambling to prescription drug testing, to bring statistical principles to lifeDiscover how to measure spread, calculate odds through probability, and understand the normal, binomial, geometric, and Poisson distributionsConduct sampling, use correlation and regression, do hypothesis testing, perform chi square analysis, and moreBefore you know it, you'll not only have mastered statistics, you'll also see how they work in the real world. Head First Statistics will help you pass your statistics course, and give you a firm understanding of the subject so you can apply the knowledge throughout your life. Read more

This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. Read more

Most mathematical examples illustrate the truth of a statement; conversely, counterexamples demonstrate a statement's falsity if changing the conditions. Mathematicians have always prized counterexamples as intrinsically enjoyable objects of study as well as valuable tools for teaching, learning, and research. This third edition of the definitive book on counterexamples in probability and stochastic processes presents the author's revisions and corrections in addition to a substantial new appendix. Suitable as a supplementary source for advanced undergraduates and graduate courses in the field of probability and stochastic processes, this volume features a wide variety of topics that are challenging in both content and detail. The text consists of four chapters and twenty-five sections. Each section begins with short introductory notes of basic definitions and main results. Counterexamples related to the main results follow, along with motivation for questions and counterstatements that range in difficulty. A familiarity with basic notions and results in probability and stochastic processes is assumed, and a chapter of supplementary remarks provides a wealth of information about original sources as well as references for further studies. Read more

When it comes to learning statistics, Mann delivers the information that business professionals need. The new edition incorporates the most up-to-date methods and applications to present the latest information in the field. It focuses on explaining how to apply the concepts through case studies and numerous examples. Data integrated throughout the chapters come from a wide range of disciplines and media sources. Over 200 examples are included along with marginal notes and step-by-step solutions. The Decide for Yourself feature also helps business professionals explore real-world problems and solutions. Read more