Bayesian Computation with R

Abstract

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 availabity of computational algorithms to compute the range of integrals that are necessary in a Bayesian posterior analysis. Due to the speed of modern cputers, 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 de fine 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 dplays. 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 Comphensive R Archive Network (CRAN).