CRAN Task View: Bayesian Inference

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 JAGS, OpenBUGS, WinBUGS, Stan, and TensorFlow.

General Purpose Model-Fitting Packages

• The arm package contains R functions for Bayesian inference using lm, glm, mer and polr objects.
• BACCO is an R bundle for Bayesian analysis of random functions. BACCO contains three sub-packages: emulator, calibrator, and approximator, that perform Bayesian emulation and calibration of computer programs.
• bayesforecast provides various functions for Bayesian time series analysis using ‘Stan’ for full Bayesian inference. A wide range of distributions and models are supported, allowing users to fit Seasonal ARIMA, ARIMAX, Dynamic Harmonic Regression, GARCH, t-student innovation GARCH models, asymmetric GARCH, Random Walks, stochastic volatility models for univariate time series.
  
• bayesm provides R functions for Bayesian inference for various models widely used in marketing and micro-econometrics. The models include linear regression models, multinomial logit, multinomial probit, multivariate probit, multivariate mixture of normals (including clustering), density estimation using finite mixtures of normals as well as Dirichlet Process priors, hierarchical linear models, hierarchical multinomial logit, hierarchical negative binomial regression models, and linear instrumental variable models.
• BayesianTools is an R package for general-purpose MCMC and SMC samplers, as well as plot and diagnostic functions for Bayesian statistics, with a particular focus on calibrating complex system models. Implemented samplers include various Metropolis MCMC variants (including adaptive and/or delayed rejection MH), the T-walk, two differential evolution MCMCs, two DREAM MCMCs, and a sequential Monte Carlo (SMC) particle filter.
• 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 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 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.

Application-Specific Packages

ANOVA

• bayesanova provides a Bayesian version of the analysis of variance based on a three-component Gaussian mixture for which a Gibbs sampler produces posterior draws.
• AovBay provides the classical analysis of variance, the nonparametric equivalent of Kruskal Wallis, and the Bayesian approach.

Bayes factor/model comparison/Bayesian model averaging

• bain computes approximated adjusted fractional Bayes factors for equality, inequality, and about equality constrained hypotheses.
• 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.
• BayesVarSel calculate Bayes factors in linear models and then to provide a formal Bayesian answer to testing and variable selection problems.
• The BMA package has functions for Bayesian model averaging for linear models, generalized linear models, and survival models. The complementary package ensembleBMA uses the BMA package to create probabilistic forecasts of ensembles using a mixture of normal distributions.
• BMS 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 priors.
• 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).
• RoBMA implements Bayesian model-averaging for meta-analytic models, including models correcting for publication bias.
• BAS is a package for Bayesian Variable Selection and Model Averaging in linear and generalized linear models using prior distributions on coefficients from Zellner’s g-prior or mixtures of g-priors.

Bayesian tree models

• dbarts fits Bayesian additive regression trees (Chipman, George, and McCulloch 2010).
• bartCause contains a variety of methods to generate typical causal inference estimates using Bayesian Additive Regression Trees (BART) as the underlying regression model (Hill 2012).
• bartcs fits Bayesian Regression Additive Trees (BART) models to select true confounders from a large set of potential confounders and to estimate average treatment effect (Kim et al. 2023).

Causal inference

• bama performs mediation analysis in the presence of high-dimensional mediators based on the potential outcome framework. Bayesian Mediation Analysis (BAMA), developed by Song et al (2019).
• bartCause contains a variety of methods to generate typical causal inference estimates using Bayesian Additive Regression Trees (BART) as the underlying regression model (Hill 2012).
• BayesCACE performs CACE (Complier Average Causal Effect analysis) on either a single study or meta-analysis of datasets with binary outcomes, using either complete or incomplete noncompliance information.
• baycn is a package for a Bayesian hybrid approach for inferring Directed Acyclic Graphs (DAGs) for continuous, discrete, and mixed data.
• BayesTree implements BART (Bayesian Additive Regression Trees) by Chipman, George, and McCulloch (2006).
• BDgraph provides statistical tools for Bayesian structure learning in undirected graphical models for multivariate continuous, discrete, and mixed data.
• blavaan fits a variety of Bayesian latent variable models, including confirmatory factor analysis, structural equation models, and latent growth curve 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 .
• CausalImpact implements a Bayesian approach to causal impact estimation in time series, as described in Brodersen et al. (2015).

Computational 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.
• abcrf performs Approximate Bayesian Computation (ABC) model choice and parameter inference via random forests.
• 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.
• bang provides functions for the Bayesian analysis of some simple commonly-used models, without using Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling.
• bayesboot provides functions for performing the Bayesian bootstrap as introduced by Rubin (1981).
• bayesian fits Bayesian models using ‘brms’/‘Stan’ with ‘parsnip’/‘tidymodels.’
• BayesLN allows to easily carry out a proper Bayesian inferential procedure by fixing a suitable distribution (the generalized inverse Gaussian) as prior for the variance.
• dclone provides low level functions for implementing maximum likelihood estimating procedures for complex models using data cloning and MCMC methods.
• EntropyMCMC is an R package for MCMC simulation and convergence evaluation using entropy and Kullback-Leibler divergence estimation.
• 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 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.
• mcmcse allows estimation of multivariate effective sample size and calculation of Monte Carlo standard errors.
• The hitro.new() function in Runuran provides an MCMC sampler based on the Hit-and-Run algorithm in combination with the Ratio-of-Uniforms method.

Discrete data

• ammiBayes offers flexible multi-environment trials analysis via MCMC method for Additive Main Effects and Multiplicative Model (AMMI) for ordinal data.
  
• BANOVA includes functions for Hierarchical Bayes ANOVA models with normal response, t response, Binomial (Bernoulli) response, Poisson response, ordered multinomial response and multinomial response variables.
• The BART package provide flexible nonparametric modeling of covariates for continuous, binary, categorical and time-to-event outcomes.
• BayesComm performs Bayesian multivariate binary (probit) regression models for analysis of ecological communities.
• bayescopulareg provides tools for Bayesian copula generalized linear models (GLMs).
• bayescount provides a set of functions to allow analysis of count data (such as faecal egg count data) using Bayesian MCMC methods.
• BayesGWQS fits Bayesian grouped weighted quantile sum (BGWQS) regressions for one or more chemical groups with binary outcomes.
• BayesLogit provides tools for sampling from the PolyaGamma distribution based on Polson, Scott, and Windle (2013).
• 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.
• 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.
• zic provides functions for an MCMC analysis of zero-inflated count models including stochastic search variable selection.

Experiment/Contingency table/meta analysis/AB testing methods

• abtest provides functions for Bayesian A/B testing including prior elicitation options based on Kass and Vaidyanathan (1992).
• acebayes finds optimal Bayesian experimental design using the approximate coordinate exchange (ACE) algorithm.
• APFr implements a multiple testing approach to the choice of a threshold gamma on the p-values using the Average Power Function (APF) and Bayes False Discovery Rate (FDR) robust estimation.
• ashr implements an Empirical Bayes approach for large-scale hypothesis testing and false discovery rate (FDR) estimation based on the methods proposed in Stephens (2016).
• bamdit provides functions for Bayesian meta-analysis of diagnostic test data which are based on a scale mixtures bivariate random-effects model.
• BASS is a package for Bayesian fitting and sensitivity analysis methods for adaptive spline surfaces.
• The bayefdr implements the Bayesian FDR control described by Newton et al. (2004).
• The bayesAB provides a suite of functions that allow the user to analyze A/B test data in a Bayesian framework.
• BayesCombo combines diverse evidence across multiple studies to test a high level scientific theory. The methods can also be used as an alternative to a standard meta-analysis.
• bayesmeta is an R package to perform meta-analyses within the common random-effects model framework.
• bspmma is a package for Bayesian semiparametric models for meta-analysis.
• CPBayes performs a Bayesian meta-analysis method for studying cross-phenotype genetic associations.
• 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 tables.

Graphics

• basicMCMCplots provides methods for examining posterior MCMC samples from a single chain using trace plots and density plots, and from multiple chains by comparing posterior medians and credible intervals from each chain.
• 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.

Hierarchical models

• baggr compares meta-analyses of data with hierarchical Bayesian models in Stan, including convenience functions for formatting data, plotting and pooling measures specific to meta-analysis.
• dirichletprocess performs nonparametric Bayesian analysis using Dirichlet processes without the need to program the inference algorithms.
• The lmm package contains R functions to fit linear mixed models using MCMC methods.
• MCMCglmm is package for fitting Generalised Linear Mixed Models using MCMC methods.
• 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.
• vglmer estimates generalized linear mixed effects models using variational Bayes; limited types of splines can also be used as predictors. It provides the ability to integrate these models in ensembles using the SuperLearner package.

High dimensional methods/machine learning methods

• abglasso implements a Bayesian adaptive graphical lasso data-augmented block Gibbs sampler.
• bartMachine allows an advanced implementation of Bayesian Additive Regression Trees with expanded features for data analysis and visualization.
• The bayesGAMpackage is designed to provide a user friendly option to fit univariate and multivariate response Generalized Additive Models (GAM) using Hamiltonian Monte Carlo (HMC) with few technical burdens.
• BCBCSF provides functions to predict the discrete response based on selected high dimensional features, such as gene expression data.

Factor analysis/item response theory models

• 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 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.

Missing data

• 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.

Mixture models

• 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 algorithm.
• BayesBinMix provides a fully Bayesian inference for estimating the number of clusters and related parameters to heterogeneous binary data.
• BayesBinMix performs fully Bayesian inference for estimating the number of clusters and related parameters to heterogeneous binary data.
• bmixture provides statistical tools for Bayesian estimation for the finite mixture of distributions, mainly mixture of Gamma, Normal and t-distributions.
• REBayes is a package for empirical Bayes estimation using Kiefer-Wolfowitz maximum likelihood estimation.

Network models/Matrix-variate distribution

• BayesianNetwork provides a ‘Shiny’ web application for creating interactive Bayesian Network models, learning the structure and parameters of Bayesian networks, and utilities for classic network analysis.
• Bergm performs Bayesian analysis for exponential random graph models using advanced computational algorithms.
• 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.
• 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 above-diagonal part of a square matrix), using a model-based eigenvalue decomposition and regression using MCMC methods.
• gRain is a package for probability propagation in graphical independence networks, also known as Bayesian networks or probabilistic expert systems.
• 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.
• 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.
• sna, an R package for social network analysis, contains functions to generate posterior samples from Butt’s Bayesian network accuracy model using Gibbs sampling.
• ssgraph is for Bayesian inference in undirected graphical models using spike-and-slab priors for multivariate continuous, discrete, and mixed data.
• SequenceSpikeSlab contains fast functions to calculate the exact Bayes posterior for the Sparse Normal Sequence Model, implementing the algorithms described in Van Erven and Szabo (2021).

Quantile regression

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

Shrinkage/Variable selection/Gaussian process

• basad provides a Bayesian variable selection approach using continuous spike and slab prior distributions.
• BayesGPfit performs Bayesian inferences on nonparametric regression via Gaussian Processes with a modified exponential square kernel using a basis expansion approach.
• BayesianGLasso implements a data-augmented block Gibbs sampler for simulating the posterior distribution of concentration matrices for specifying the topology and parameterization of a Gaussian Graphical Model (GGM).
• BLR provides R functions to fit parametric regression models using different types of shrinkage methods.
• 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.
• 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.
• 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.

Spatial models

• CARBayes implements a class of univariate and multivariate spatial generalised linear mixed models for areal unit data, with inference in a Bayesian setting using Markov chain Monte Carlo (MCMC) simulation. Also, see CARBayesdata.
• CARBayesST, which implements a class of univariate and multivariate spatio-temporal generalised linear mixed models for areal unit data, with inference in a Bayesian setting using Markov chain Monte Carlo (MCMC) simulation.
• CircSpaceTime implementation of Bayesian models for spatial and spatio-temporal interpolation of circular data using Gaussian Wrapped and Gaussian Projected distributions.
• 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.
• spBayes provides R functions that fit Gaussian spatial process models for univariate as well as multivariate point-referenced data using MCMC methods.
• 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.
• 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.

Survival models

• 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.

Time series models

• BayesARIMAX is a package for Bayesian estimation of ARIMAX model. Autoregressive Integrated Moving Average (ARIMA) model is very popular univariate time series model. Its application has been widened by the incorporation of exogenous variable(s) (X) in the model and modified as ARIMAX by Bierens (1987).
• bayesDccGarch performs Bayesian estimation of dynamic conditional correlation GARCH model for multivariate time series volatility (Fioruci et al. 2014).
• bayesdfa implements Bayesian dynamic factor analysis with ‘Stan’.
• The bayesGARCH package provides a function which perform the Bayesian estimation of the GARCH(1,1) model with Student’s t innovations.
• bayesianVARs implements efficient algorithms for the fully Bayesian estimation of vectorautoregressions (VARs) featuring stochastic volatility (SV) using various continuous shrinkage priors.
• bayeslongitudinal adjusts longitudinal regression models using Bayesian methodology for covariance structures of composite symmetry (SC), autoregressive ones of order 1 AR (1) and autoregressive moving average of order (1,1) ARMA (1,1).
• BAYSTAR provides functions for Bayesian estimation of threshold autoregressive models.
• bspec performs Bayesian inference on the (discrete) power spectrum of time series.
• bsvars offers Bayesian estimation of structural vector autoregressive models using MCMC. It considers a wide range of models, including homo- and heteroskedastic ones and those with non-normal structural shocks, all of which feature three-level equation-specific hierarchical priors. It facilitates estimating the causal dynamic effects of shocks, predictions, and other structural analyses.
• bsvarSIGNs is a package for Bayesian analysis of structural vector autoregressive models identified by sign, zero, and narrative restrictions.
• BVAR is a package for estimating hierarchical Bayesian vector autoregressive models.
• bvarsv is a package for Bayesian estimation of an influential time-varying parameter structural vector autoregression with stochastic volatility proposed by Giorgio Primiceri in his 2005 paper published in the Review of Economic Studies. It facilitates forecasting and impulse response analysis.
• DIRECT provides a Bayesian clustering method for replicated time series or replicated measurements from multiple experimental conditions.
• 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.
• factorstochvol contains samplers for estimating (sparse) latent factor stochastic volatility models with interweaving.
• mvgam fits Bayesian dynamic generalized additive models to sets of time series, using a wide range of observation families. Estimation is performed using Markov Chain Monte Carlo with Hamiltonian Monte Carlo in the software Stan.
• 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.
• Rbeast implements a Bayesian model averaging method via RJMCMC to decompose time series into abrupt changes, trend, and seasonality, useful for changepoint detection, time series decomposition, nonlinear trend analysis, and time series segmentation.
• shrinkTVP fits a heteroskedastic time series regression with time-varying parameters modeled with state-space equations. It features a flexible triple-gamma prior allowing to cut time variation in any of the parameters automatically if data does not support it.
• 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.
• 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.
• stochvol provides efficient algorithms for fully Bayesian estimation of stochastic volatility (SV) models.

Other models

• bayesammi performs Bayesian estimation of the additive main effects and multiplicative interaction (AMMI) model.
• BayesBP is a package for Bayesian estimation using Bernstein polynomial fits rate matrix.
• BayesCR proposes a parametric fit for censored linear regression models based on SMSN distributions, from a Bayesian perspective.
• bayesdistreg implements Bayesian Distribution Regression methods. This package contains functions for three estimators (non-asymptotic, semi-asymptotic and asymptotic) and related routines for Bayesian Distribution Regression in Huang and Tsyawo (2018).
• bayesDP provides functions for data augmentation using the Bayesian discount prior method for single arm and two-arm clinical trials in Haddad et al. (2017).
• BayesFM provides a collection of procedures to perform Bayesian analysis on a variety of factor models.
• BayesGOF performs four interconnected tasks: (i) characterizes the uncertainty of the elicited parametric prior; (ii) provides exploratory diagnostic for checking prior-data conflict; (iii) computes the final statistical prior density estimate; and (iv) executes macro- and micro-inference.
• Bayesiangammareg adjusts the Gamma regression models from a Bayesian perspective described by Cepeda and Urdinola (2012).
• BayesLCA performs Bayesian Latent Class Analysis using several different methods.
• BayesMallows performs Bayesian preference learning with the Mallows rank model.
• BayesMassBal (archived) is a package for Bayesian data reconciliation of separation processes.
• 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).
• coalescentMCMC provides a flexible framework for coalescent analyses in R.
• deBInfer provides R functions for Bayesian parameter inference in differential equations using MCMC methods.
• densEstBayes provides Bayesian density estimates for univariate continuous random samples are provided using the Bayesian inference engine paradigm.
• 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).
• 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.
• The gbayes() function in Hmisc derives the posterior (and optionally) the predictive distribution when both the prior and the likelihood are Gaussian, and when the statistic of interest comes from a two-sample problem.
• The 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.
• mombf performs model selection based on non-local priors, including MOM, eMOM and iMOM priors..
• prevalence provides functions for the estimation of true prevalence from apparent prevalence in a Bayesian framework. MCMC sampling is performed via JAGS/rjags.
• PReMiuM is a package for profile regression, which is a Dirichlet process Bayesian clustering where the response is linked non-parametrically 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 vcov.gam() function the mgcv package can extract a Bayesian posterior covariance matrix of the parameters from a fitted gam object.

Bayesian models for specific disciplines

• AnaCoDa is a collection of models to analyze genome scale codon data using a Bayesian framework.
• The BACCT implements the Bayesian Augmented Control (BAC, a.k.a. Bayesian historical data borrowing) method under clinical trial setting by calling ‘Just Another Gibbs Sampler’ (‘JAGS’) software.
  
• BaSkePro provides tools to perform Bayesian inference of carcass processing/transport strategy and bone attrition from archaeofaunal skeletal profiles characterized by percentages of MAU (Minimum Anatomical Units).
• bayesbio provides miscellaneous functions for bioinformatics and Bayesian statistics.
• bayesCT performs simulation and analysis of Bayesian adaptive clinical trials for binomial, Gaussian, and time-to-event data types, incorporates historical data and allows early stopping for futility or early success.
• BayesCTDesign provides a set of functions to help clinical trial researchers calculate power and sample size for two-arm Bayesian randomized clinical trials that do or do not incorporate historical control data.
• bayes4psy contains several Bayesian models for data analysis of psychological tests.
• bayesianETAS is a package for Bayesian estimation of the Epidemic Type Aftershock Sequence (ETAS) model for earthquake occurrences.
• BayesianLaterality provides functions to implement a Bayesian model for predicting hemispheric dominance from observed laterality indices (Sorensen and Westerhausen 2020).
• bayesImageS is an R package for Bayesian image analysis using the hidden Potts model.
• bayesLife makes probabilistic projections of life expectancy for all countries of the world, using a Bayesian hierarchical model.
• 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.
• 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.

Post-estimation tools

• 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 samplers.
• bayesplot provides plotting functions for posterior analysis, MCMC diagnostics, prior and posterior predictive checks, and other visualizations to support the applied Bayesian workflow.
• 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 top-level arguments.
• ramps implements Bayesian geostatistical analysis of Gaussian processes using a reparameterized and marginalized posterior sampling algorithm.

Packages for learning Bayesian statistics

• BaM provide functions and datasets for “Bayesian Methods: A Social and Behavioral Sciences Approach” by Jeff Gill (Chapman and Hall/CRC, 2002/2007/2014).
• 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, Poisson, 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 runjags.
• All of these BUGS engines use graphical models for model specification. As such, the GraphicalModels task view may be of interest.
• 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 optimization.
• rstanarm estimates previously compiled regression models using the rstan package, which provides the R interface to the Stan C++ library for Bayesian estimation.
• 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.

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 e-mail the maintainer with suggestion or by submitting an issue or pull request in the GitHub repository linked above.

CRAN packages

Related links

• Bayesian Statistics and Marketing (bayesm)
• BayesX
• BOA
• BRugs in CRANextras
• Just Another Gibbs Sampler (JAGS)
• MCMCpack
• NIMBLE
• OpenBUGS
• Stan
• TensorFlow
• The BUGS Project (WinBUGS)

Other resources

• CRAN Task View: GraphicalModels
• CRAN Task View: Spatial
• Bioconductor Package: vbmp