Applied Bayesian Statistics

With R and OpenBUGS Examples

Author: Mary Kathryn Cowles

Publisher: Springer Science & Business Media

ISBN: 1461456967

Category: Mathematics

Page: 232

View: 3449

This book is based on over a dozen years teaching a Bayesian Statistics course. The material presented here has been used by students of different levels and disciplines, including advanced undergraduates studying Mathematics and Statistics and students in graduate programs in Statistics, Biostatistics, Engineering, Economics, Marketing, Pharmacy, and Psychology. The goal of the book is to impart the basics of designing and carrying out Bayesian analyses, and interpreting and communicating the results. In addition, readers will learn to use the predominant software for Bayesian model-fitting, R and OpenBUGS. The practical approach this book takes will help students of all levels to build understanding of the concepts and procedures required to answer real questions by performing Bayesian analysis of real data. Topics covered include comparing and contrasting Bayesian and classical methods, specifying hierarchical models, and assessing Markov chain Monte Carlo output. Kate Cowles taught Suzuki piano for many years before going to graduate school in Biostatistics. Her research areas are Bayesian and computational statistics, with application to environmental science. She is on the faculty of Statistics at The University of Iowa.
Posted in Mathematics

The Oxford Handbook of Applied Bayesian Analysis

Author: Anthony O' Hagan,Mike West

Publisher: OUP Oxford

ISBN: 0191613894

Category: Mathematics

Page: 924

View: 2862

Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry. This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & Social Sciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.
Posted in Mathematics

Applied Bayesian Statistical Studies in Biology and Medicine

Author: M. di Bacco,G. d'Amore,F. Scalfari

Publisher: Springer Science & Business Media

ISBN: 146130217X

Category: Medical

Page: 258

View: 8086

This volume presents the results of biological and medical research with the statistical methods used to obtain them. Nowadays the fields of biology and experimental medicine rely on techniques for processing of experimental data and for the evaluation of hypotheses. It is increasingly necessary to stimulate awareness of the importance of statistical techniques (and of the possible traps that they can hide) by using real data in concrete situations drawn from research activity.
Posted in Medical

Introduction to Applied Bayesian Statistics and Estimation for Social Scientists

Author: Scott M. Lynch

Publisher: Springer Science & Business Media

ISBN: 0387712658

Category: Social Science

Page: 359

View: 8212

This book outlines Bayesian statistical analysis in great detail, from the development of a model through the process of making statistical inference. The key feature of this book is that it covers models that are most commonly used in social science research - including the linear regression model, generalized linear models, hierarchical models, and multivariate regression models - and it thoroughly develops each real-data example in painstaking detail.
Posted in Social Science

Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives

Author: Donald B. Rubin,Andrew Gelman,Xiao-Li Meng

Publisher: John Wiley & Sons

ISBN: 9780470090435

Category: Mathematics

Page: 407

View: 2516

This book brings together a collection of articles onstatistical methods relating to missing data analysis, includingmultiple imputation, propensity scores, instrumental variables, andBayesian inference. Covering new research topicsand real-world examples which do not feature in manystandard texts. The book is dedicated to Professor Don Rubin(Harvard). Don Rubin has made fundamental contributions tothe study of missing data. Key features of the book include: Comprehensive coverage of an imporant area for both researchand applications. Adopts a pragmatic approach to describing a wide range ofintermediate and advanced statistical techniques. Covers key topics such as multiple imputation, propensityscores, instrumental variables and Bayesian inference. Includes a number of applications from the social and healthsciences. Edited and authored by highly respected researchers in thearea.
Posted in Mathematics

Applied Bayesian Modelling

Author: Peter Congdon

Publisher: Wiley

ISBN: 9780471486954

Category: Mathematics

Page: 478

View: 4079

The use of Bayesian statistics has grown significantly in recent years, and will undoubtedly continue to do so. Applied Bayesian Modelling is the follow-up to the author’s best selling book, Bayesian Statistical Modelling, and focuses on the potential applications of Bayesian techniques in a wide range of important topics in the social and health sciences. The applications are illustrated through many real-life examples and software implementation in WINBUGS – a popular software package that offers a simplified and flexible approach to statistical modelling. The book gives detailed explanations for each example – explaining fully the choice of model for each particular problem. The book · Provides a broad and comprehensive account of applied Bayesian modelling. · Describes a variety of model assessment methods and the flexibility of Bayesian prior specifications. · Covers many application areas, including panel data models, structural equation and other multivariate structure models, spatial analysis, survival analysis and epidemiology. · Provides detailed worked examples in WINBUGS to illustrate the practical application of the techniques described. All WINBUGS programs are available from an ftp site. The book provides a good introduction to Bayesian modelling and data analysis for a wide range of people involved in applied statistical analysis, including researchers and students from statistics, and the health and social sciences. The wealth of examples makes this book an ideal reference for anyone involved in statistical modelling and analysis.
Posted in Mathematics

Applied Bayesian Forecasting and Time Series Analysis

Author: Andy Pole,Mike West,Jeff Harrison

Publisher: CRC Press

ISBN: 1482267438

Category: Mathematics

Page: 480

View: 7862

Practical in its approach, Applied Bayesian Forecasting and Time Series Analysis provides the theories, methods, and tools necessary for forecasting and the analysis of time series. The authors unify the concepts, model forms, and modeling requirements within the framework of the dynamic linear mode (DLM). They include a complete theoretical development of the DLM and illustrate each step with analysis of time series data. Using real data sets the authors: Explore diverse aspects of time series, including how to identify, structure, explain observed behavior, model structures and behaviors, and interpret analyses to make informed forecasts Illustrate concepts such as component decomposition, fundamental model forms including trends and cycles, and practical modeling requirements for routine change and unusual events Conduct all analyses in the BATS computer programs, furnishing online that program and the more than 50 data sets used in the text The result is a clear presentation of the Bayesian paradigm: quantified subjective judgements derived from selected models applied to time series observations. Accessible to undergraduates, this unique volume also offers complete guidelines valuable to researchers, practitioners, and advanced students in statistics, operations research, and engineering.
Posted in Mathematics

Applied Bayesian and Classical Inference

The Case of The Federalist Papers

Author: F. Mosteller,D. L. Wallace

Publisher: Springer Science & Business Media

ISBN: 1461252563

Category: Mathematics

Page: 303

View: 614

The new version has two additions. First, at the suggestion of Stephen Stigler I we have replaced the Table of Contents by what he calls an Analytic Table of Contents. Following the title of each section or subsection is a description of the content of the section. This material helps the reader in several ways, for example: by giving a synopsis of the book, by explaining where the various data tables are and what they deal with, by telling what theory is described where. We did several distinct full studies for the Federalist papers as well as many minor side studies. Some or all may offer information both to the applied and the theoretical reader. We therefore try to give in this Contents more than the few cryptic words in a section heading to ~peed readers in finding what they want. Seconq, we have prepared an extra chapter dealing with authorship work published from. about 1969 to 1983. Although a chapter cannot compre hensively Gover a field where many books now appear, it can mention most ofthe book-length works and the main thread of authorship' studies published in English. We founq biblical authorship studies so extensive and com plicated that we thought it worthwhile to indicate some papers that would bring out the controversies that are taking place. We hope we have given the flavor of developments over the 15 years mentioned. We have also corrected a few typographical errors.
Posted in Mathematics

Bayesian Statistical Modelling

Author: Peter Congdon

Publisher: John Wiley & Sons

ISBN: 0470035935

Category: Mathematics

Page: 596

View: 8087

Bayesian methods combine the evidence from the data at hand with previous quantitative knowledge to analyse practical problems in a wide range of areas. The calculations were previously complex, but it is now possible to routinely apply Bayesian methods due to advances in computing technology and the use of new sampling methods for estimating parameters. Such developments together with the availability of freeware such as WINBUGS and R have facilitated a rapid growth in the use of Bayesian methods, allowing their application in many scientific disciplines, including applied statistics, public health research, medical science, the social sciences and economics. Following the success of the first edition, this reworked and updated book provides an accessible approach to Bayesian computing and analysis, with an emphasis on the principles of prior selection, identification and the interpretation of real data sets. The second edition: Provides an integrated presentation of theory, examples, applications and computer algorithms. Discusses the role of Markov Chain Monte Carlo methods in computing and estimation. Includes a wide range of interdisciplinary applications, and a large selection of worked examples from the health and social sciences. Features a comprehensive range of methodologies and modelling techniques, and examines model fitting in practice using Bayesian principles. Provides exercises designed to help reinforce the reader’s knowledge and a supplementary website containing data sets and relevant programs. Bayesian Statistical Modelling is ideal for researchers in applied statistics, medical science, public health and the social sciences, who will benefit greatly from the examples and applications featured. The book will also appeal to graduate students of applied statistics, data analysis and Bayesian methods, and will provide a great source of reference for both researchers and students. Praise for the First Edition: “It is a remarkable achievement to have carried out such a range of analysis on such a range of data sets. I found this book comprehensive and stimulating, and was thoroughly impressed with both the depth and the range of the discussions it contains.” – ISI - Short Book Reviews “This is an excellent introductory book on Bayesian modelling techniques and data analysis” – Biometrics “The book fills an important niche in the statistical literature and should be a very valuable resource for students and professionals who are utilizing Bayesian methods.” – Journal of Mathematical Psychology
Posted in Mathematics

Applied Bayesian Hierarchical Methods

Author: Peter D. Congdon

Publisher: CRC Press

ISBN: 9781584887218

Category: Mathematics

Page: 604

View: 1525

The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables and in methods where parameters can be treated as random collections. Emphasizing computational issues, the book provides examples of the following application settings: meta-analysis, data structured in space or time, multilevel and longitudinal data, multivariate data, nonlinear regression, and survival time data. For the worked examples, the text mainly employs the WinBUGS package, allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. It also incorporates BayesX code, which is particularly useful in nonlinear regression. To demonstrate MCMC sampling from first principles, the author includes worked examples using the R package. Through illustrative data analysis and attention to statistical computing, this book focuses on the practical implementation of Bayesian hierarchical methods. It also discusses several issues that arise when applying Bayesian techniques in hierarchical and random effects models.
Posted in Mathematics

Bayesian Data Analysis, Third Edition

Author: Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin

Publisher: CRC Press

ISBN: 1439898200

Category: Mathematics

Page: 675

View: 2218

Winner of the 2016 De Groot Prize from the International Society for Bayesian Analysis Now 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 Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The 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.
Posted in Mathematics

Bayesian Process Monitoring, Control and Optimization

Author: Bianca M. Colosimo,Enrique del Castillo

Publisher: CRC Press

ISBN: 1420010700

Category: Business & Economics

Page: 352

View: 3584

Although there are many Bayesian statistical books that focus on biostatistics and economics, there are few that address the problems faced by engineers. Bayesian Process Monitoring, Control and Optimization resolves this need, showing you how to oversee, adjust, and optimize industrial processes. Bridging the gap between application and development, this reference adopts Bayesian approaches for actual industrial practices. Divided into four parts, it begins with an introduction that discusses inferential problems and presents modern methods in Bayesian computation. The next part explains statistical process control (SPC) and examines both univariate and multivariate process monitoring techniques. Subsequent chapters present Bayesian approaches that can be used for time series data analysis and process control. The contributors include material on the Kalman filter, radar detection, and discrete part manufacturing. The last part focuses on process optimization and illustrates the application of Bayesian regression to sequential optimization, the use of Bayesian techniques for the analysis of saturated designs, and the function of predictive distributions for optimization. Written by international contributors from academia and industry, Bayesian Process Monitoring, Control and Optimization provides up-to-date applications of Bayesian processes for industrial, mechanical, electrical, and quality engineers as well as applied statisticians.
Posted in Business & Economics

Die Berechnung der Zukunft

Warum die meisten Prognosen falsch sind und manche trotzdem zutreffen - Der New York Times Bestseller

Author: Nate Silver

Publisher: Heyne Verlag

ISBN: 3641112702

Category: Business & Economics

Page: 656

View: 936

Zuverlässige Vorhersagen sind doch möglich! Nate Silver ist der heimliche Gewinner der amerikanischen Präsidentschaftswahlen 2012: ein begnadeter Statistiker, als »Prognose-Popstar« und »Wundernerd« weltberühmt geworden. Er hat die Wahlergebnisse aller 50 amerikanischen Bundesstaaten absolut exakt vorausgesagt – doch damit nicht genug: Jetzt zeigt Nate Silver, wie seine Prognosen in Zukunft Terroranschläge, Umweltkatastrophen und Finanzkrisen verhindern sollen. Gelingt ihm die Abschaffung des Zufalls? Warum werden Wettervorhersagen immer besser, während die Terrorattacken vom 11.09.2001 niemand kommen sah? Warum erkennen Ökonomen eine globale Finanzkrise nicht einmal dann, wenn diese bereits begonnen hat? Das Problem ist nicht der Mangel an Informationen, sondern dass wir die verfügbaren Daten nicht richtig deuten. Zuverlässige Prognosen aber würden uns helfen, Zufälle und Ungewissheiten abzuwehren und unser Schicksal selbst zu bestimmen. Nate Silver zeigt, dass und wie das geht. Erstmals wendet er seine Wahrscheinlichkeitsrechnung nicht nur auf Wahlprognosen an, sondern auf die großen Probleme unserer Zeit: die Finanzmärkte, Ratingagenturen, Epidemien, Erdbeben, den Klimawandel, den Terrorismus. In all diesen Fällen gibt es zahlreiche Prognosen von Experten, die er überprüft – und erklärt, warum sie meist falsch sind. Gleichzeitig schildert er, wie es gelingen kann, im Rauschen der Daten die wesentlichen Informationen herauszufiltern. Ein unterhaltsamer und spannender Augenöffner!
Posted in Business & Economics

Bayesian Models for Categorical Data

Author: Peter Congdon

Publisher: John Wiley & Sons

ISBN: 0470092386

Category: Mathematics

Page: 446

View: 459

The use of Bayesian methods for the analysis of data has grown substantially in areas as diverse as applied statistics, psychology, economics and medical science. Bayesian Methods for Categorical Data sets out to demystify modern Bayesian methods, making them accessible to students and researchers alike. Emphasizing the use of statistical computing and applied data analysis, this book provides a comprehensive introduction to Bayesian methods of categorical outcomes. * Reviews recent Bayesian methodology for categorical outcomes (binary, count and multinomial data). * Considers missing data models techniques and non-standard models (ZIP and negative binomial). * Evaluates time series and spatio-temporal models for discrete data. * Features discussion of univariate and multivariate techniques. * Provides a set of downloadable worked examples with documented WinBUGS code, available from an ftp site. The author's previous 2 bestselling titles provided a comprehensive introduction to the theory and application of Bayesian models. Bayesian Models for Categorical Data continues to build upon this foundation by developing their application to categorical, or discrete data - one of the most common types of data available. The author's clear and logical approach makes the book accessible to a wide range of students and practitioners, including those dealing with categorical data in medicine, sociology, psychology and epidemiology.
Posted in Mathematics

Introduction to Bayesian Statistics

Author: William M. Bolstad,James M. Curran

Publisher: John Wiley & Sons

ISBN: 1118593227

Category: Mathematics

Page: 624

View: 9315

"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods." There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features: Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods Exercises throughout the book that have been updated to reflect new applications and the latest software applications Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics.
Posted in Mathematics

Bayesian Statistics, A Review

Author: D. V. Lindley

Publisher: SIAM

ISBN: 9780898710021

Category: Mathematics

Page: 83

View: 380

A study of those statistical ideas that use a probability distribution over parameter space. The first part describes the axiomatic basis in the concept of coherence and the implications of this for sampling theory statistics. The second part discusses the use of Bayesian ideas in many branches of statistics.
Posted in Mathematics

Markov Chain Monte Carlo

Stochastic Simulation for Bayesian Inference, Second Edition

Author: Dani Gamerman,Hedibert F. Lopes

Publisher: CRC Press

ISBN: 9781584885870

Category: Mathematics

Page: 344

View: 2347

While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition presents a concise, accessible, and comprehensive introduction to the methods of this valuable simulation technique. The second edition includes access to an internet site that provides the code, written in R and WinBUGS, used in many of the previously existing and new examples and exercises. More importantly, the self-explanatory nature of the codes will enable modification of the inputs to the codes and variation on many directions will be available for further exploration. Major changes from the previous edition: · More examples with discussion of computational details in chapters on Gibbs sampling and Metropolis-Hastings algorithms · Recent developments in MCMC, including reversible jump, slice sampling, bridge sampling, path sampling, multiple-try, and delayed rejection · Discussion of computation using both R and WinBUGS · Additional exercises and selected solutions within the text, with all data sets and software available for download from the Web · Sections on spatial models and model adequacy The self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. The book will appeal to everyone working with MCMC techniques, especially research and graduate statisticians and biostatisticians, and scientists handling data and formulating models. The book has been substantially reinforced as a first reading of material on MCMC and, consequently, as a textbook for modern Bayesian computation and Bayesian inference courses.
Posted in Mathematics

Bayesian Methods in Health Economics

Author: Gianluca Baio

Publisher: CRC Press

ISBN: 1439895562

Category: Mathematics

Page: 244

View: 5826

Health economics is concerned with the study of the cost-effectiveness of health care interventions. This book provides an overview of Bayesian methods for the analysis of health economic data. After an introduction to the basic economic concepts and methods of evaluation, it presents Bayesian statistics using accessible mathematics. The next chapters describe the theory and practice of cost-effectiveness analysis from a statistical viewpoint, and Bayesian computation, notably MCMC. The final chapter presents three detailed case studies covering cost-effectiveness analyses using individual data from clinical trials, evidence synthesis and hierarchical models and Markov models. The text uses WinBUGS and JAGS with datasets and code available online.
Posted in Mathematics

Bayesian Methods

An Analysis for Statisticians and Interdisciplinary Researchers

Author: Thomas Leonard,John S. J. Hsu

Publisher: Cambridge University Press

ISBN: 9780521004145

Category: Mathematics

Page: 333

View: 908

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 practical examples, worked examples, and exercises. It will be essential reading for all statisticians, statistics students, and related interdisciplinary researchers.
Posted in Mathematics

Bayesian Economics Through Numerical Methods

A Guide to Econometrics and Decision-Making with Prior Information

Author: Jeffrey H. Dorfman

Publisher: Springer Science & Business Media

ISBN: 0387226354

Category: Business & Economics

Page: 110

View: 8804

Providing researchers in economics, finance, and statistics with an up-to-date introduction to applying Bayesian techniques to empirical studies, this book covers the full range of the new numerical techniques which have been developed over the last thirty years. Notably, these are: Monte Carlo sampling, antithetic replication, importance sampling, and Gibbs sampling. The author covers both advances in theory and modern approaches to numerical and applied problems, and includes applications drawn from a variety of different fields within economics, while also providing a quick overview of the underlying statistical ideas of Bayesian thought. The result is a book which presents a roadmap of applied economic questions that can now be addressed empirically with Bayesian methods. Consequently, many researchers will find this a readily readable survey of this growing topic.
Posted in Business & Economics