Geometry Driven Statistics

Statistic: A Concise Mathematical Introduction for Students and Scientists offers a one academic term text that prepares the student to broaden their skills in statistics, probability and inference, prior to selecting their follow-on courses in their chosen fields, whether it be engineering, computer science, programming, data sciences, business or economics.  The book places focus early on continuous measurements, as well as discrete random variables. By invoking simple and intuitive models and geometric probability, discrete and continuous experiments and probabilities are discussed throughout the book in a natural way. Classical probability, random variables, and inference are discussed, as well as material on understanding data and topics of special interest. Topics discussed include: • Classical equally likely outcomes • Variety of models of discrete and continuous probability laws • Likelihood function and ratio • Inference • Bayesian statistics With the growth in the volume of data generated in many disciplines that is enabling the growth in data science, companies now demand statistically literate scientists and this textbook is the answer, suited for undergraduates studying science or engineering, be it computer science, economics, life sciences, environmental, business, amongst many others. Basic knowledge of bivariate calculus, R language, Matematica and JMP is useful, however there is an accompanying website including sample R and Mathematica code to help instructors and students.

A visually intuitive approach to statistical data analysis Visual Statistics brings the most complex and advanced statistical methods within reach of those with little statistical training by using animated graphics of the data. Using ViSta: The Visual Statistics System-developed by Forrest Young and Pedro Valero-Mora and available free of charge on the Internet-students can easily create fully interactive visualizations from relevant mathematical statistics, promoting perceptual and cognitive understanding of the data's story. An emphasis is placed on a paradigm for understanding data that is visual, intuitive, geometric, and active, rather than one that relies on convoluted logic, heavy mathematics, systems of algebraic equations, or passive acceptance of results. A companion Web site complements the book by further demonstrating the concept of creating interactive and dynamic graphics. The book provides users with the opportunity to view the graphics in a dynamic way by illustrating how to analyze statistical data and explore the concepts of visual statistics. Visual Statistics addresses and features the following topics: * Why use dynamic graphics? * A history of statistical graphics * Visual statistics and the graphical user interface * Visual statistics and the scientific method * Character-based statistical interface objects * Graphics-based statistical interfaces * Visualization for exploring univariate data This is an excellent textbook for undergraduate courses in data analysis and regression, for students majoring or minoring in statistics, mathematics, science, engineering, and computer science, as well as for graduate-level courses in mathematics. The book is also ideal as a reference/self-study guide for engineers, scientists, and mathematicians. With contributions by highly regarded professionals in the field, Visual Statistics not only improves a student's understanding of statistics, but also builds confidence to overcome problems that may have previously been intimidating.

Presents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function This book addresses mathematical statistics for upper-undergraduates and first year graduate students, tying chapters on estimation, confidence intervals, hypothesis testing, and statistical models together to present a unifying focus on the likelihood function. It also emphasizes the important ideas in statistical modeling, such as sufficiency, exponential family distributions, and large sample properties. Mathematical Statistics: An Introduction to Likelihood Based Inference makes advanced topics accessible and understandable and covers many topics in more depth than typical mathematical statistics textbooks. It includes numerous examples, case studies, a large number of exercises ranging from drill and skill to extremely difficult problems, and many of the important theorems of mathematical statistics along with their proofs. In addition to the connected chapters mentioned above, Mathematical Statistics covers likelihood-based estimation, with emphasis on multidimensional parameter spaces and range dependent support. It also includes a chapter on confidence intervals, which contains examples of exact confidence intervals along with the standard large sample confidence intervals based on the MLE's and bootstrap confidence intervals. There’s also a chapter on parametric statistical models featuring sections on non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. Prepares students with the tools needed to be successful in their future work in statistics data science Includes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage Emphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties Includes sections on Bayesian estimation and credible intervals Features examples, problems, and solutions Mathematical Statistics: An Introduction to Likelihood Based Inference is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and/or statistical inference.

Medical Statistics provides the necessary statistical tools to enable researchers to undertake and understand evidence-based clinical research. It is a practical guide to conducting statistical research and interpreting statistics in the context of how the participants were recruited, how the study was designed, what types of variables were used, what effect size was found, and what the P values mean. It guides researchers through the process of selecting the correct statistics and show how to best report results for presentation and publication. Clear and concise explanations, combined with plenty of examples and tabulated explanations are based on the authors’ popular medical statistics courses. The table of contents is divided into sections according to whether data are continuous or categorical in nature as this distinction is fundamental to selecting the correct statistics. Each chapter provides a clear step-by-step guide to each statistical test with practical instructions on how to generate and interpret the numbers, and present the results as scientific tables or graphs. The chapters conclude with critical appraisal guidelines to help researchers review the reporting of results from each type of statistical test. This new edition includes a new chapter on repeated measures and mixed models and a helpful glossary of terms provides an easy reference that applies to all chapters.

A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.

Holistic approach to understanding medical statistics This hands-on guide is much more than a basic medical statistics introduction. It equips you with the statistical tools required for evidence-based clinical research. Each chapter provides a clear step-by-step guide to each statistical test with practical instructions on how to generate and interpret the numbers, and present the results as scientific tables or graphs. Showing you how to: analyse data with the help of data set examples (Click here to download datasets) select the correct statistics and report results for publication or presentation understand and critically appraise results reported in the literature Each statistical test is linked to the research question and the type of study design used. There are also checklists for critically appraising the literature and web links to useful internet sites. Clear and concise explanations, combined with plenty of examples and tabulated explanations are based on the authors’ popular medical statistics courses. Critical appraisal guidelines at the end of each chapter help the reader evaluate the statistical data in their particular contexts.

Explores mathematical statistics in its entirety—from the fundamentals to modern methods This book introduces readers to point estimation, confidence intervals, and statistical tests. Based on the general theory of linear models, it provides an in-depth overview of the following: analysis of variance (ANOVA) for models with fixed, random, and mixed effects; regression analysis is also first presented for linear models with fixed, random, and mixed effects before being expanded to nonlinear models; statistical multi-decision problems like statistical selection procedures (Bechhofer and Gupta) and sequential tests; and design of experiments from a mathematical-statistical point of view. Most analysis methods have been supplemented by formulae for minimal sample sizes. The chapters also contain exercises with hints for solutions. Translated from the successful German text, Mathematical Statistics requires knowledge of probability theory (combinatorics, probability distributions, functions and sequences of random variables), which is typically taught in the earlier semesters of scientific and mathematical study courses. It teaches readers all about statistical analysis and covers the design of experiments. The book also describes optimal allocation in the chapters on regression analysis. Additionally, it features a chapter devoted solely to experimental designs. Classroom-tested with exercises included Practice-oriented (taken from day-to-day statistical work of the authors) Includes further studies including design of experiments and sample sizing Presents and uses IBM SPSS Statistics 24 for practical calculations of data Mathematical Statistics is a recommended text for advanced students and practitioners of math, probability, and statistics.

A new edition of the classic, groundbreaking book on robust statistics Over twenty-five years after the publication of its predecessor, Robust Statistics, Second Edition continues to provide an authoritative and systematic treatment of the topic. This new edition has been thoroughly updated and expanded to reflect the latest advances in the field while also outlining the established theory and applications for building a solid foundation in robust statistics for both the theoretical and the applied statistician. A comprehensive introduction and discussion on the formal mathematical background behind qualitative and quantitative robustness is provided, and subsequent chapters delve into basic types of scale estimates, asymptotic minimax theory, regression, robust covariance, and robust design. In addition to an extended treatment of robust regression, the Second Edition features four new chapters covering: Robust Tests Small Sample Asymptotics Breakdown Point Bayesian Robustness An expanded treatment of robust regression and pseudo-values is also featured, and concepts, rather than mathematical completeness, are stressed in every discussion. Selected numerical algorithms for computing robust estimates and convergence proofs are provided throughout the book, along with quantitative robustness information for a variety of estimates. A General Remarks section appears at the beginning of each chapter and provides readers with ample motivation for working with the presented methods and techniques. Robust Statistics, Second Edition is an ideal book for graduate-level courses on the topic. It also serves as a valuable reference for researchers and practitioners who wish to study the statistical research associated with robust statistics.

The first book of its kind, Orthodontically Driven Corticotomy describes how to apply this innovative technique to orthodontic treatment protocols. More than simply discussing orthodontic applications, the editors demonstrate how corticotomies enhance inter- and multidisciplinary treatments. Different surgical approaches are described, with indications on how to select the most appropriate one, to increase efficiency of orthodontic movement, and minimize the surgical exposure for the patient at the same time. Readers learn how to apply the technique to expand the basal bone, regenerate periodontal tissues, combine corticotomy and anchorage devices, manage partial edentulism, treat impacted teeth, and become more efficient in orthodontic treatment. Surgical steps are demonstrated with more than 650 clinical photographs and 200 illustrations.

Discover the latest developments and current practices in survey sampling Survey sampling is an important component of research in many fields, and as the importance of survey sampling continues to grow, sophisticated sampling techniques that are both economical and scientifically reliable are essential to planning statistical research and the design of experiments. Sampling Statistics presents estimation techniques and sampling concepts to facilitate the application of model-based procedures to survey samples. The book begins with an introduction to standard probability sampling concepts, which provides the foundation for studying samples selected from a finite population. The development of the theory of complex sampling methods is detailed, and subsequent chapters explore the construction of estimators, sample design, replication variance estimation, and procedures such as nonresponse adjustment and small area estimation where models play a key role. A final chapter covers analytic studies in which survey data are used for the estimation of parameters for a subject matter model. The author draws upon his extensive experience with survey samples in the book's numerous examples. Both the production of «general use» databases and the analytic study of a limited number of characteristics are discussed. Exercises at the end of each chapter allow readers to test their comprehension of the presented concepts and techniques, and the references provide further resources for study. Sampling Statistics is an ideal book for courses in survey sampling at the graduate level. It is also a valuable reference for practicing statisticians who analyze survey data or are involved in the design of sample surveys.