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Bayesian Computation with R

Bayesian Computation with R Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. Early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model. The construction and implementation of Markov Chain Monte Carlo (MCMC) methods is introduced. These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling. ; This book introduces Bayesian modeling by the use of computation using the R language. It presents the basic tenets of Bayesian thinking by use of familiar one- and two-parameter inferential problems, while several examples illustrate the use of R to interface with WinBUGS. ; There has been dramatic growth in the development and application of Bayesian inference in statistics. Berger (2000) documents the increase in Bayesian activity by the number of published research articles, the number of books,andtheextensivenumberofapplicationsofBayesianarticlesinapplied disciplines such as science and engineering. One reason for the dramatic growth in Bayesian modeling is the availab- ity of computational algorithms to compute the range of integrals that are necessary in a Bayesian posterior analysis. Due to the speed of modern c- puters, it is now possible to use the Bayesian paradigm to ?t very complex models that cannot be ?t by alternative frequentist methods. To ?t Bayesian models, one needs a statistical computing environment. This environment should be such that one can • write short scripts to de?ne a Bayesian model • use or write functions to summarize a posterior distribution • use functions to simulate from the posterior distribution • construct graphs to illustrate the posterior inference An environment that meets these requirements is the R system. R provides a wide range of functions for data manipulation, calculation, and graphical d- plays. Moreover, it includes a well-developed, simple programming language that users can extend by adding new functions. Many such extensions of the language in the form of packages are easily downloadable from the Comp- hensive R Archive Network (CRAN).; An Introduction to R.- to Bayesian Thinking.- Single-Parameter Models.- Multiparameter Models.- to Bayesian Computation.- Markov Chain Monte Carlo Methods.- Hierarchical Modeling.- Model Comparison.- Regression Models.- Gibbs Sampling.- Using R to Interface with WinBUGS.; From the reviews: The book is a concise presentation of a wide range of Bayesian inferential problems and the computational methods to solve them. The detailed and thorough presentation style, with complete R code for the examples, makes it a welcome companion to a theoretical text on Bayesian inference.... Smart students of statistics will want to have both R and Bayesian inference in their portfolio. Jim Albert's book is a good place to try out R while learning various computational methods for Bayesian inference. (Jouni Kerman, Teh American Statistician, February 2009, Vol. 63, No.1) "This is a compact text, with 11 chapters. Overall it is well written and contains a plethora of interesting examples … . Each chapter ends with short notes on further reading, a summary of R commands that are introduced, and a collection of excellent exercises to test understanding of the material. … this book would be a useful companion to an introductory Bayesian text in a classroom setting or as a primer on R for a Bayesian practitioner." (John Verzani, SIAM reviews, Vol. 50 (4), December, 2008) "This textbook is a compact introduction to modern computational Bayesian statistics. Without caring too much about mathematical details, the author gives an overall view of the main problems in statistics … . The examples and the applications provided are intended for a general audience of students." (Mauro Gasparini, Zentralblatt MATH, Vol. 1160, 2009) “A book about Bayesian computation is highly welcome. … The book contains many interesting examples and is especially stimulating for students who start writing their own Bayesian programs. … This book serves this demand of students perfectly. … Thus, the book can be highly recommended for all introductory Bayes courses, preferably if the students had a statistics course with an introduction to R (or Splus) before.”­­­ (Wolfgang Polasek, Statistical Papers, Vol. 52, 2011) ; There has been a dramatic growth in the development and application of Bayesian inferential methods. Some of this growth is due to the availability of powerful simulation-based algorithms to summarize posterior distributions. There has been also a growing interest in the use of the system R for statistical analyses. R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry. Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. The early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model. The construction and implementation of Markov Chain Monte Carlo (MCMC) methods is introduced. These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling. Algorithms written in R are used to develop Bayesian tests and assess Bayesian models by use of the posterior predictive distribution. The use of R to interface with WinBUGS, a popular MCMC computing language, is described with several illustrative examples. This book is a suitable companion book for an introductory course on Bayesian methods and is valuable to the statistical practitioner who wishes to learn more about the R language and Bayesian methodology. The LearnBayes package, written by the author and available from the CRAN website, contains all of the R functions described in the book. Jim Albert is Professor of Statistics at Bowling Green State University. He is Fellow of the American Statistical Association and is past editor of The American Statistician . His books include Ordinal Data Modeling (with Val Johnson), Workshop Statistics: Discovery with Data, A Bayesian Approach (with Allan Rossman), and Bayesian Computation using Minitab . ; Introduces Bayesian modeling by use of computation using the R language; Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. Early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model. The construction and implementation of Markov Chain Monte Carlo (MCMC) methods is introduced. These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling. Algorithms written in R are used to develop Bayesian tests and assess Bayesian models by use of the posterior predictive distribution. The use of R to interface with WinBUGS, a popular MCMC computing language, is described with several illustrative examples. ; US http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Bayesian Computation with R

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References (11)

Publisher
Springer New York
Copyright
Copyright © Springer Basel AG
DOI
10.1007/978-0-387-71385-4
Publisher site
See Book on Publisher Site

Abstract

Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. Early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model. The construction and implementation of Markov Chain Monte Carlo (MCMC) methods is introduced. These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling. ; This book introduces Bayesian modeling by the use of computation using the R language. It presents the basic tenets of Bayesian thinking by use of familiar one- and two-parameter inferential problems, while several examples illustrate the use of R to interface with WinBUGS. ; There has been dramatic growth in the development and application of Bayesian inference in statistics. Berger (2000) documents the increase in Bayesian activity by the number of published research articles, the number of books,andtheextensivenumberofapplicationsofBayesianarticlesinapplied disciplines such as science and engineering. One reason for the dramatic growth in Bayesian modeling is the availab- ity of computational algorithms to compute the range of integrals that are necessary in a Bayesian posterior analysis. Due to the speed of modern c- puters, it is now possible to use the Bayesian paradigm to ?t very complex models that cannot be ?t by alternative frequentist methods. To ?t Bayesian models, one needs a statistical computing environment. This environment should be such that one can • write short scripts to de?ne a Bayesian model • use or write functions to summarize a posterior distribution • use functions to simulate from the posterior distribution • construct graphs to illustrate the posterior inference An environment that meets these requirements is the R system. R provides a wide range of functions for data manipulation, calculation, and graphical d- plays. Moreover, it includes a well-developed, simple programming language that users can extend by adding new functions. Many such extensions of the language in the form of packages are easily downloadable from the Comp- hensive R Archive Network (CRAN).; An Introduction to R.- to Bayesian Thinking.- Single-Parameter Models.- Multiparameter Models.- to Bayesian Computation.- Markov Chain Monte Carlo Methods.- Hierarchical Modeling.- Model Comparison.- Regression Models.- Gibbs Sampling.- Using R to Interface with WinBUGS.; From the reviews: The book is a concise presentation of a wide range of Bayesian inferential problems and the computational methods to solve them. The detailed and thorough presentation style, with complete R code for the examples, makes it a welcome companion to a theoretical text on Bayesian inference.... Smart students of statistics will want to have both R and Bayesian inference in their portfolio. Jim Albert's book is a good place to try out R while learning various computational methods for Bayesian inference. (Jouni Kerman, Teh American Statistician, February 2009, Vol. 63, No.1) "This is a compact text, with 11 chapters. Overall it is well written and contains a plethora of interesting examples … . Each chapter ends with short notes on further reading, a summary of R commands that are introduced, and a collection of excellent exercises to test understanding of the material. … this book would be a useful companion to an introductory Bayesian text in a classroom setting or as a primer on R for a Bayesian practitioner." (John Verzani, SIAM reviews, Vol. 50 (4), December, 2008) "This textbook is a compact introduction to modern computational Bayesian statistics. Without caring too much about mathematical details, the author gives an overall view of the main problems in statistics … . The examples and the applications provided are intended for a general audience of students." (Mauro Gasparini, Zentralblatt MATH, Vol. 1160, 2009) “A book about Bayesian computation is highly welcome. … The book contains many interesting examples and is especially stimulating for students who start writing their own Bayesian programs. … This book serves this demand of students perfectly. … Thus, the book can be highly recommended for all introductory Bayes courses, preferably if the students had a statistics course with an introduction to R (or Splus) before.”­­­ (Wolfgang Polasek, Statistical Papers, Vol. 52, 2011) ; There has been a dramatic growth in the development and application of Bayesian inferential methods. Some of this growth is due to the availability of powerful simulation-based algorithms to summarize posterior distributions. There has been also a growing interest in the use of the system R for statistical analyses. R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry. Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. The early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model. The construction and implementation of Markov Chain Monte Carlo (MCMC) methods is introduced. These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling. Algorithms written in R are used to develop Bayesian tests and assess Bayesian models by use of the posterior predictive distribution. The use of R to interface with WinBUGS, a popular MCMC computing language, is described with several illustrative examples. This book is a suitable companion book for an introductory course on Bayesian methods and is valuable to the statistical practitioner who wishes to learn more about the R language and Bayesian methodology. The LearnBayes package, written by the author and available from the CRAN website, contains all of the R functions described in the book. Jim Albert is Professor of Statistics at Bowling Green State University. He is Fellow of the American Statistical Association and is past editor of The American Statistician . His books include Ordinal Data Modeling (with Val Johnson), Workshop Statistics: Discovery with Data, A Bayesian Approach (with Allan Rossman), and Bayesian Computation using Minitab . ; Introduces Bayesian modeling by use of computation using the R language; Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. Early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model. The construction and implementation of Markov Chain Monte Carlo (MCMC) methods is introduced. These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling. Algorithms written in R are used to develop Bayesian tests and assess Bayesian models by use of the posterior predictive distribution. The use of R to interface with WinBUGS, a popular MCMC computing language, is described with several illustrative examples. ; US

Published: Jul 7, 2007

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