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.

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.

loo
provides functions for efficient approximate leaveoneout crossvalidation (LOO) for Bayesian models
using Markov chain Monte Carlo. The approximation uses Pareto smoothed importance sampling (PSIS), a new procedure
for regularizing importance weights. As a byproduct of the calculations,
loo
also provides standard errors for
estimated predictive errors and for the comparison of predictive errors between models.
The package also provides methods for using stacking and other model weighting techniques to average Bayesian predictive distributions.

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.

acebayes
finds optimal Bayesian experimental
design using the approximate coordinate exchange (ACE)
algorithm.

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.

BAS
is a package for Bayesian Variable
Selection and Model Averaging in linear models and
generalized linear models using stochastic or deterministic
sampling without replacement from posterior
distributions. Prior distributions on coefficients are from
Zellner's gprior or mixtures of gpriors corresponding to
the ZellnerSiow Cauchy Priors or the mixture of gpriors for
linear models or mixtures of gpriors in generalized linear
models.

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.

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.

bayestestR
provides utilities to describe posterior distributions and Bayesian models.
It includes pointestimates such as Maximum A Posteriori (MAP), measures of dispersion (Highest Density Interval) and
indices used for nullhypothesis testing (such as ROPE percentage, pd and Bayes factors).

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.

bbricks
provides a class of frequently used
Bayesian parametric and nonparametric model structures,as well
as a set of tools for common analytical tasks.

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.

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.

Bergm
performs Bayesian analysis for exponential random
graph models using advanced computational algorithms.

BEST
provides an alternative to ttests,
producing posterior estimates for group means and standard
deviations and their differences and effect sizes.

The
BGVAR
package fits Bayesian Global Vector Autoregression (BGVAR) models
with different prior setups and the possibility to introduce stochastic volatility. Builtin priors include the Minnesota,
the stochastic search variable selection and NormalGamma (NG) prior.

blavaan
fits a variety of Bayesian latent variable models,
including confirmatory factor analysis, structural equation models, and latent growth curve models.

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.

BNSP
is a package for Bayeisan non and
semiparametric model fitting. It handles Dirichlet process
mixtures and spikeslab for multivariate (and univariate)
response analysis, with nonparametric models for the means,
the variances and the correlation matrix.

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.

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

BVAR
is a package for estimating hierarchical Bayesian
vector autoregressive models.

coalescentMCMC
provides a flexible framework
for coalescent analyses in R.

conting
performs Bayesian analysis of complete
and incomplete contingency tables.

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.

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.

EntropyMCMC
is an R package for MCMC simulation
and convergence evaluation using entropy and KullbackLeibler
divergence estimation.

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.

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. See the
Spatial
view for more information.

LAWBL
is an R package latent (variable) analysis with with different Bayesian learning methods,
including the partially confirmatory factor analysis, its generalized version, and the partially confirmatory item response model.

The
lmm
package contains R functions to fit
linear mixed models using MCMC methods.

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.

mcmcse
allows estimation of multivariate
effective sample size and calculation of Monte Carlo standard errors.

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..

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.

NGSSEML
gives codes for formulating and
specifying the nonGaussian statespace models in the R
language. Inferences for the parameters of the model can be
made under the classical and Bayesian.

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.

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
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.

ssMousetrack
estimates previously compiled
statespace modeling for mousetracking experiment using the
rstan
package, which provides the R interface to
the Stan C++ library for Bayesian estimation.

stableGR
allows for stable estimation of the
GelmanRubin statistic with improved cutoffs and provides
estimates of how many more MCMC samples are needed.

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

BayesPostEst
allows to generate and plot
postestimation quantities after estimating Bayesian regression
models. Functionality includes predicted probabilities and first
differences as well as model checks. The functions can be used
with MCMC output generated by any Bayesian estimation tool
including JAGS, BUGS,
MCMCpack, and Stan.

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.

plotMCMC
extends
coda
by adding
convenience functions to make it easier to create multipanel
plots. The graphical parameters have sensible defaults and are
easy to modify via toplevel arguments.

ramps
implements Bayesian geostatistical
analysis of Gaussian processes using a reparameterized and
marginalized posterior sampling algorithm.
Packages for learning Bayesian statistics

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.

pcFactorStan
provides convenience functions
and preprogrammed Stan models related to the paired
comparison factor model. Its purpose is to make fitting paired
comparison data using Stan easy.

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.