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Statistical Epidemiology
by Shane Pascoe Graham LawStatistics are a vital skill for epidemiologists and form an essential part of clinical medicine and public health. This textbook introduces students to statistical epidemiology methods in a carefully structured and accessible format. With clearly defined learning outcomes, the suggested chapter orders can be tailored to the needs of students at both undergraduate and graduate level from a range of academic backgrounds. The book covers study design, measuring disease, bias, error, analysis and modelling and is illustrated with figures, focus boxes, study questions and examples applicable to everyday clinical problems. Drawing on the authors' extensive teaching experience, the text provides an introduction to core statistical epidemiology that will be a valuable resource for students and lecturers in health and medical sciences and applied statistics, health staff, clinical researchers and data managers.
Statistical Evaluation of Diagnostic Performance: Topics in ROC Analysis (Chapman & Hall/CRC Biostatistics Series)
by Kelly H. Zou Aiyi Liu Andriy I. Bandos Lucila Ohno-Machado Howard E. RocketteStatistical evaluation of diagnostic performance in general and Receiver Operating Characteristic (ROC) analysis in particular are important for assessing the performance of medical tests and statistical classifiers, as well as for evaluating predictive models or algorithms. This book presents innovative approaches in ROC analysis, which are releva
Statistical Evidence: A Likelihood Paradigm (Chapman And Hall/crc Monographs On Statistics And Applied Probability Ser. #71)
by Richard RoyallInterpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.
Statistical Foundations of Data Science (Chapman & Hall/CRC Data Science Series)
by Jianqing Fan Runze Li Cun-Hui Zhang Hui ZouStatistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
Statistical Fundamentals: Using Microsoft Excel for Univariate and Bivariate Analysis
by Alfred P. RovaiThe purpose of this book is to provide a working background of descriptive and inferential statistics and step-by-step examples of how to perform various statistical procedures using Microsoft Excel's native operators and functions. Automated procedures are also described using Excel's Analysis TookPak and AnalystSoft StatPlus.
Statistical Genomics: Linkage, Mapping, and QTL Analysis
by Ben Hui LiuGenomics, the mapping of the entire genetic complement of an organism, is the new frontier in biology. This handbook on the statistical issues of genomics covers current methods and the tried-and-true classical approaches.
Statistical Geoinformatics for Human Environment Interface (Chapman & Hall/CRC Applied Environmental Statistics)
by Wayne L. Myers Ganapati P. PatilStatistical Geoinformatics for Human Environment Interface presents two paradigms for studying both space and interface with regard to human/environment: localization and multiple indicators. The first approach localizes thematic targets by treating space as a pattern of vicinities, with the pattern being a square grid and the placement of viciniti
Statistical Hypothesis Testing in Context: Reproducibility, Inference, and Science
by Michael P. Fay Erica H. BrittainFay and Brittain present statistical hypothesis testing and compatible confidence intervals, focusing on application and proper interpretation. The emphasis is on equipping applied statisticians with enough tools - and advice on choosing among them - to find reasonable methods for almost any problem and enough theory to tackle new problems by modifying existing methods. After covering the basic mathematical theory and scientific principles, tests and confidence intervals are developed for specific types of data. Essential methods for applications are covered, such as general procedures for creating tests (e.g., likelihood ratio, bootstrap, permutation, testing from models), adjustments for multiple testing, clustering, stratification, causality, censoring, missing data, group sequential tests, and non-inferiority tests. New methods developed by the authors are included throughout, such as melded confidence intervals for comparing two samples and confidence intervals associated with Wilcoxon-Mann-Whitney tests and Kaplan-Meier estimates. Examples, exercises, and the R package asht support practical use.
Statistical Hypothesis Testing with Microsoft ® Office Excel ® (Synthesis Lectures on Mathematics & Statistics)
by Robert HirschThis book provides a comprehensive treatment of the logic behind hypothesis testing. Readers will learn to understand statistical hypothesis testing and how to interpret P-values under a variety of conditions including a single hypothesis test, a collection of hypothesis tests, and tests performed on accumulating data. The author explains how a hypothesis test can be interpreted to draw conclusions, and descriptions of the logic behind frequentist (classical) and Bayesian approaches to interpret the results of a statistical hypothesis test are provided. Both approaches have their own strengths and challenges, and a special challenge presents itself when hypothesis tests are repeatedly performed on accumulating data. Possible pitfalls and methods to interpret hypothesis tests when accumulating data are also analyzed. This book will be of interest to researchers, graduate students, and anyone who has to interpret the results of statistical analyses.
Statistical Hypothesis Testing with SAS and R
by Sonja Kuhnt Dirk TaegerA comprehensive guide to statistical hypothesis testing with examples in SAS and RWhen analyzing datasets the following questions often arise:Is there a short hand procedure for a statistical test available in SAS or R?If so, how do I use it?If not, how do I program the test myself?This book answers these questions and provides an overview of the most commonstatistical test problems in a comprehensive way, making it easy to find and performan appropriate statistical test.A general summary of statistical test theory is presented, along with a basicdescription for each test, including the necessary prerequisites, assumptions, theformal test problem and the test statistic. Examples in both SAS and R are provided,along with program code to perform the test, resulting output and remarksexplaining the necessary program parameters.Key features:* Provides examples in both SAS and R for each test presented.* Looks at the most common statistical tests, displayed in a clear and easy to follow way.* Supported by a supplementary website http://www.d-taeger.de featuring exampleprogram code.Academics, practitioners and SAS and R programmers will find this book a valuableresource. Students using SAS and R will also find it an excellent choice for referenceand data analysis.
Statistical Implications of Turing's Formula
by Zhiyi ZhangFeatures a broad introduction to recent research on Turing's formula and presents modern applications in statistics, probability, information theory, and other areas of modern data science Turing's formula is, perhaps, the only known method for estimating the underlying distributional characteristics beyond the range of observed data without making any parametric or semiparametric assumptions. This book presents a clear introduction to Turing's formula and its connections to statistics. Topics with relevance to a variety of different fields of study are included such as information theory; statistics; probability; computer science inclusive of artificial intelligence and machine learning; big data; biology; ecology; and genetics. The author provides examinations of many core statistical issues within modern data science from Turing's perspective. A systematic approach to long-standing problems such as entropy and mutual information estimation, diversity index estimation, domains of attraction on general alphabets, and tail probability estimation is presented in light of the most up-to-date understanding of Turing's formula. Featuring numerous exercises and examples throughout, the author provides a summary of the known properties of Turing's formula and explains how and when it works well; discusses the approach derived from Turing's formula in order to estimate a variety of quantities, all of which mainly come from information theory, but are also important for machine learning and for ecological applications; and uses Turing's formula to estimate certain heavy-tailed distributions. In summary, this book: * Features a unified and broad presentation of Turing's formula, including its connections to statistics, probability, information theory, and other areas of modern data science * Provides a presentation on the statistical estimation of information theoretic quantities * Demonstrates the estimation problems of several statistical functions from Turing's perspective such as Simpson's indices, Shannon's entropy, general diversity indices, mutual information, and Kullback-Leibler divergence * Includes numerous exercises and examples throughout with a fundamental perspective on the key results of Turing's formula Statistical Implications of Turing's Formula is an ideal reference for researchers and practitioners who need a review of the many critical statistical issues of modern data science. This book is also an appropriate learning resource for biologists, ecologists, and geneticists who are involved with the concept of diversity and its estimation and can be used as a textbook for graduate courses in mathematics, probability, statistics, computer science, artificial intelligence, machine learning, big data, and information theory. Zhiyi Zhang, PhD, is Professor of Mathematics and Statistics at The University of North Carolina at Charlotte. He is an active consultant in both industry and government on a wide range of statistical issues, and his current research interests include Turing's formula and its statistical implications; probability and statistics on countable alphabets; nonparametric estimation of entropy and mutual information; tail probability and biodiversity indices; and applications involving extracting statistical information from low-frequency data space. He earned his PhD in Statistics from Rutgers University.
Statistical Inference
by Michael J. PanikA concise, easily accessible introduction to descriptive and inferential techniquesStatistical Inference: A Short Course offers a concise presentation of the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures.The author conducts tests on the assumption of randomness and normality, provides nonparametric methods when parametric approaches might not work. The book also explores how to determine a confidence interval for a population median while also providing coverage of ratio estimation, randomness, and causality. To ensure a thorough understanding of all key concepts, Statistical Inference provides numerous examples and solutions along with complete and precise answers to many fundamental questions, including:How do we determine that a given dataset is actually a random sample?With what level of precision and reliability can a population sample be estimated?How are probabilities determined and are they the same thing as odds?How can we predict the level of one variable from that of another?What is the strength of the relationship between two variables?The book is organized to present fundamental statistical concepts first, with later chapters exploring more advanced topics and additional statistical tests such as Distributional Hypotheses, Multinomial Chi-Square Statistics, and the Chi-Square Distribution. Each chapter includes appendices and exercises, allowing readers to test their comprehension of the presented material.Statistical Inference: A Short Course is an excellent book for courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.
Statistical Inference (Chapman & Hall/CRC Texts in Statistical Science)
by George Casella Roger BergerThis 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. Features The classic graduate-level textbook on statistical inference Develops elements of statistical theory from first principles of probability Written in a lucid style accessible to anyone with some background in calculus Covers all key topics of a standard course in inference Hundreds of examples throughout to aid understanding Each chapter includes an extensive set of graduated exercises Statistical 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.
Statistical Inference (Chapman And Hall/crc Monographs On Statistics And Applied Probability Ser. #7)
by S.D. SilveyStatistics is a subject with a vast field of application, involving problems which vary widely in their character and complexity.However, in tackling these, we use a relatively small core of central ideas and methods. This book attempts to concentrateattention on these ideas: they are placed in a general settingand illustrated by relatively simple examples, avoidingwherever possible the extraneous difficulties of complicatedmathematical manipulation.In order to compress the central body of ideas into a smallvolume, it is necessary to assume a fair degree of mathematicalsophistication on the part of the reader, and the book is intendedfor students of mathematics who are already accustomed tothinking in rather general terms about spaces and functions
Statistical Inference (Dover Books On Mathematics Ser.)
by Vijay K. RohatgiUnified treatment of probability and statistics examines and analyzes the relationship between the two fields, exploring inferential issues. Numerous problems, examples, and diagrams--some with solutions--plus clear-cut, highlighted summaries of results. Advanced undergraduate to graduate level. Contents: 1. Introduction. 2. Probability Model. 3. Probability Distributions. 4. Introduction to Statistical Inference. 5. More on Mathematical Expectation. 6. Some Discrete Models. 7. Some Continuous Models. 8. Functions of Random Variables and Random Vectors. 9. Large-Sample Theory. 10. General Methods of Point and Interval Estimation. 11. Testing Hypotheses. 12. Analysis of Categorical Data. 13. Analysis of Variance: k-Sample Problems. Appendix-Tables. Answers to Odd-Numbered Problems. Index. Unabridged republication of the edition published by John Wiley & Sons, New York, 1984. 144 Figures. 35 Tables. Errata list prepared by the author
Statistical Inference (Second Edition)
by George Casella Roger L. BergerThis book 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 are natural extensions and consequences of previous concepts. Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.
Statistical Inference Based on Divergence Measures (Statistics: A Series of Textbooks and Monographs)
by Leandro PardoThe idea of using functionals of Information Theory, such as entropies or divergences, in statistical inference is not new. However, in spite of the fact that divergence statistics have become a very good alternative to the classical likelihood ratio test and the Pearson-type statistic in discrete models, many statisticians remain unaware of this p
Statistical Inference Based on Kernel Distribution Function Estimators (SpringerBriefs in Statistics)
by Rizky Reza Fauzi Yoshihiko MaesonoThis book presents a study of statistical inferences based on the kernel-type estimators of distribution functions. The inferences involve matters such as quantile estimation, nonparametric tests, and mean residual life expectation, to name just some. Convergence rates for the kernel estimators of density functions are slower than ordinary parametric estimators, which have root-n consistency. If the appropriate kernel function is used, the kernel estimators of the distribution functions recover the root-n consistency, and the inferences based on kernel distribution estimators have root-n consistency. Further, the kernel-type estimator produces smooth estimation results. The estimators based on the empirical distribution function have discrete distribution, and the normal approximation cannot be improved—that is, the validity of the Edgeworth expansion cannot be proved. If the support of the population density function is bounded, there is a boundary problem, namely the estimator does not have consistency near the boundary. The book also contains a study of the mean squared errors of the estimators and the Edgeworth expansion for quantile estimators.
Statistical Inference Based on the likelihood (Monographs On Statistics And Applied Probability #Vol. 68)
by Adelchi AzzaliniThe Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods. This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood.Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data.
Statistical Inference Under Mixture Models (ICSA Book Series in Statistics)
by Jiahua ChenThis book puts its weight on theoretical issues related to finite mixture models. It shows that a good applicant, is an applicant who understands the issues behind each statistical method. This book is intended for applicants whose interests include some understanding of the procedures they are using, while they do not have to read the technical derivations.At the same time, many researchers find most theories and techniques necessary for the development of various statistical methods, without chasing after one set of research papers, after another. Even though the book emphasizes the theory, it provides accessible numerical tools for data analysis. Readers with strength in developing statistical software, may find it useful.
Statistical Inference and Probability (The SAGE Quantitative Research Kit)
by John MacInnesAn experienced author in the field of data analytics and statistics, John Macinnes has produced a straight-forward text that breaks down the complex topic of inferential statistics with accessible language and detailed examples. It covers a range of topics, including: · Probability and Sampling distributions · Inference and regression · Power, effect size and inverse probability Part of The SAGE Quantitative Research Kit, this book will give you the know-how and confidence needed to succeed on your quantitative research journey.
Statistical Inference and Probability (The SAGE Quantitative Research Kit)
by John MacInnesAn experienced author in the field of data analytics and statistics, John Macinnes has produced a straight-forward text that breaks down the complex topic of inferential statistics with accessible language and detailed examples. It covers a range of topics, including: · Probability and Sampling distributions · Inference and regression · Power, effect size and inverse probability Part of The SAGE Quantitative Research Kit, this book will give you the know-how and confidence needed to succeed on your quantitative research journey.
Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars
by Deborah G. MayoMounting failures of replication in social and biological sciences give a new urgency to critically appraising proposed reforms. This book pulls back the cover on disagreements between experts charged with restoring integrity to science. It denies two pervasive views of the role of probability in inference: to assign degrees of belief, and to control error rates in a long run. If statistical consumers are unaware of assumptions behind rival evidence reforms, they can't scrutinize the consequences that affect them (in personalized medicine, psychology, etc.). The book sets sail with a simple tool: if little has been done to rule out flaws in inferring a claim, then it has not passed a severe test. Many methods advocated by data experts do not stand up to severe scrutiny and are in tension with successful strategies for blocking or accounting for cherry picking and selective reporting. Through a series of excursions and exhibits, the philosophy and history of inductive inference come alive. Philosophical tools are put to work to solve problems about science and pseudoscience, induction and falsification.
Statistical Inference as a Bargaining Game
by Eduardo LeyA report from the International Monetary Fund.
Statistical Inference for Fractional Diffusion Processes
by B. L. RaoStochastic processes are widely used for model building in the social, physical, engineering and life sciences as well as in financial economics. In model building, statistical inference for stochastic processes is of great importance from both a theoretical and an applications point of view.This book deals with Fractional Diffusion Processes and statistical inference for such stochastic processes. The main focus of the book is to consider parametric and nonparametric inference problems for fractional diffusion processes when a complete path of the process over a finite interval is observable.Key features:Introduces self-similar processes, fractional Brownian motion and stochastic integration with respect to fractional Brownian motion.Provides a comprehensive review of statistical inference for processes driven by fractional Brownian motion for modelling long range dependence.Presents a study of parametric and nonparametric inference problems for the fractional diffusion process.Discusses the fractional Brownian sheet and infinite dimensional fractional Brownian motion.Includes recent results and developments in the area of statistical inference of fractional diffusion processes.Researchers and students working on the statistics of fractional diffusion processes and applied mathematicians and statisticians involved in stochastic process modelling will benefit from this book.