A Comparison Of The Bayesian And Frequentist Approaches To Estimation

The main theme of this monograph is “comparative statistical inference. ” While the topics covered have been carefully selected (they are, for example, restricted to pr- lems of statistical estimation), my aim is to provide ideas and examples which will assist a statistician, or a statistical practitioner, in comparing the performance one can expect from using either Bayesian or classical (aka, frequentist) solutions in - timation problems. Before investing the hours it will take to read this monograph, one might well want to know what sets it apart from other treatises on comparative inference. The two books that are closest to the present work are the well-known tomes by Barnett (1999) and Cox (2006). These books do indeed consider the c- ceptual and methodological differences between Bayesian and frequentist methods. What is largely absent from them, however, are answers to the question: “which - proach should one use in a given problem?” It is this latter issue that this monograph is intended to investigate. There are many books on Bayesian inference, including, for example, the widely used texts by Carlin and Louis (2008) and Gelman, Carlin, Stern and Rubin (2004). These books differ from the present work in that they begin with the premise that a Bayesian treatment is called for and then provide guidance on how a Bayesian an- ysis should be executed. Similarly, there are many books written from a classical perspective.

Drawing upon the recent explosion of research in the field, a diverse group of scholars surveys the latest strategies for solving ecological inference problems, the process of trying to infer individual behavior from aggregate data. The uncertainties and information lost in aggregation make ecological inference one of the most difficult areas of statistical inference, but these inferences are required in many academic fields, as well as by legislatures and the Courts in redistricting, marketing research by business, and policy analysis by governments. This wide-ranging collection of essays offers many fresh and important contributions to the study of ecological inference.

This extraordinary three-volume work, written in an engaging and rigorous style by a world authority in the field, provides an accessible, comprehensive introduction to the full spectrum of mathematical and statistical techniques underpinning contemporary methods in data-driven learning and inference. This second volume, Inference, builds on the foundational topics established in volume I to introduce students to techniques for inferring unknown variables and quantities, including Bayesian inference, Monte Carlo Markov Chain methods, maximum-likelihood estimation, hidden Markov models, Bayesian networks, and reinforcement learning. A consistent structure and pedagogy is employed throughout this volume to reinforce student understanding, with over 350 end-of-chapter problems (including solutions for instructors), 180 solved examples, almost 200 figures, datasets and downloadable Matlab code. Supported by sister volumes Foundations and Learning, and unique in its scale and depth, this textbook sequence is ideal for early-career researchers and graduate students across many courses in signal processing, machine learning, statistical analysis, data science and inference.

This volume provides alternatives for tackling existing empirical, methodological, and analytical challenges. It does so by providing a broad overview of less established, as well as emerging methods, which are of great relevance for current research on professional learning and development. As such, it offers a comprehensive collection of state-of-the-art methodologies and future directions within the workplace learning and professional development research. By describing these novel approaches and providing empirical illustrations, the book promotes innovative methodologies for investigating professional learning and development. It also supports scholars to understand upcoming empirical research and methods and encourages novice as well as established researchers to adopt new empirical strategies beyond traditional ones that have the potential to enrich a better understanding of professional learning and development.

Provides a Solid Foundation for Statistical Modeling and Inference and Demonstrates Its Breadth of Applicability Stochastic Modeling and Mathematical Statistics: A Text for Statisticians and Quantitative Scientists addresses core issues in post-calculus probability and statistics in a way that is useful for statistics and mathematics majors as well as students in the quantitative sciences. The book’s conversational tone, which provides the mathematical justification behind widely used statistical methods in a reader-friendly manner, and the book’s many examples, tutorials, exercises and problems for solution, together constitute an effective resource that students can read and learn from and instructors can count on as a worthy complement to their lectures. Using classroom-tested approaches that engage students in active learning, the text offers instructors the flexibility to control the mathematical level of their course. It contains the mathematical detail that is expected in a course for "majors" but is written in a way that emphasizes the intuitive content in statistical theory and the way theoretical results are used in practice. More than 1000 exercises and problems at varying levels of difficulty and with a broad range of topical focus give instructors many options in assigning homework and provide students with many problems on which to practice and from which to learn.

Statistics in Medicine, Fourth Edition, helps medical and biomedical investigators design and answer questions about analyzing and interpreting data and predicting the sample size required to achieve useful results. It makes medical statistics easy for the non-biostatistician by outlining common methods used in 90% of medical research. The text covers how to plan studies from conception to publication, what to do with data, and follows with step-by-step instructions for biostatistical methods from the simplest levels, to more sophisticated methods now used in medical articles. Examples from almost every medical specialty, and from dentistry, nursing, pharmacy and health care management are provided. This book does not require background knowledge of statistics or mathematics beyond high school algebra and provides abundant clinical examples and exercises to reinforce concepts. It is a valuable source for biomedical researchers, healthcare providers and anyone who conducts research or quality improvement projects. Expands and revises important topics, such as basic concepts behind descriptive statistics and testing, descriptive statistics in three dimensions, the relationship between statistical testing and confidence intervals, and more Presents an easy-to-follow format with medical examples, step-by-step methods and check-yourself exercises Explains statistics for users with little statistical and mathematical background Encompasses all research development stages, from conceiving a study, planning it in detail, carrying out the methods, putting obtained data in analyzable form, analyzing and interpreting the results, and publishing the study

Bayesian and Frequentist Regression Methods provides a modern account of both Bayesian and frequentist methods of regression analysis. Many texts cover one or the other of the approaches, but this is the most comprehensive combination of Bayesian and frequentist methods that exists in one place. The two philosophical approaches to regression methodology are featured here as complementary techniques, with theory and data analysis providing supplementary components of the discussion. In particular, methods are illustrated using a variety of data sets. The majority of the data sets are drawn from biostatistics but the techniques are generalizable to a wide range of other disciplines.

Control of Autonomous Aerial Vehicles is an edited book that provides a single-volume snapshot on the state of the art in the field of control theory applied to the design of autonomous unmanned aerial vehicles (UAVs), aka “drones”, employed in a variety of applications. The homogeneous structure allows the reader to transition seamlessly through results in guidance, navigation, and control of UAVs, according to the canonical classification of the main components of a UAV’s autopilot. Each chapter has been written to assist graduate students and practitioners in the fields of aerospace engineering and control theory. The contributing authors duly present detailed literature reviews, conveying their arguments in a systematic way with the help of diagrams, plots, and algorithms. They showcase the applicability of their results by means of flight tests and numerical simulations, the results of which are discussed in detail. Control of Autonomous Aerial Vehicles will interest readers who are researchers, practitioners or graduate students in control theory, autonomous systems or robotics, or in aerospace, mechanical or electrical engineering.