Bayesian Variable Selection and Model Averaging using Bayesian Adaptive Sampling

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 from Liang et al (2008) for linear models or mixtures of g-priors from Li and Clyde (2019) in generalized linear models. Other model selection criteria include AIC, BIC and Empirical Bayes estimates of g. Sampling probabilities may be updated based on the sampled models using sampling w/out replacement or an efficient MCMC algorithm which samples models using a tree structure of the model space as an efficient hash table. See Clyde, Ghosh and Littman (2010) for details on the sampling algorithms. Uniform priors over all models or beta-binomial prior distributions on model size are allowed, and for large p truncated priors on the model space may be used to enforce sampling models that are full rank. The user may force variables to always be included in addition to imposing constraints that higher order interactions are included only if their parents are included in the model. This material is based upon work supported by the National Science Foundation under Division of Mathematical Sciences grant 1106891. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.


BAS 1.5.3

Bug Fixes

Fixed errors identified on cran checks

  • initialize R2_m = 0.0 in lm_mcmcbas.c (lead to NA's with clang on debian and fedora )

  • switch to default of pivot = TRUE in bas.lm, adding tol as an argument to control tolerance in cholregpovot for improved stability across platforms with singular or nearly singular designs.

  • valgrind messages: Conditional jump or move depends on uninitialised value(s). Initialize vectors allocated via R_alloc in lm_deterministic.c and glm_deterministic.c.

BAS 1.5.2


  • Included an option pivot=TRUE in bas.lm to fit the models using a pivoted Cholesky decomposition to allow models that are rank-deficient. Enhancment #24 and Bug #21. Currently coefficients that are not-estimable are set to zero so that predict and other methods will work as before. The vector rank is added to the output (see documenation for bas.lm) and the degrees of freedom methods that assume a uniform prior for obtaining estimates (AIC and BIC) are adjusted to use rank rather than size.

  • Added option force.heredity=TRUEto force lower order terms to be included if higher order terms are present (hierarchical constraint) for method='MCMC' and method='BAS' with bas.lm and bas.glm. Updated Vignette to illustrate. enhancement #19. Checks to see if parents are included using include.always pass issue #26.

  • Added option drop.always.included to image.bas so that variables that are always included may be excluded from the image. By default all are shown enhancement #23

  • Added option drop.always.included and subset to plot.bas so that variables that are always included may be excluded from the plot showing the marginal posterior inclusion probabilities (which=4). By default all are shown enhancement #23

  • update fitted.bas to use predict so that code covers both GLM and LM cases with type='link' or type='response'

  • Updates to package for CII Best Practices certification

  • Added Code Coverage support and more extensive tests using test_that.


  • fixed issue #36 Errors in prior = "ZS-null" when R2 is not finite or out of range due to model being not full rank. Change in gexpectations function in file bayesreg.c

  • fixed issue #35 for method="MCMC+BAS" in bas.glm in glm_mcmcbas.c when no values are provided for MCMC.iterations or n.models and defaults are used. Added unit test in test-bas-glm.R

  • fixed issue #34 for bas.glm where variables in include.always had marginal inclusion probabilities that were incorrect. Added unit test in test-bas-glm.R

  • fixed issue #33 for Jeffreys prior where marginal inclusion probabilities were not renomalized after dropping intercept model

  • fixed issue #32 to allow vectorization for phi1 function in R/cch.R and added unit test to "tests/testthat/test-special-functions.R"

  • fixed issue #31 to coerce g to be a REAL for g.prior prior and IC.prior in bas.glm; added unit-test "tests/testthat/test-bas-glm.R"

  • fixed issue #30 added n as hyperparameter if NULL and coerced to be a REAL for intrinsic prior in bas.glm; added unit-test

  • fixed issue #29 added n as hyperparameter if NULL and coerced to be a REAL for prior in bas.glm; added unit-test

  • fixed issue #28 fixed length of MCMC estimates of marginal inclusion probabilities; added unit-test

  • fixed issue #27 where expected shrinkage with the JZS prior was greater than 1. Added unit test.

  • fixed output include.always to include the intercept issue #26 always so that drop.always.included = TRUE drops the intercept and any other variables that are forced in. include.always and force.heredity=TRUE can now be used together with method="BAS".

  • added warning if marginal likelihoods/posterior probabilities are NA with default model fitting method with suggestion that models be rerun with pivot = TRUE. This uses a modified Cholesky decomposition with pivoting so that if the model is rank deficient or nearly singular the dimensionality is reduced. Bug #21.

  • corrected count for first model with method='MCMC' which lead to potential model with 0 probabiliy and errors in image.

  • coerced predicted values to be a vector under BMA (was a matrix)

  • fixed size with using method=deterministic in bas.glm (was not updated)

  • fixed problem in confint with horizontal=TRUE when intervals are point mass at zero.


  • suppress warning when sampling probabilities are 1 or 0 and the number of models is decremented
    Issue #25

  • changed force.heredity.bas to renormalize the prior probabilities rather than to use a new prior probability based on heredity constraints. For future, add new priors for models based on heredity. See comment on issue #26.

  • Changed License to GPL 3.0

BAS 1.5.1 June 6, 2018


  • added S3 method variable.names to extract variable names in the highest probability model, median probability model, and best probability model for objects created by predict.


  • Fixed incorrect documentation in predict.basglm which had that type = "link" was the default for prediction issue #18

BAS 1.5.0 May 2, 2018


  • add na.action for handling NA's for predict methods issue #10

  • added include.always as new argument to bas.lm. This allows a formula to specify which terms should always be included in all models. By default the intercept is always included.

  • added a section to the vignette to illustrate weighted regression and the force.heredity.bas function to group levels of a factor so that they enter or leave the model together.


  • fixed problem if there is only one model for image function;
    github issue #11

  • fixed error in bas.lm with non-equal weights where R2 was incorrect. issue #17


  • deprecate the predict argument in predict.bas, predict.basglm and internal functions as it is not utilized

BAS 1.4.9 March 24, 2018


  • fixed bug in confint.coef.bas when parm is a character string
  • added parentheses in betafamily.c line 382 as indicated in CRAN check for R devel


  • added option to determine k for Bayes.outlier if prior probability of no outliers is provided

BAS 1.4.8 March 10, 2018


  • fixed issue with scoping in eval of data in predict.bas if dataname is defined in local env.

  • fixed issue 10 in github (predict for estimator='BPM' failed if there were NA's in the X data. Delete NA's before finding the closest model.

  • fixed bug in 'JZS' prior - merged pull request #12 from vandenman/master

  • fixed bug in bas.glm when default betaprior (CCH) is used and inputs were INTEGER instead of REAL

  • removed warning with use of 'ZS-null' for backwards compatibility

Features added

  • updated print.bas to reflect changes in print.lm

  • Added Bayes.outlier function to calculate posterior probabilities of outliers using the method from Chaloner & Brant for linear models.

BAS 1.4.7 October 22, 2017


  • Added new method for bas.lm to obtain marginal likelihoods with the Zellner-Siow Priors for "prior= 'JZS' using QUADMATH routines for numerical integration. The optional hyperparameter alpha may now be used to adjust the scaling of the ZS prior where g ~ G(1/2, alpha*n/2) as in the BayesFactor package of Morey, with a default of alpha=1 corresponding to the ZS prior used in Liang et al (2008). This also uses more stable evaluations of log(1 + x) to prevent underflow/overflow.

  • Priors ZS-full for bas.lm is planned to be deprecated.

  • replaced math functions to use portable C code from Rmath and consolidated header files

BAS 1.4.6 May 24, 2017


  • Added force.heredity.interaction function to allow higher order interactions to be included only if their "parents" or lower order interactions or main effects were included. Currently tested with two way interactions. This is implemented post-sampling; future updates will add this at the sampling stage which will reduce memory usage and sampling times by reducing the number of models under consideration.


  • Fixed unprotected ANS in C code in glm_sampleworep.c and sampleworep.c after call to PutRNGstate and possible stack imbalance in glm_mcmc.

  • Fixed problem with predict for estimator=BPM when newdata was one row

BAS 1.4.5 March 28, 2017


  • Fixed non-conformable error with predict when new data was from a dataframe with one row.

  • Fixed problem with missing weights for prediction using the median probability model with no new data.

BAS 1.4.4 March 14, 2017


  • Extract coefficent summaries, credible intervals and plots for the HPM and MPM in addition to the default BMA by adding a new estimator argument to the coef function. The new n.models argument to coef provides summaries based on the top n.models highest probability models to reduce computation time. 'n.models = 1' is equivalent to the highest probability model.

  • use of newdata that is a vector is now depricated for predict.bas; newdata must be a dataframe or missing, in which case fitted values based on the dataframe used in fitting is used

  • factor levels are handled as in lm or glm for prediction when there may be only level of a factor in the newdata


  • fixed issue for prediction when newdata has just one row

  • fixed missing id in plot.bas for which=3

BAS 1.4.3 February 18, 2017


  • Register symbols for foreign function calls
  • bin2int is now deprecated
  • fixed default MCMC.iteration in bas.lm to agree with documentation
  • updated vignette to include more examples, outlier detection, and finding the best predictive probability model
  • set a flag for MCMC sampling renormalize that selects whether the Monte Carlo frequencies are used to estimate posterior model and marginal inclusion probabilities (default renormalize = FALSE) or that marginal likelihoods time prior probabilities that are renormalized to sum to 1 are used. (the latter is the only option for the other methods); new slots for probne0.MCMC, probne0.RN, postprobs.RN and postprobs.MCMC.

Bug fixes

  • fixed problem with prior.bic, robust, and hyper.g.n where default had missing n that was not set in hyperparameters
  • fixed error in predict and plot for GLMs when family is provided as a function

BAS 1.4.2 October 12, 2016


  • added df to the object returned by bas.glm to simplify coefficients function.

Bug Fixes

  • corrected expected value of shrinkage for intrinsic, hyper-g/n and TCCH priors for glms

BAS 1.4.1 September 17, 2016

Bug Fixes

  • the modification in 1.4.0 to automatically handle NA's led to errors if the response was transformed as part of the forumula; this is fixed


  • added subset argument to bas.lm and bas.glm

BAS 1.4.0 August 25, 2016

New features

  • added na.action for bas.lm and bas.glm to omit missing data.
  • new function to plot credible intervals created by confint.pred.bas or confint.coef.bas. See the help files for an example or the vignette.
  • added option in predict.basglm.
  • Added testBF as a betaprior option for bas.glm to implement Bayes Fatcors based on the likelihood ratio statistic's distribution for GLMs.
  • DOI for this version is

BAS 1.3.0 July 15, 2016

New Features

A vignette has been added at long last! This illustrates several of the new features in BAS such as

  • new functions for computing credible intervals for fitted and predicted values confint.pred.bas()
  • new function for adding credible intervals for coefficients confint.coef.bas()
  • added posterior standard deviations for fitted values and predicted values in predict.bas()


  • deprecated use of type to specify estimator in fitted.bas and replaced with estimator so that predict() and fitted() are compatible with other S3 methods.
  • updated funtions to be of class bas to avoid NAMESPACE conficts with other libraries

BAS 1.2.2 June 29, 2016

New Features

  • added option to find "Best Predictive Model" or "BPM" for fitted.bas or predict.bas
  • added local Empirical Bayes prior and fixed g-prior for bas.glm
  • added diagnostic() function for checking convergence of bas objects created with method = "MCMC""
  • added truncated power prior as in Yang, Wainwright & Jordan (2016)

Minor Changes

  • bug fix in plot.bas that appears with Sweave
  • bug fix in coef.bma when there is just one predictor

BAS 1.2.1 April 16, 2016

  • bug fix for method="MCMC" with truncated prior distributions where MH ratio was incorrect allowing models with 0 probability to be sampled.
  • fixed error in Zellner-Siow prior (ZS-null) when n=p+1 or saturated model where log marginal likelihood should be 0

BAS 1.2.0 April 11, 2016

  • removed unsafe code where Rbestmarg (input) was being overwritten in .Call which would end up in corruption of the constant pool of the byte-code (Thanks to Tomas Kalibera for catching this!)
  • fixed issue with dimensions for use with Simple Linear Regression

BAS 1.1.0 March 31, 2016

New Features

  • added truncated Beta-Binomial prior and truncated Poisson (works only with MCMC currently)
  • improved code for finding fitted values under the Median
  • deprecated method = "AMCMC" and issue warning message

Minor Changes

  • Changed S3 method for plot and image to use class bas rather than bma to avoid name conflicts with other packages

BAS 1.09

- added weights for linear models
- switched LINPACK calls in bayesreg to LAPACK finally should be
- fixed bug in intercept calculation for glms
- fixed inclusion probabilities to be a vector in the global EB
methods for linear models

BAS 1.08

- added intrinsic prior for GLMs
- fixed problems for linear models for p > n and R2 not correct

BAS 1.07

- added phi1 function from Gordy (1998)  confluent hypergeometric
function of two variables  also known as one of the Horn
hypergeometric functions or Humbert's phi1
- added Jeffrey's prior on g
- added the general tCCH prior and special cases of the hyper-g/n.
- TODO check shrinkage functions for all	

BAS 1.06

- new improved Laplace approximation for hypergeometric1F1
- added class basglm for predict
- predict function now handles glm output
- added dataframe option for newdata in predict.bas and predict.basglm
- renamed coefficients in output to be 'mle' in bas.lm to be consistent across
lm and glm versions so that predict methods can handle both
cases.  (This may lead to errors in other external code that
expects object$ols or object$coefficients)
- fixed bug with initprobs that did not include an intercept for bas.lm

BAS 1.05

- added thinning option for MCMC method for bas.lm
- returned posterior expected shrinkage for bas.glm
- added option for initprobs = "marg-eplogp" for using marginal
SLR models to create starting probabilities or order variables
especially for p > n case
- added standalone function for hypergeometric1F1 using Cephes
library and a Laplace aproximation
-Added class "BAS" so that predict and fitted functions (S3
methods) are not masked by functions in the BVS package: to do
modify the rest of the S3 methods.

BAS 1.04

- added bas.glm for model averaging/section using mixture of g-priors for
GLMs.  Currently limited to Logistic Regression
- added Poisson family for

BAS 1.0

- cleaned up  MCMC method code

BAS 0.93

- removed internal print statements in bayesglm.c
- Bug fixes in AMCMC algorithm

BAS 0.92

- fixed glm-fit.R  so that hyperparameter for BIC is numeric

BAS 0.91

- added new AMCMC algorithm

BAS 0.91

- bug fix in bayes.glm

BAS 0.90

- added C routines for fitting glms

BAS 0.85

- fixed problem with duplicate models if n.models was > 2^(p-1) by

restricting n.models

- save original X as part of object so that fitted.bma gives the

correct fitted values (broken in version 0.80)

BAS 0.80

- Added `hypergeometric2F1` function that is callable by R
- centered X's in bas.lm so that the intercept has the correct

shrinkage - changed predict.bma to center newdata using the mean(X) - Added new Adaptive MCMC option (method = "AMCMC") (this is not stable at this point)

BAS 0.7

-Allowed pruning of model tree to eliminate rejected models

BAS 0.6

- Added MCMC option to create starting values for BAS (`method = "MCMC+BAS"`)

BAS 0.5

-Cleaned up all .Call routines so that all objects are duplicated or

allocated within code

BAS 0.45

- fixed ch2inv that prevented building on Windows in bayes glm_fit

BAS 0.4

- fixed fortran calls to use F77_NAME macro 
- changed  allocation of objects for .Call to prevent some objects from being overwritten.  

BAS 0.3

- fixed function to include prior probabilities on models
- fixed update function 

BAS 0.2

- fixed predict.bma to allow newdata to be a matrix or vector with the

column of ones for the intercept optionally included. - fixed help file for predict - added modelprior argument to bas.lm so that users may now use the beta-binomial prior distribution on model size in addition to the default uniform distribution - added functions uniform(), beta-binomial() and Bernoulli() to create model prior objects - added a vector of user specified initial probabilities as an option for argument initprobs in bas.lm and removed the separate argument user.prob

Reference manual

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1.5.5 by Merlise Clyde, 2 years ago,

Report a bug at

Browse source code at

Authors: Merlise Clyde [aut, cre, cph] , Michael Littman [ctb] , Quanli Wang [ctb] , Joyee Ghosh [ctb] , Yingbo Li [ctb] , Don van de Bergh [ctb]

Documentation:   PDF Manual  

Task views: Bayesian Inference

GPL (>= 3) license

Imports stats, graphics, utils, grDevices

Suggests MASS, knitr, ggplot2, GGally, rmarkdown, roxygen2, dplyr, glmbb, pkgdown, testthat, covr

See at CRAN