Last updated on 2021-04-22
by Jong Hee Park
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
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, WinBUGS,
Stan, and TensorFlow.
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
- 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
- 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
- loo provides functions for efficient approximate
leave-one-out cross-validation (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 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 (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 random-walk Metropolis algorithm for a continuous random
- 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
Bayesian packages for specific models or methods
- abc package implements several ABC algorithms
for performing parameter estimation and model selection.
Cross-validation 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)
- AdMit provides functions to perform the fitting
of an adapative mixture of Student-t 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 Metropolis-Hastings
- The BaBooN package contains two variants of
Bayesian Bootstrap Predictive Mean Matching to multiply impute
- 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
- The BART package provide flexible
nonparametric modeling of covariates for continuous, binary,
categorical and time-to-event outcomes.
- BASis 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 g-prior or mixtures of g-priors corresponding to
the Zellner-Siow Cauchy Priors or the mixture of g-priors for
linear models or mixtures of g-priors in generalized linear
- 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
meta-analyses within the common random-effects model
- BayesTree implements BART (Bayesian Additive
Regression Trees) by Chipman, George, and McCulloch
- 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 two-sample designs, one-way
designs, general ANOVA designs, and linear regression.
- bayestestR provides utilities to describe posterior
distributions and Bayesian models.
It includes point-estimates such as Maximum A Posteriori (MAP),
measures of dispersion (Highest Density Interval) and
indices used for null-hypothesis 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 Nadaraya-Watson type multivariate kernel regression with
- 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
- 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 t-tests,
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. Built-in priors include the Minnesota,
the stochastic search variable selection and Normal-Gamma (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
- 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
- bmixture provides statistical tools for
Bayesian estimation for the finite mixture of distributions,
mainly mixture of Gamma, Normal and t-distributions.
- BMS is Bayesian Model Averaging library for
linear models with a wide choice of (customizable)
priors. Built-in priors include coefficient priors (fixed,
flexible and hyper-g priors), and 5 kinds of model
- Bmix is a bare-bones implementation of sampling
algorithms for a variety of Bayesian stick-breaking
(marginally DP) mixture models, including particle learning
and Gibbs sampling for static DP mixtures, particle learning
for dynamic BAR stick-breaking, and DP mixture
- bnlearn is a package for Bayesian network
structure learning (via constraint-based, score-based and
hybrid algorithms), parameter learning (via ML and Bayesian
estimators) and inference.
- BNSP is a package for Bayeisan non- and
semi-parametric model fitting. It handles Dirichlet process
mixtures and spike-slab 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
multi-gene 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,
- 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
- bspec performs Bayesian inference on the
(discrete) power spectrum of time series.
- bspmma is a package for Bayesian semiparametric
models for meta-analysis.
- 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.
- causact provides R functions for visualizing and running
inference on generative directed acyclic graphs (DAGs).
Once a generative DAG is created, the package automates Bayesian inference
via the greta package and TensorFlow.
- 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
- dina estimates the Deterministic Input, Noisy "And" Gate (DINA)
cognitive diagnostic model parameters using the Gibbs sampler.
edina performs a Bayesian estimation of the exploratory deterministic
input, noisy and gate (EDINA) cognitive diagnostic model.
- 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
- 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
- eigenmodel estimates the parameters of a model
for symmetric relational data (e.g., the above-diagonal part
of a square matrix), using a model-based eigenvalue
decomposition and regression using MCMC methods.
- EntropyMCMC is an R package for MCMC simulation
and convergence evaluation using entropy and Kullback-Leibler
- errum performs a Bayesian estimation of the
exploratory reduced reparameterized unified model (ErRUM).
rrum implements Gibbs sampling algorithm for
Bayesian estimation of the Reduced Reparameterized Unified Model (rrum).
- 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.
- 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
steady-state solver from rootSolve.
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
- 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
- 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 unit-level
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 two-sided
- The mcmcensemble package provides ensemble samplers for
affine-invariant Monte Carlo Markov Chain, which allow a faster convergence
for badly scaled estimation problems. Two samplers are proposed:
the 'differential.evolution' sampler and the 'stretch' sampler.
- 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 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
non-local 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 non-Gaussian state-space 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 Gamma-Poisson Shrinker (GPS) model to
find unusually large cell counts in large, sparse contingency
- pacbpred perform estimation and prediction in
high-dimensional additive models, using a sparse PAC-Bayesian
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
- 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.
- PReMiuM is a package for profile regression,
which is a Dirichlet process Bayesian clustering where the
response is linked non-parametrically to the covariate
- revdbayes provides functions for the Bayesian
analysis of extreme value models using direct random sampling
from extreme value posterior distributions.
hitro.new() function in
Runuran provides an MCMC sampler based on the
Hit-and-Run algorithm in combination with the
- 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 matrix-variate
Bingham-von Mises-Fisher 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
- 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
- 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
- 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.
- spikeSlabGAM implements Bayesian variable
selection, model choice, and regularized estimation in
(geo-)additive mixed models for Gaussian, binomial, and
- spTimer fits, spatially predict and temporally
forecast large amounts of space-time data using Bayesian
Gaussian Process Models, Bayesian Auto-Regressive (AR) Models,
and Bayesian Gaussian Predictive Processes based AR Models.
- ssgraph is for Bayesian inference in undirected
graphical models using spike-and-slab priors for multivariate
continuous, discrete, and mixed data.
- ssMousetrack estimates previously compiled
state-space modeling for mouse-tracking 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
Gelman-Rubin 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)
- 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.
vcov.gam() function the mgcv
package can extract a Bayesian posterior covariance matrix of
the parameters from a fitted
- zic provides functions for an MCMC analysis of
zero-inflated count models including stochastic search
- 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
'publication-ready' output. MCMC output may be derived from
Bayesian model output fit with JAGS, Stan, or other MCMC
- 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
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 top-level 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
- 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
- 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
- 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, zero-inflated,
hurdle, and even non-linear models all in a multilevel
context. shinybrms is a graphical user interface (GUI) for
fitting Bayesian regression models using the package brms.
- greta allows users to write statistical models in R
and fit them by MCMC and optimisation on CPUs and GPUs, using Google 'TensorFlow'.
greta lets you write your own model like in BUGS, JAGS and Stan,
except that you write models right in R, it scales well to massive datasets,
and it is easy to extend and build on.
- 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
- All of these BUGS engines use graphical models for model
specification. As such, the gR task view may be
- rstan provides R functions to parse, compile,
test, estimate, and analyze Stan models by accessing the
header-only 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
- pcFactorStan provides convenience functions
and pre-programmed 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
The Bayesian Inference Task View is written by Jong Hee Park (Seoul National University, South Korea),
Andrew D. Martin (Washington University in St. Louis, MO, USA),
and Kevin M. Quinn (UC Berkeley, Berkeley, CA, USA).
Please email the task
view maintainer with suggestions.