Bayesian Computation with R, Second Edition. Jim Albert. Springer. 2009

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Bayesian Computation with R
Authors
  Jim Albert
Publisher: Springer.
Pub Date: 2009
Pages: 304
ISBN 978-0-387-92297-3 e-ISBN 978-0-387-92298-0

Preface
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, and the extensive number of applications of Bayesian articles in applied
disciplines such as science and engineering.
One reason for the dramatic growth in Bayesian modeling is the availability
of computational algorithms to compute the range of integrals that are
necessary in a Bayesian posterior analysis. Due to the speed of modern computers,
it is now possible to use the Bayesian paradigm to fit very complex
models that cannot be fit by alternative frequentist methods.
To fit Bayesian models, one needs a statistical computing environment.
This environment should be such that one can:
? write short scripts to define 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 displays.
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 Comprehensive
R Archive Network (CRAN).
The purpose of this book is to illustrate Bayesian modeling by computations
using the R language. At Bowling Green State University, I have taught
an introductory Bayesian inference class to students in masters and doctoral
programs in statistics for which this book would be appropriate. This book
would serve as a useful companion to the introductory Bayesian texts by Gelman
et al. (2003), Carlin and Louis (2009), Press (2003), Gill (2008), or Lee
(2004). The book would also be valuable to the statistical practitioner who
wishes to learn more about the R language and Bayesian methodology.
Chapters 2, 3, and 4 illustrate the use of R for Bayesian inference for
standard one- and two-parameter problems. These chapters discuss the use
of different types of priors, the use of the posterior distribution to perform
different types of inferences, and the use of the predictive distribution. The
base package of R provides functions to simulate from all of the standard
probability distributions, and these functions can be used to simulate from a
variety of posterior distributions. Modern Bayesian computing is introduced
in Chapters 5 and 6. Chapter 5 discusses the summarization of the posterior
distribution using posterior modes and introduces rejection sampling and the
Monte Carlo approach for computing integrals. Chapter 6 introduces the fundamental
ideas of Markov chain Monte Carlo (MCMC) methods and the use
of MCMC output analysis to decide if the batch of simulated draws provides
a reasonable approximation to the posterior distribution of interest. The remaining
chapters illustrate the use of these computational algorithms for a
variety of Bayesian applications. Chapter 7 introduces the use of exchangeable
models in the simultaneous estimation of a set of Poisson rates. Chapter
8 describes Bayesian tests of simple hypotheses and the use of Bayes factors
in comparing models. Chapter 9 describes Bayesian regression models, and
Chapter 10 describes several applications, such as robust modeling, binary
regression with a probit link, and order-restricted inference, that are wellsuited
for the Gibbs sampling algorithm. Chapter 11 describes the use of R
to interface with WinBUGS, a popular program for implementing MCMC
algorithms.
An R package, LearnBayes, available from the CRAN site, has been written
to accompany this text. This package contains all of the Bayesian R functions
and datasets described in the book. One goal in writing LearnBayes is
to provide guidance for the student and applied statistician in writing short R
functions for implementing Bayesian calculations for their specific problems.
Also the LearnBayes package will make it easier for users to use the growing
number of R packages for fitting a variety of Bayesian models.
Changes in the Second Edition
I appreciate the many comments and suggestions that I have received from
readers of the first edition. Although this book is not intended to be a selfcontained
book on Bayesian thinking or using R, it hopefully provides a useful
entry into Bayesian methods and computation.
The second edition contains several new topics, including the use of mixtures
of conjugate priors (Section 3.5), the use of the SIR algorithm to explore
the sensitivity of Bayesian inferences with respect to changes in the prior (Section
7.9), and the use of Zellner’s g priors to choose between models in linear
regression (Section 9.3). There are more illustrations of the construction of informative
prior distributions, including the construction of a beta prior using
knowledge about percentiles (Section 2.4), the use of the conditional means
prior in logistic regression (Section 4.4), and the use of a multivariate normal
prior in probit modeling (Section 10.3). I have become more proficient in the
R language, and the R code illustrations have changed according to the new
version of the LearnBayes package. It is easier for a user to write an R function
to compute the posterior density, and the laplace function provides a
more robust method of finding the posterior mode using the optim function
in the base package. The R code examples avoid the use of loops and illustrate
some of the special functions of R, such as sapply. This edition illustrates the
use of the lattice package in producing attractive graphs. Since the book
seems useful for self-learning, the number of exercises in the book has been
increased from 58 to 72.
I would like to express my appreciation to the people who provided assistance
in preparing this book. John Kimmel, my editor, was most helpful in
encouraging me to write this book and providing valuable feedback. I thank
Patricia Williamson and Sherwin Toribio for providing useful suggestions. Bill
Jeffreys, Peter Lee, John Shonder, and the reviewers gave many constructive
comments on the first edition. I appreciate all of the students at Bowling Green
who have enrolled in my Bayesian statistics class over the years. Finally, but
certainly not least, I wish to thank my wife, Anne, and my children, Lynne,
Bethany, and Steven, for encouragement and inspiration.
Bowling Green, Ohio Jim Albert
December 2008


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Bayesian Computation with R, Second Edition. Jim Albert. Springer. 2009.pdf
Bayesian Computation with R, Second Edition. Jim Albert. Springer. 2009.pdf
Bayesian Computation with R, Second Edition. Jim Albert. Springer. 2009.pdf
Bayesian Computation with R, Second Edition. Jim Albert. Springer. 2009.pdf
Bayesian Computation with R, Second Edition. Jim Albert. Springer. 2009.pdf
Bayesian Computation with R, Second Edition. Jim Albert. Springer. 2009.pdf
Bayesian Computation with R, Second Edition. Jim Albert. Springer. 2009.pdf
Bayesian Computation with R, Second Edition. Jim Albert. Springer. 2009.pdf
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