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 postestimation analysis.
Finally, we review packages that link R to other Bayesian sampling engines such as
JAGS
,
OpenBUGS
,
WinBUGS
, and
Stan
.
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 subpackages: 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 microeconometrics. 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.

LaplacesDemon
seeks to provide a complete Bayesian environment,
including numerous MCMC algorithms, Laplace Approximation with multiple optimization algorithms,
scores of examples, dozens of additional probability distributions, numerous MCMC diagnostics,
Bayes factors, posterior predictive checks, a variety of plots, elicitation,
parameter and variable importance, and numerous additional utility functions.

MCMCpack
provides modelspecific 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 (linear regression,
binary probit, ordinal probit, Poisson, panel), 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 randomwalk Metropolis algorithm for
a continuous random vector.

The
nimble
package provides a general MCMC system that allows customizable MCMC for
models written in the BUGS/JAGS model language. Users can choose samplers and write new samplers. Models and samplers are
automatically compiled via generated C++. The package also supports other
methods such as particle filtering or whatever users write in its algorithm
language.
Bayesian packages for specific models or methods

abc
package implements several ABC algorithms for performing parameter estimation and model selection.
Crossvalidation tools are also available for measuring the accuracy of ABC estimates, and to calculate the misclassification
probabilities of different models.

abn
is a package for modelling multivariate data using additive Bayesian networks.
It provides routines to help determine optimal Bayesian network models for a given data set, where these models are used to identify statistical dependencies in messy, complex data.

AdMit
provides functions to perform the fitting of an adapative mixture of Studentt distributions
to a target 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 MetropolisHastings algorithm.

The
BaBooN
package contains two variants of Bayesian Bootstrap Predictive Mean Matching to
multiply impute missing data.

bamlss
provides an infrastructure for estimating probabilistic distributional regression models
in a Bayesian framework. The distribution parameters may capture location, scale, shape, etc.
and every parameter may depend on complex additive terms similar to a generalized additive model.

The
BART
package provide flexible nonparametric modeling of covariates for continuous, binary,
categorical and timetoevent outcomes.

The
BAS
package implements BMA for regression models using gpriors and mixtures of gpriors.
BAS
utilizes an efficient algorithm to sample models without replacement.

The
bayesGARCH
package provides a function which perform the Bayesian estimation of the
GARCH(1,1) model with Student's t innovations.

bayesImageS
is an R package for Bayesian image analysis using the hidden Potts model.

bayesmeta
is an R package to perform metaanalyses within the common randomeffects model framework.

BayesSummaryStatLM
provides two functions: one function that computes summary statistics of
data and one function that carries out the MCMC posterior sampling for Bayesian linear regression models where summary statistics are used as input.

BayesTree
implements BART (Bayesian Additive Regression Trees)
by Chipman, George, and McCulloch (2006).

bayesQR
supports Bayesian quantile regression using the asymmetric Laplace distribution,
both continuous as well as binary dependent variables.

BayesFactor
provides a suite of functions for computing various Bayes factors for simple designs, including contingency tables,
one and twosample designs, oneway designs, general ANOVA designs, and linear regression.

BayesVarSel
calculate Bayes factors in linear models and then to provide a
formal Bayesian answer to testing and variable selection problems.

BayHaz
contains a suite of R functions for Bayesian estimation of smooth hazard rates via
Compound Poisson Process (CPP) priors.

BAYSTAR
provides functions for Bayesian estimation of threshold autoregressive models.

bbemkr
implements Bayesian bandwidth estimation for NadarayaWatson
type multivariate kernel regression with Gaussian error.

BCE
contains function to estimates taxonomic compositions from
biomarker data using a Bayesian approach.

BCBCSF
provides functions to predict the discrete response based on selected high dimensional features,
such as gene expression data.

bclust
builds a dendrogram with log posterior as a natural distance defined by the model.
It is also capable to computing Bayesian discrimination probabilities equivalent to the implemented Bayesian clustering.
SpikeandSlab models are adopted in a way to be able to produce an importance measure for clustering
and discriminant variables.

bcp
implements a Bayesian analysis of changepoint problem using
Barry and Hartigan product partition model.

BDgraph
provides statistical tools for Bayesian structure learning in undirected
graphical models for multivariate continuous, discrete, and mixed data.

bisoreg
implements the Bayesian isotonic regression with Bernstein polynomials.

BLR
provides R functions to fit parametric regression models using different types of shrinkage methods.

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.

bmixture
provides statistical tools for Bayesian estimation for
the finite mixture of distributions, mainly mixture of Gamma, Normal and tdistributions.

BMS
is Bayesian Model Averaging library for linear models with a wide choice of (customizable) priors.
Builtin priors include coefficient priors (fixed, flexible and hyperg priors), and 5 kinds of model priors.

Bmix
is a barebones implementation of sampling algorithms for a variety of Bayesian stickbreaking
(marginally DP) mixture models, including particle learning and Gibbs sampling for static DP mixtures,
particle learning for dynamic BAR stickbreaking, and DP mixture regression.

bnlearn
is a package for Bayesian network structure learning
(via constraintbased, scorebased and hybrid algorithms), parameter learning (via ML and Bayesian estimators) and inference.

BoomSpikeSlab
provides functions to do spike and slab regression
via the stochastic search variable selection algorithm. It handles probit, logit, poisson, and student T data.

bqtl
can be used to fit quantitative trait loci (QTL) models.
This package allows Bayesian estimation of multigene models
via Laplace approximations and provides tools for interval mapping of genetic loci.
The package also contains graphical tools for QTL analysis.

bridgesampling
provides R functions for estimating marginal likelihoods,
Bayes factors, posterior model probabilities, and normalizing constants in general,
via different versions of bridge sampling (Meng and Wong, 1996).

bsamGP
provides functions to perform Bayesian inference using a spectral analysis of Gaussian process priors.
Gaussian processes are represented with a Fourier series based on cosine basis functions.
Currently the package includes parametric linear models, partial linear additive models with/without shape restrictions,
generalized linear additive models with/without shape restrictions, and density estimation model.

bspec
performs Bayesian inference on the (discrete) power spectrum of time series.

bspmma
is a package for Bayesian semiparametric models for metaanalysis.

BSquare
models the quantile process as a function of predictors.

bsts
is a package for time series regression using dynamic linear models using MCMC.

BVS
is a package for Bayesian variant selection and Bayesian model uncertainty
techniques for genetic association studies.

catnet
is a package that handles discrete Bayesian network models and provides
inference using the frequentist approach.

coalescentMCMC
provides a flexible framework for coalescent analyses in R.

dclone
provides low level functions for implementing maximum likelihood estimating procedures
for complex models using data cloning and MCMC methods.

deBInfer
provides R functions for Bayesian parameter inference
in differential equations using MCMC methods.

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.

ebdbNet
can be used to infer the adjacency matrix of a network from time course data
using an empirical Bayes estimation procedure based on Dynamic Bayesian Networks.

eigenmodel
estimates the parameters of a model for symmetric relational data
(e.g., the abovediagonal part of a square matrix), using a modelbased
eigenvalue decomposition and regression using MCMC methods.

evdbayes
provides tools for Bayesian analysis of extreme value models.

exactLoglinTest
provides functions for loglinear models that compute
Monte Carlo estimates of conditional Pvalues for goodness of fit tests.

factorQR
is a package to fit Bayesian quantile regression models
that assume a factor structure for at least part of the design matrix.

FME
provides functions to help in fitting models to data, to perform Monte Carlo,
sensitivity and identifiability analysis. It is intended to work with models be written as a set of
differential equations that are solved either by an integration routine from deSolve,
or a steadystate solver from rootSolve.

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 twosample problem.

ggmcmc
is a tool for assessing and diagnosing convergence of Markov Chain Monte Carlo simulations,
as well as for graphically display results from full MCMC analysis.

gRain
is a package for probability propagation in graphical independence networks,
also known as Bayesian networks or probabilistic expert systems.

growcurves
is a package for Bayesian semi and nonparametric growth curve models
that additionally include multiple membership random effects.

The
HI
package has functions to implement a geometric approach
to transdimensional MCMC methods and random direction multivariate
Adaptive Rejection Metropolis Sampling.

The
hbsae
package provides functions to compute small area estimates based on a basic area or unitlevel model.
The model is fit using restricted maximum likelihood, or in a hierarchical Bayesian way.

iterLap
performs an iterative Laplace approximation to build a global approximation of the posterior (using
mixture distributions) and then uses importance sampling for simulation based inference.

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 uncertainty in pedigree configurations estimated from molecular markers and phenotypic data.

matchingMarkets
implements a structural model based on a Gibbs sampler to correct for the bias
from endogenous matching (e.g. group formation or twosided matching).

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
mlogitBMA
Provides a modified function
bic.glm()
of the
BMA
package that
can be applied to multinomial logit (MNL) data.

The
MNP
package fits multinomial probit models using MCMC methods.

mombf
performs model selection based on nonlocal priors, including MOM, eMOM and iMOM priors..

monomvn
is an R package for estimation of multivariate normal and Studentt data of arbitrary
dimension where the pattern of missing data is monotone.

NetworkChange
is an R package for change point analysis in longitudinal network data.
It implements a hidden Markovmultilinear tensor regression model. Model diagnostic tools using marginal likelihoods
and WAIC are provided.

openEBGM
calculates Empirical Bayes Geometric Mean (EBGM) and quantile scores from the posterior distribution
using the GammaPoisson Shrinker (GPS) model to find unusually large cell counts in large, sparse contingency tables.

pacbpred
perform estimation and prediction in highdimensional additive models,
using a sparse PACBayesian point of view and a MCMC algorithm.

predmixcor
provides functions to predict the binary response based
on high dimensional binary features modeled with Bayesian mixture models.

prevalence
provides functions for the estimation of true prevalence from apparent prevalence in a
Bayesian framework. MCMC sampling is performed via JAGS/rjags.

profdpm
facilitates profile inference
(inference at the posterior mode) for a class of product
partition models.

The
pscl
package provides R functions to fit
itemresponse theory models using MCMC methods
and to compute highest density regions for the Beta distribution and the inverse gamma distribution.

The
PAWL
package implements parallel adaptive
MetropolisHastings and sequential Monte Carlo samplers for sampling from multimodal target distributions.

PReMiuM
is a package for profile regression, which is a Dirichlet process Bayesian clustering
where the response is linked nonparametrically to the covariate profile.

revdbayes
provides functions for the Bayesian analysis of extreme value models using
direct random sampling from extreme value posterior distributions.

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.

The
hitro.new()
function in
Runuran
provides an MCMC sampler
based on the HitandRun algorithm in combination with the RatioofUniforms method.

RSGHB
can be used to estimate models using a hierarchical Bayesian framework and provides flexibility in allowing
the user to specify the likelihood function directly instead of assuming predetermined model structures.

rstiefel
simulates random orthonormal matrices from linear and quadratic exponential family distributions on the
Stiefel manifold using the Gibbs sampling method. The most general type of distribution covered is
the matrixvariate Binghamvon MisesFisher distribution.

RxCEcolInf
fits the R x C inference model described in Greiner and Quinn (2009).

SamplerCompare
provides a framework for running sets of MCMC samplers on sets of
distributions with a variety of tuning parameters, along with plotting
functions to visualize the results of those simulations.

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.

sbgcop
estimates parameters of a Gaussian copula, treating the univariate marginal distributions as
nuisance parameters as described in Hoff(2007). It also provides a semiparametric imputation procedure for missing
multivariate data.

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 pointreferenced data using MCMC methods.

spikeslab
provides functions for prediction and variable selection using spike and slab regression.

spikeSlabGAM
implements Bayesian variable selection, model choice, and regularized estimation in
(geo)additive mixed models for Gaussian, binomial, and Poisson responses.

spTimer
fits, spatially predict and temporally forecast large amounts of spacetime data using
Bayesian Gaussian Process Models, Bayesian AutoRegressive (AR) Models, and Bayesian Gaussian Predictive Processes
based AR Models.

ssgraph
is for Bayesian inference in undirected graphical models
using spikeandslab priors for multivariate continuous, discrete, and mixed data.

stochvol
provides efficient algorithms for fully Bayesian estimation of stochastic volatility (SV) models.

The
tgp
package implements Bayesian treed Gaussian process models:
a spatial 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.

vbmp
is a package for variational Bayesian multinomial probit regression with Gaussian process priors.
It estimates class membership posterior probability employing variational and sparse approximation to the full posterior.
This software also incorporates feature weighting by means of Automatic Relevance Determination.

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 zeroinflated count models including stochastic search variable selection.
Postestimation tools

BayesValidate
implements a software validation method for Bayesian softwares.

MCMCvis
performs key functions (visualizes, manipulates, and summarizes)
for MCMC analysis. Functions support simple and straightforward subsetting of model parameters within the calls,
and produce presentable and 'publicationready' output.
MCMC output may be derived from Bayesian model output fit with JAGS, Stan, or other MCMC samplers.

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.
Packages for learning Bayesian statistics

AtelieR
is a GTK interface for teaching basic concepts in statistical inference,
and doing elementary bayesian statistics (inference on proportions, multinomial counts, means and variances).

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
.

BayesX
provides functionality for exploring and visualizing estimation results
obtained with the software package
BayesX
.

Boom
provides a C++ library for Bayesian modeling, with an emphasis on Markov chain Monte Carlo.

BRugs
provides an R interface to
OpenBUGS
.
It works under Windows and Linux.
BRugs
used to be available from CRAN, now it is
located at the
CRANextras
repository.

brms
implements Bayesian multilevel models in R using
Stan
. A wide range of distributions and link functions are supported,
allowing users to fit linear, robust linear, binomial, Pois son, survival, response times, ordinal, quantile, zeroinflated,
hurdle, and even nonlinear models all in a multilevel context.

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.

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.

rstan
provides R functions to parse, compile, test, estimate, and analyze Stan
models by accessing the headeronly Stan library provided by the `StanHeaders' package.
The
Stan
project develops a probabilistic programming language that implements
full Bayesian statistical inference via MCMC and (optionally penalized) maximum likelihood estimation via optimization.

R2BayesX
provides an R interface to estimate structured additive regression (STAR) models with 'BayesX'.
The Bayesian Inference Task View is written by Jong Hee Park (Seoul National University, South Korea),
Andrew D. Martin (University of Michigan, Ann Arbor, MI, USA),
and Kevin M. Quinn (UC Berkeley, Berkeley, CA, USA).
Please email the
task view maintainer
with suggestions.