Applied researchers interested in Bayesian statistics are increasingly attracted to R because of the ease of which one can code algorithms to sample from posterior distributions as well as the significant number of packages contributed to the Comprehensive R Archive Network (CRAN) that provide tools for Bayesian inference. This task view catalogs these tools. In this task view, we divide those packages into four groups based on the scope and focus of the packages. We first review R packages that provide Bayesian estimation tools for a wide range of models. We then discuss packages that address specific Bayesian models or specialized methods in Bayesian statistics. This is followed by a description of packages used for post-estimation analysis. Finally, we review packages that link R to other Bayesian sampling engines such as JAGS, OpenBUGS, and WinBUGS.

Bayesian packages for general model fitting

• The arm package contains R functions for Bayesian inference using lm, glm, mer and polr objects.
• BACCO is an R bundle for Bayesian analysis of random functions. BACCO contains three sub-packages: emulator, calibrator, and approximator, that perform Bayesian emulation and calibration of computer programs.
• bayesm provides R functions for Bayesian inference for various models widely used in marketing and micro-econometrics. The models include linear regression models, multinomial logit, multinomial probit, multivariate probit, multivariate mixture of normals (including clustering), density estimation using finite mixtures of normals as well as Dirichlet Process priors, hierarchical linear models, hierarchical multinomial logit, hierarchical negative binomial regression models, and linear instrumental variable models.
• bayesSurv contains R functions to perform Bayesian inference for survival regression models with flexible error and random effects distributions.
• DPpackage contains R functions for Bayesian nonparametric and semiparametric models. DPpackage currently includes semiparametric models for density estimation, ROC curve analysis, interval censored data, binary regression models, generalized linear mixed models, and IRT type models.
• MCMCpack provides model-specific Markov chain Monte Carlo (MCMC) algorithms for wide range of models commonly used in the social and behavioral sciences. It contains R functions to fit a number of regression models (linear regression, logit, ordinal probit, probit, Poisson regression, etc.), measurement models (item response theory and factor models), changepoint models (binary and Poisson), and models for ecological inference. It also contains a generic Metropolis sampler that can be used to fit arbitrary models.
• The mcmc package consists of an R function for a random-walk Metropolis algorithm for a continuous random vector.

Bayesian packages for specific models or methods

• AdMit provides functions to perform the fitting of an adapative mixture of Student-t distributions to a tgarget density through its kernel function. The mixture approximation can be used as the importance density in importance sampling or as the candidate density in the Metropolis-Hastings algorithm.
• The bark package impelements BARK (Bayesian Additive Regression Kernels) with feature selection.
• The BAS package implements BMA for regression models using g-priors and mixtures of g-priors. BAS utilizes an efficient aglorithm to sample models without replacement.
• BayHaz contains a suite of R functions for Bayesian estimation of smooth hazard rates via Compound Poisson Process (CPP) priors.
• The bayesGARCH package provides a function which perform the Bayesian estimation of the GARCH(1,1) model with Student's t innovations.
• BAYSTAR provides functions for Bayesian estimation of threshold autoregressive models.
• BayesTree implements BART (Bayesian Additive Regression Trees) by Chipman, George, and McCulloch (2006).
• BCE contains function to estimates taxonomic compositions from biomarker data using a Bayesian approach.
• bcp implements a Bayesian analysis of changepoint problem using Barry and Hartigan product partition model.
• The BMA package has functions for Bayesian model averaging for linear models, generalized linear models, and survival models. The complementary package ensembleBMA uses the BMA package to create probabilistic forecasts of ensembles using a mixture of normal distributions.
• BMS implements Bayesian Model Averaging for univariate linear models under Zellner’s g prior. Options include fixed and flexible g priors, 5 kinds of model prior concepts, and model sampling via model enumeration or MCMC samplers. Post-processing allows for inference according to different concepts and for plotting
• BPHO is a package for Bayesian prediction of higher-order interactions using slice sampling method.
• bqtl can be used to fit quantitative trait loci (QTL) models. This package allows Bayesian estimation of multi-gene models via Laplace approximations and provides tools for interval mapping of genetic loci. The package also contains graphical tools for QTL analysis.
• bspec performs Bayesian inference on the (discrete) power spectrum of time series.
• cslogistic has a function that performs a Bayesian analaysis of a conditionally specified logistic regression model.
• dclone provides low level functions for implementing maximum likelihood estimating procedures for complex models using data cloning and MCMC methods.
• deal provides R functions for Bayesian network analysis; the current version of covers discrete and continuous variables under Gaussian network structure.
• dlm is a package for Bayesian (and likelihood) analysis of dynamic linear models. It includes the calculations of the Kalman filter and smoother, and the forward filtering backward sampling algorithm.
• EbayesThresh implements Bayesian estimation for thresholding methods. Although the original model is developed in the context of wavelets, this package is useful when researchers need to take advantage of possible sparsity in a parameter set.
• eco fits Bayesian ecological inference models in two by two tables using MCMC methods.
• evdbayes provides tools for Bayesian analysis of extreme value models.
• exactLoglinTest provides functions for log-linear models that compute Monte Carlo estimates of conditional P-values for goodness of fit tests.
• The HI package has functions to implement a geometric approach to transdimensional MCMC methods and random direction multivariate Adaptive Rejection Metropolis Sampling.
• The gbayes() function in Hmisc derives the posterior (and optionally) the predictive distribution when both the prior and the likelihood are Gaussian, and when the statistic of interest comes from a two-sample problem.
• The function krige.bayes() in the geoR package performs Bayesian analysis of geostatistical data allowing specification of different levels of uncertainty in the model parameters. The binom.krige.bayes() function in the geoRglm package implements Bayesian posterior simulation and spatial prediction for the binomial spatial model (see the Spatial view for more information).
• The lmm package contains R functions to fit linear mixed models using MCMC methods.
• MasterBayes is an R package that implements MCMC methods to integrate over uncertainity in pedigree configurations estimated from molecular markers and phenotypic data.
• MCMCglmm is package for fitting Generalised Linear Mixed Models using MCMC methods.
• The mcmcsamp() function in lme4 allows MCMC sampling for the linear mixed model and generalized linear mixed model.
• The MNP package fits multinomial probit models using MCMC methods.
• monomvn is an R package for stimation of multivariate normal and Student-t data of arbitrary dimension where the pattern of missing data is monotone.
• MSBVAR is an R package for estimating Bayesian Vector Autoregression models and Bayesian structural Vector Autoregression models.
• The pscl package provides R functions to fit item-response theory models using MCMC methods and to compute highest density regions for the Beta distribution and the inverse gamma distribution.
• The Ratings package contains functions to implement the methods to improve the presentation and interpretation of online ratings data.
• The RJaCGH package implements Bayesian analysis of CGH microarrays using hidden Markov chain models. The selection of the number of states is made via their posterior probability computed by reversible jump Markov chain Monte Carlo Methods.
• RxCEcolInf fits the R x C inference model described in Greiner and Quinn (2009).
• SampleSizeMeans contains a set of R functions for calculating sample size requirements using three different Bayesian criteria in the context of designing an experiment to estimate a normal mean or the difference between two normal means.
• SampleSizeProportions contains a set of R functions for calculating sample size requirements using three different Bayesian criteria in the context of designing an experiment to estimate the difference between two binomial proportions.
• SimpleTable provides a series of methods to conduct Bayesian inference and sensitivity analysis for causal effects from 2 x 2 and 2 x 2 x K tables.
• sna, an R package for social network analysis, contains functions to generate posterior samples from Butt's Bayesian network accuracy model using Gibbs sampling.
• spBayes provides R functions that fit Gaussian spatial process models for univariate as well as multivariate point-referenced data using MCMC methods.
• spikeslab provides functions for prediction and variable selection using spike and slab regression.
• The tgp package implements Bayesian treed Gaussian process models: a spaptial modeling and regression package providing fully Bayesian MCMC posterior inference for models ranging from the simple linear model, to nonstationary treed Gaussian process, and others in between.
• The vcov.gam() function the mgcv package can extract a Bayesian posterior covariance matrix of the parameters from a fitted gam object.
• zic provides functions for an MCMC analysis of zero-inflated count models including stochastic search variable selection.

Post-estimation tools

• BayesValidate implements a software validation method for Bayesian softwares.
• The boa package provides functions for diagnostics, summarization, and visualization of MCMC sequences. It imports draws from BUGS format, or from plain matrices. boa provides the Gelman and Rubin, Geweke, Heidelberger and Welch, and Raftery and Lewis diagnostics, the Brooks and Gelman multivariate shrink factors.
• The coda (Convergence Diagnosis and Output Analysis) package is a suite of functions that can be used to summarize, plot, and and diagnose convergence from MCMC samples. coda also defines an mcmc object and related methods which are used by other packages. It can easily import MCMC output from WinBUGS, OpenBUGS, and JAGS, or from plain matrices. coda contains the Gelman and Rubin, Geweke, Heidelberger and Welch, and Raftery and Lewis diagnostics.
• ramps implements Bayesian geostatistical analysis of Gaussian processes using a reparameterized and marginalized posterior sampling algorithm.
• scapeMCMC is a Bayesian companion package of scape which deals with age and time structured population models. It provides multipanel MCMC diagnostic plots with aestically pleasing defaults and graphical parameters that are easy to change.

Packages for learning Bayesian statistics

• The BaM package is an R package associated with Jeff Gill's book, "Bayesian Methods: A Social and Behavioral Sciences Approach, Second Edition" (CRC Press, 2007).
• BayesDA provides R functions and datasets for "Bayesian Data Analysis, Second Edition" (CRC Press, 2003) by Andrew Gelman, John B. Carlin, Hal S. Stern, and Donald B. Rubin.
• The Bolstad package contains a set of R functions and data sets for the book Introduction to Bayesian Statistics, by Bolstad, W.M. (2007).
• The LearnBayes package contains a collection of functions helpful in learning the basic tenets of Bayesian statistical inference. It contains functions for summarizing basic one and two parameter posterior distributions and predictive distributions and MCMC algorithms for summarizing posterior distributions defined by the user. It also contains functions for regression models, hierarchical models, Bayesian tests, and illustrations of Gibbs sampling.

Packages that link R to other sampling engines

• bayesmix is an R package to fit Bayesian mixture models using JAGS .
• BRugs provides an R interface on Windows machines to OpenBUGS . It works only under Windows and used to be available from CRAN, now it is located at the CRANextras repository.
• There are two packages that can be used to interface R with WinBUGS . R2WinBUGS provides a set of functions to call WinBUGS on a Windows system and a Linux system; rbugs supports Linux systems through OpenBUGS on Linux (LinBUGS).
• glmmBUGS writes BUGS model files, formats data, and creates starting values for generalized linear mixed models.
• There are three packages that provide R interface with Just Another Gibbs Sampler (JAGS) : rjags, R2jags, and runjags.
• All of these BUGS engines use graphical models for model specification. As such, the gR task view may be of interest.

The Bayesian Inference Task View is written by Jong Hee Park (University of Chicago, IL, USA), Andrew D. Martin (Washington University, St. Louis, MO, USA), and Kevin M. Quinn (UC Berkeley, Berkeley, CA, USA). Please email the task view maintainer with suggestions.