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PrefaceThere 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 probabi...
