Introduction to Bayesian Statistics

This book describes the Bayesian approach to statistics at a level suitable for final year undergraduate and Masters students. It is unusual in presenting Bayesian statistics with a practical flavor and an emphasis on mainstream statistics, showing how to infer scientific, medical, and social conclusions from numerical data. The authors draw on many years of experience with practical and research programs and describe many statistical methods, not readily available elsewhere. A first chapter on Fisherian methods, together with a strong overall emphasis on likelihood, makes the text suitable for mainstream statistics courses whose instructors wish to follow mixed or comparative philosophies. The other chapters contain important sections relating to many areas of statistics such as the linear model, categorical data analysis, time series and forecasting, mixture models, survival analysis, Bayesian smoothing, and non-linear random effects models. The text includes a large number of practi

This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; and pooling rules and Bayesian dynamics for sets of probabilities. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists.

Wong (mathematics and statistics, York U., Canada) updates his 1991 textbook for a standard graduate course in partial differential equations for students who have completed a course in real variables

Statisticians rely heavily on making models of 'causal situations' in order to fully explain and predict events. Modelling therefore plays a vital part in all applications of statistics and is a compo

Engineers and applied geophysicists routinely encounter interpolation and estimation problems when analysing data from field observations. Introduction to Geostatistics presents practical techniques for the estimation of spatial functions from sparse data. The author's unique approach is a synthesis of classic and geostatistical methods with a focus on the most practical linear minimum-variance estimation methods, and includes suggestions on how to test and extend the applicability of such methods. The author includes many useful methods (often not covered in other geostatistics books) such as estimating variogram parameters, evaluating the need for a variable mean, parameter estimation and model testing in complex cases (e.g. anisotropy, variable mean, and multiple variables), and using information from deterministic mathematical models. Well illustrated with exercises and worked examples taken from hydrogeology, Introduction to Geostatistics assumes no background in statistics and

A comprehensive and self-contained introduction to the field, carefully balancing mathematical theory and practical applications. It starts at an elementary level, developing concepts of multivariate

Highly useful text studies the logarithmic measures of information and their application to testing statistical hypotheses. Topics include introduction and definition of measures of information, their

A comprehensive and self-contained introduction to the field, carefully balancing mathematical theory and practical applications. It starts at an elementary level, developing concepts of multivariate

The design and analysis of experiments is typically taught as part of a second level course in statistics. Many different types and levels of students will require this information in order to progres

International agreements, such as those governing arms control or the environment, virtually always require some degree of verification of information, in order that compliance can be established. To ensure that the verification process can be regarded as efficient, effective and impartial, it is important to have a mathematical model of it. One can be derived by applying methods from statistics and the theory of non-cooperative games, developed in part by John Nash, who received a Nobel prize in 1994 for his work. The methods permit the development of rational verification strategies, as well as such fundamental concepts as guaranteed probability of detection, timeliness of inspections and the deterrence of illegal activity. In this 1996 book, the required theory is introduced gradually in the context of specific real-world examples. The only prerequisites are simple calculus and statistics, so the book should be accessible to a broad range of scientists and non-scientists, in industr

This two-volume work aims to present as completely as possible the methods of statistical inference with special reference to their economic applications. The reader will find a description not only of the classical concepts and results of mathematical statistics, but also of concepts and methods recently developed for the specific needs of econometrics. The authors have sought to avoid an overly technical presentation and go to some lengths to encourage an intuitive understanding of the results by providing numerous examples throughout. The breadth of approaches and the extensive coverage of the two volumes provide for a thorough and entirely self-contained course in modern econometrics. Volume 1 provides an introduction to general concepts and methods in statistics and econometrics, and goes on to cover estimation and prediction. Volume 2 focuses on testing, confidence regions, model selection, and asymptotic theory.

This two-volume work aims to present as completely as possible the methods of statistical inference with special reference to their economic applications. The reader will find a description not only of the classical concepts and results of mathematical statistics, but also of concepts and methods recently developed for the specific needs of econometrics. The authors have sought to avoid an overly technical presentation and go to some lengths to encourage an intuitive understanding of the results by providing numerous examples throughout. The breadth of approaches and the extensive coverage of the two volumes provide for a thorough and entirely self-contained course in modern econometrics. Volume 1 provides an introduction to general concepts and methods in statistics and econometrics, and goes on to cover estimation and prediction. Volume 2 focuses on testing, confidence regions, model selection, and asymptotic theory.

This easy-to-understand introduction emphasizes the areas of probability theory and statistics that are important in environmental monitoring, data analysis, research, environmental field surveys, and

Statistics is a subject of many uses and surprisingly few effective practitioners. The traditional road to statistical knowledge is blocked, for most, by a formidable wall of mathematics. The approach

An updated and revised edition of the popular introduction to statistics for students of economics or business, suitable for a one- or two-semester course. Presents an approach that is generally avail

This is the third edition of a successful textbook, now with material added to illustrate the potential of computers for biologists. It is a lucid introduction to the principles and more elementary techniques of statistical reasoning, particularly as they are relevant to the biologist. Special attention is paid to the validity and use of statistical procedures, the interpretation of results, and the meanings of the conclusions which can then be drawn. The understanding of statistical methods is aided by full explanations of how calculations are built up. A particular feature of this edition is the inclusion, of new material to demonstrate the potential usefulness of computers in biological statistical analysis and to this end computer analyses of a selection of the examples are presented, using several different statistical languages. The examples are designed to guide and encourage the biologist to pursue the use of these languages further. The book assumes no mathematical training an

Discusses probability theory and to many methods used in problems of statistical inference. The Third Edition features material on descriptive statistics. Cramer-Rao bounds for variance of estimators,

This classic, calculus-based introduction to the theory and application of statistics provides an unusually comprehensive depth and breadth of coverage and reflects the latest in statistical thinking

本書深入淺出介紹重要的統計概念，以生動有趣的實例解說統計方法，提倡科學推理的四個支柱，從資料蒐集到統計結果的解讀，並一再強調這些在研究的重要性。書中「概念複習」單元，可讓讀者馬上練習所學到的統計概念，以增進對核心內容的理解；章末的作業採用「主動式學習作業」的方式，讓讀者在閱讀概念解說時可主動積極地練習作業，以理解與活用。本書特色• 以「科學推理的四個支柱」為架構，幫助讀者充分思考統計結果並建立研究結論。• 強調效果量與信賴區間的重要性。• 相當篇幅的「作業」，幫助讀者理解與活用所學得的統計概念和方法。• 使用開源統計軟體 JASP、jamovi 進行統計分析。適用課程︰統計學、統計學概論、社會統計學、心理與教育統計學等相關課程。適用對象︰大學與技專校院學生或實務工作者。

Providing a concise and accessible overview of the design, implementation and management of medical software, this textbook will equip students with a solid understanding of critical considerations for both standalone medical software (software as a medical device/SaMD) and software that is integrated into hardware devices. It includes: practical discussion of key regulatory documents and industry standards, and how these translate into concrete considerations for medical software design; detailed coverage of the medical software lifecycle process ; accessible introduction to quality and risk management systems in the context of medical software; succinct coverage of essential topics in data science, machine learning, statistics, cybersecurity, software engineering and healthcare bring readers up-to-speed; six cautionary real-world case studies illustrate the dangers of improper or careless software processes. Accompanied by online resources for instructors, this is the ideal introduct

Designed as a textbook for a one or two-term introduction to mathematical statistics for students training to become data scientists, Foundations of Statistics for Data Scientists: With R and Python is an in-depth presentation of the topics in statistical science with which any data scientist should be familiar, including probability distributions, descriptive and inferential statistical methods, and linear modelling. The book assumes knowledge of basic calculus, so the presentation can focus on 'why it works' as well as 'how to do it.' Compared to traditional "mathematical statistics" textbooks, however, the book has less emphasis on probability theory and more emphasis on using software to implement statistical methods and to conduct simulations to illustrate key concepts. All statistical analyses in the book use R software, with an appendix showing the same analyses with Python.The book also introduces modern topics that do not normally appear in mathematical statistics texts but ar

將所學知識內化，透過思考、練習題目精進數學能力。《學霸筆記》中學生數學練習冊設計600個練習題，就像你的個人家庭教師，點出概念，帶領你一步步分解題目，解出答案。Introducing a brand new companion title to the Big Fat Notebooks and its bestselling title, Math―The Big Fat Middle School Math Workbook. Because just like music or a sport or learning a new language, the only way to achieve math competency, let alone excellence, is through practice. Whether used as a supplement to BFN Math or on its own, this consumable, lie-flat workbook is filled with exercises and over 600 problrems to help students work through everything that’s being taught in middle school math and reinforce what they’re learning. Each chapter begins with a brief recap of a key concept―such as the number system, expressions and equations, introduction to geometry, statistics and probability―followed by an example of a problem and steps needed to solve it, and then exercises and word problems for practice, test review, and remedial help. And in the back, students won’t find a simpl

This lucid, accessible introduction to supervised machine learning presents core concepts in a focused and logical way that is easy for beginners to follow. The author assumes basic calculus, linear algebra, probability and statistics but no prior exposure to machine learning. Coverage includes widely used traditional methods such as SVMs, boosted trees, HMMs, and LDAs, plus popular deep learning methods such as convolution neural nets, attention, transformers, and GANs. Organized in a coherent presentation framework that emphasizes the big picture, the text introduces each method clearly and concisely “from scratch” based on the fundamentals. All methods and algorithms are described by a clean and consistent style, with a minimum of unnecessary detail. Numerous case studies and concrete examples demonstrate how the methods can be applied in a variety of contexts.

This lucid, accessible introduction to supervised machine learning presents core concepts in a focused and logical way that is easy for beginners to follow. The author assumes basic calculus, linear algebra, probability and statistics but no prior exposure to machine learning. Coverage includes widely used traditional methods such as SVMs, boosted trees, HMMs, and LDAs, plus popular deep learning methods such as convolution neural nets, attention, transformers, and GANs. Organized in a coherent presentation framework that emphasizes the big picture, the text introduces each method clearly and concisely “from scratch” based on the fundamentals. All methods and algorithms are described by a clean and consistent style, with a minimum of unnecessary detail. Numerous case studies and concrete examples demonstrate how the methods can be applied in a variety of contexts.

Designed for a single-semester course, this concise and approachable text covers all of the essential concepts needed to understand modern communications systems. Balancing theory with practical implementation, it presents key ideas as a chain of functions for a transmitter and receiver, covering topics such as amplification, up- and down-conversion, modulation, dispersive channel compensation, error-correcting codes, acquisition, multiple-antenna and multiple-input multiple-output antenna techniques, and higher level communications functions. Analog modulations are also presented, and all of the basic and advanced mathematics, statistics, and Fourier theory needed to understand the concepts covered is included. Supported online with PowerPoint slides, a solutions manual, and additional MATLAB-based simulation problems, it is ideal for a first course in communications for senior undergraduate and graduate students.

The Fourth Edition of Statistics: A Gentle Introduction shows students that an introductory statistics class doesn’t need to be difficult or dull. This text minimizes students’ anxieties about math by

The Third Edition of this popular and engaging text consolidates the interdisciplinary streams of cognitive science to present a unified narrative of cognitive science as a discipline in its own right. It teaches students to apply the techniques and theories of the cognitive scientist's 'toolkit' - the vast range of methods and tools that cognitive scientists use to study the mind. Thematically organized, Cognitive Science underscores the problems and solutions of cognitive science rather than more narrowly examining individually the subjects that contribute to it - psychology, neuroscience, linguistics, and so on. The generous use of examples, illustrations, and applications demonstrates how theory is applied to unlock the mysteries of the human mind. Drawing upon cutting-edge research, the text has been substantially revised, with new material on Bayesian approaches to the mind and on deep learning. An extensive on-line set of resources is available to aid instructors and students al

The Third Edition of this popular and engaging text consolidates the interdisciplinary streams of cognitive science to present a unified narrative of cognitive science as a discipline in its own right. It teaches students to apply the techniques and theories of the cognitive scientist's 'toolkit' - the vast range of methods and tools that cognitive scientists use to study the mind. Thematically organized, Cognitive Science underscores the problems and solutions of cognitive science rather than more narrowly examining individually the subjects that contribute to it - psychology, neuroscience, linguistics, and so on. The generous use of examples, illustrations, and applications demonstrates how theory is applied to unlock the mysteries of the human mind. Drawing upon cutting-edge research, the text has been substantially revised, with new material on Bayesian approaches to the mind and on deep learning. An extensive on-line set of resources is available to aid instructors and students al

Recent years have witnessed an explosion in the volume and variety of data collected in all scientific disciplines and industrial settings. Such massive data sets present a number of challenges to researchers in statistics and machine learning. This book provides a self-contained introduction to the area of high-dimensional statistics, aimed at the first-year graduate level. It includes chapters that are focused on core methodology and theory - including tail bounds, concentration inequalities, uniform laws and empirical process, and random matrices - as well as chapters devoted to in-depth exploration of particular model classes - including sparse linear models, matrix models with rank constraints, graphical models, and various types of non-parametric models. With hundreds of worked examples and exercises, this text is intended both for courses and for self-study by graduate students and researchers in statistics, machine learning, and related fields who must understand, apply, and ad

Statistics: Principles and Methods, 8th Edition provides students and business professionals with a comprehensive introduction to statistics concepts, terminology, and methods with a wide array of pra