Bayesian Computation with R
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).
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Arguments assigned assume Bayes factor beta binomial Chapter command compute the posterior computes the log computes the logarithm construct Contour plot dataset defined denote describe display distribution with mean Figure function laplace gamma Gibbs sampling given graph histogram hyperparameters hypothesis independent inference inputs interval estimates iterations joint posterior distribution LearnBayes package likelihood function marginal posterior Markov chain matrix of simulated Metropolis mortality rates noninformative prior normal approximation normal distribution observed output Poisson population posterior distribution posterior mean posterior mode posterior predictive posterior probability predictive density predictive distribution prior density prior distribution proportion proposal density random sample random walk regression model rejection sampling sample mean scale parameter sigma simulated draws simulated sample simulated values Springer Science+Business Media standard deviation standard error starting value statistic summarize Suppose Table theta true uniform prior variable variance variance-covariance matrix WinBUGS