CRAN Task View: Bayesian Inference
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
Bayesian packages for general model fitting
package contains R functions for Bayesian inference using lm, glm,
mer and polr objects.
is an R bundle for Bayesian analysis of random functions.
contains three sub-packages: emulator, calibrator, and approximator,
that perform Bayesian emulation and calibration of computer programs.
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.
contains R functions to perform Bayesian inference for survival
regression models with flexible error and random effects distributions.
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.
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.
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.
package consists of an R function for a random-walk Metropolis algorithm for
a continuous random vector.
Bayesian packages for specific models or methods
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.
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.
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.
package contains two variants of Bayesian Bootstrap Predictive Mean Matching to
multiply impute missing data.
package implements BMA for regression models using g-priors and mixtures of g-priors.
utilizes an efficient aglorithm to sample models without replacement.
package provides a function which perform the Bayesian estimation of the
GARCH(1,1) model with Student's t innovations.
is an R package for Bayesian image analysis using the hidden Potts model.
is an R package to perform meta-analyses within the common random-effects model framework.
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.
fits a linear mixed model for ordinal categorical responses using
Bayesian inference via Monte Carlo Markov Chains. Default is Nandran and Chen algorithm
using Gaussian link function and saving just the summaries of the chains.
implements BART (Bayesian Additive Regression Trees)
by Chipman, George, and McCulloch (2006).
supports Bayesian quantile regression using the asymmetric Laplace distribution,
both continuous as well as binary dependent variables.
contains a suite of R functions for Bayesian estimation of smooth hazard rates via
Compound Poisson Process (CPP) priors.
provides functions for Bayesian estimation of threshold autoregressive models.
implements Bayesian bandwidth estimation for Nadaraya-Watson
type multivariate kernel regression with Gaussian error.
contains function to estimates taxonomic compositions from
biomarker data using a Bayesian approach.
provides functions to predict the discrete response based on selected high dimensional features,
such as gene expression data.
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.
Spike-and-Slab models are adopted in a way to be able to produce an importance measure for clustering
and discriminant variables.
implements a Bayesian analysis of changepoint problem using
Barry and Hartigan product partition model.
implements the Bayesian paradigm for fractional polynomial models
under the assumption of normally distributed error terms.
implements the Bayesian isotonic regression with Bernstein polynomials.
provides R functions to fit parametric regression models using different types of shrinkage methods.
package has functions for Bayesian model averaging for linear models,
generalized linear models, and survival models. The complementary package
package to create probabilistic forecasts of ensembles using a mixture of
is Bayesian Model Averaging library for linear models with a wide choice of (customizable) priors.
Built-in priorss include coefficient priors (fixed, flexible and hyper-g priors), and 5 kinds of model priors.
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 regression.
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.
provides functions to do spike and slab regression via the stochastic search variable selection algorithm. It handles probit, logit, poisson, and student T data.
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.
performs Bayesian inference on the (discrete) power spectrum of time series.
is a package for Bayesian semiparametric models for meta-analysis.
models the quantile process as a function of predictors.
is a package for time series regression using dynamic linear models using MCMC.
is a package for Bayesian variant selection and Bayesian model uncertainty
techniques for genetic association studies.
is a package that handles discrete Bayesian network models and provides
inference using the frequentist approach.
provides a flexible framework for coalescent analyses in R.
has a function that performs a Bayesian analaysis of
a conditionally specified logistic regression model.
provides low level functions for implementing maximum likelihood estimating procedures
for complex models using data cloning and MCMC methods.
provides R functions for Bayesian network analysis;
the current version of covers discrete and continuous variables
under Gaussian network structure.
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.
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.
fits Bayesian ecological inference models in two by two tables using MCMC methods.
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.
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.
provides tools for Bayesian analysis of extreme value models.
provides functions for log-linear models that compute
Monte Carlo estimates of conditional P-values for goodness of fit tests.
is a package to fit Bayesian quantile regression models
that assume a factor structure for at least part of the design matrix.
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.
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.
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.
is a package for Bayesian semi and nonparametric growth curve models
that additionally include multiple membership random effects.
package has functions to implement a geometric approach
to transdimensional MCMC methods and random direction multivariate
Adaptive Rejection Metropolis Sampling.
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.
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.
Bayesian analysis of geostatistical data allowing
specification of different levels of uncertainty in the model parameters.
function in the
package implements Bayesian posterior simulation and spatial prediction
for the binomial spatial model (see the
view for more information).
package contains R functions to fit linear mixed models using MCMC methods.
is an R package that implements MCMC methods to
integrate over uncertainity in pedigree configurations estimated from molecular markers and phenotypic data.
implements a structural model based on a Gibbs sampler to correct for the bias
from endogenous matching (e.g. group formation or two-sided matching).
is package for fitting Generalised Linear Mixed Models using MCMC methods.
allows MCMC sampling for
the linear mixed model and generalized linear mixed model.
Provides a modified function
can be applied to multinomial logit (MNL) data.
package fits multinomial probit models using MCMC methods.
performs model selection based on non-local priors, including MOM, eMOM and iMOM priors..
is an R package for estimation of multivariate normal and Student-t data of arbitrary
dimension where the pattern of missing data is monotone.
is an R package for estimating Bayesian Vector
Autoregression models and Bayesian structural Vector Autoregression models.
perform estimation and prediction in high-dimensional additive models,
using a sparse PAC-Bayesian point of view and a MCMC algorithm.
comprises several functions related to the Potts model definedon undirected graphs.
provides functions to predict the binary response based
on high dimensional binary features modeled with Bayesian mixture models.
provides functions for the estimation of true prevalence from apparent prevalence in a
Bayesian framework. MCMC sampling is performed via JAGS/rjags.
facilitates profile inference
(inference at the posterior mode) for a class of product
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.
package implements parallel adaptive
Metropolis-Hastings and sequential Monte Carlo samplers for sampling from multimodal target distributions.
is a package for profile regression, which is a Dirichlet process Bayesian clustering
where the response is linked non-parametrically to the covariate profile.
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.
provides an MCMC sampler
based on the Hit-and-Run algorithm in combinaton with the Ratio-of-Uniforms method.
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.
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.
fits the R x C inference model described in Greiner and Quinn (2009).
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.
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
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
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
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.
provides R functions that fit Gaussian spatial process models
for univariate as well as multivariate point-referenced data using MCMC methods.
provides functions for prediction and variable selection using spike and slab regression.
implements Bayesian variable selection, model choice, and regularized estimation in
(geo-)additive mixed models for Gaussian, binomial, and Poisson responses.
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.
provides efficient algorithms for fully Bayesian estimation of stochastic volatility (SV) models.
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.
is a package for variational Bayesian multinomial probate 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.
package can extract a
Bayesian posterior covariance matrix of the parameters from a fitted
provides functions for an MCMC analysis of zero-inflated count models including stochastic search variable selection.
implements a software validation method for Bayesian softwares.
package provides functions for diagnostics,
summarization, and visualization of MCMC sequences. It imports
draws from BUGS format, or from plain matrices.
provides the Gelman and Rubin,
Geweke, Heidelberger and Welch, and Raftery and Lewis diagnostics,
the Brooks and Gelman multivariate shrink factors.
(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.
also defines an
and related methods which are used by other packages.
It can easily import MCMC output from WinBUGS, OpenBUGS, and JAGS, or from plain
contains the Gelman and Rubin, Geweke, Heidelberger and Welch, and Raftery and Lewis diagnostics.
implements Bayesian geostatistical analysis of Gaussian processes
using a reparameterized and marginalized posterior sampling algorithm.
Packages for learning Bayesian statistics
is a GTK interface for teaching basic concepts in statistical inference,
and doing elementary bayesian statistics (inference on proportions, multinomial counts, means and variances).
package is an R package associated with Jeff Gill's book,
"Bayesian Methods: A Social and Behavioral Sciences Approach, Second Edition" (CRC Press, 2007).
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.
package contains a set of R functions and data sets for the book
Introduction to Bayesian Statistics, by Bolstad, W.M. (2007).
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
is an R package to fit Bayesian mixture models
provides functionality for exploring and visualizing estimation results
obtained with the software package
provides a C++ library for Bayesian modeling, with an emphasis on Markov chain Monte Carlo.
provides an R interface to
It works under Windows and Linux.
used to be available from CRAN, now it is
located at the
provides a Compute Unified Device Architecture (CUDA) implementation of a Bayesian multilevel model
for the analysis of brain fMRI data.
CUDA is a software platform for massively parallel high-performance computing on NVIDIA GPUs.
There are two packages that can be used to interface R with
provides a set of functions to call WinBUGS on
a Windows system and a Linux system;
supports Linux systems through
on Linux (LinBUGS).
writes BUGS model files, formats data, and creates starting values for generalized linear mixed models.
is flexible system that allows one to apply various algorithms to hierarchical models specified using the BUGS language, including MCMC, sequential Monte Carlo, and algorithms written by users. Algorithm code is automatically translated to C++, compiled, and linked back for use
There are three packages that provide R interface with
Just Another Gibbs Sampler (JAGS)
All of these BUGS engines use graphical models for model specification. As such, the
task view may be of interest.
provides R functions to parse, compile, test, estimate, and analyze Stan
models by accessing the header-only Stan library provided by the `StanHeaders' package.
project develops a probabilistic programming language that implements
full Bayesian statistical inference via MCMC and (optionally penalized) maximum likelihood estimation via optimization.
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