Bayesian Computation with R

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The development and application of Bayesian inferential methods have seen significant growth, largely due to powerful simulation-based algorithms that summarize posterior distributions. Interest in the R programming language for statistical analyses has also increased, as its open-source nature, free availability, and extensive contributor packages make it a preferred choice for statisticians. This text introduces Bayesian modeling through computation using R, starting with fundamental Bayesian concepts illustrated by one and two-parameter inferential problems. It covers computational methods like Laplace's method, rejection sampling, and the SIR algorithm within a random effects model framework. The book also introduces Markov Chain Monte Carlo (MCMC) methods, applied to various Bayesian applications including normal and binary response regression, hierarchical modeling, and robust modeling. R algorithms are utilized for developing Bayesian tests and assessing models via the posterior predictive distribution, along with interfacing R with WinBUGS for MCMC. This resource is ideal for introductory courses on Bayesian methods and for practitioners seeking to enhance their knowledge of R and Bayesian techniques. The second edition features new topics like mixtures of conjugate priors and Zellner’s g priors for model selection in linear regression, along with updated R code illustrations in line with the latest LearnBayes package.