# BAS v1.5.5

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## 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) <DOI:10.1198/016214507000001337> for linear models or mixtures of g-priors from Li and Clyde (2019) <DOI:10.1080/01621459.2018.1469992> 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) <DOI:10.1198/jcgs.2010.09049> 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.

## Functions in BAS

 Name Description TG Generalized g-Prior Distribution for Coefficients in BMA Models bodyfat Bodyfat Data climate Climate Data g.prior Families of G-Prior Distribution for Coefficients in BMA Models bayesglm.fit Fitting Generalized Linear Models and Bayesian marginal likelihood evaluation bas.lm Bayesian Adaptive Sampling for Bayesian Model Averaging and Variable Selection in Linear Models force.heredity.bas Post processing function to force constraints on interaction inclusion bas BMA objects eplogprob eplogprob - Compute approximate marginal inclusion probabilities from pvalues diagnostics BAS MCMC diagnostic plot hyper.g.n Generalized hyper-g/n Prior Distribution for g for mixtures of g-priors on Coefficients in BMA Models hyper.g Hyper-g-Prior Distribution for Coefficients in BMA Models Bayes.outlier Bayesian Outlier Detection bas.glm Bayesian Adaptive Sampling Without Replacement for Variable Selection in Generalized Linear Models confint.coef.bas Compute Credible Intervals for BAS regression coefficients from BAS objects testBF.prior Test based Bayes Factors for BMA Models tCCH Generalized tCCH g-Prior Distribution for Coefficients in BMA Models plot.coef.bas Plots the posterior distributions of coefficients derived from Bayesian model averaging hypergeometric1F1 Confluent hypergeometric2F1 function intrinsic Intrinsic Prior Distribution for Coefficients in BMA Models image.bas Images of models used in Bayesian model averaging coef.bas Coefficients of a Bayesian Model Average object hypergeometric2F1 Gaussian hypergeometric2F1 function protein Protein Activity Data variable.names.pred.bas Extract the variable names for a model from a BAS prediction object eplogprob.marg eplogprob.marg - Compute approximate marginal inclusion probabilities from pvalues which.matrix Coerce a BAS list object of models into a matrix. predict.bas Prediction Method for an object of class BAS update.bas Update BAS object using a new prior print.bas Print a Summary of Bayesian Model Averaging objects from BAS plot.confint.bas Plot Bayesian Confidence Intervals predict.basglm Prediction Method for an Object of Class basglm fitted.bas Fitted values for a BAS BMA objects beta.binomial Beta-Binomial Prior Distribution for Models beta.prime Beta-Prime Prior Distribution for Coefficients in BMA Model phi1 Compound Confluent hypergeometric function of two variables plot.bas Plot Diagnostics for an BAS Object list2matrix.bas Coerce a BAS list object into a matrix. cv.summary.bas Summaries for Out of Sample Prediction list2matrix.which Coerce a BAS list object into a matrix. confint.pred.bas Compute Credible (Bayesian Confidence) Intervals for a BAS predict object uniform Uniform Prior Distribution for Models tr.poisson Truncated Poisson Prior Distribution for Models tr.power.prior Truncated Power Prior Distribution for Models tr.beta.binomial Truncated Beta-Binomial Prior Distribution for Models robust Robust-Prior Distribution for Coefficients in BMA Model summary.bas Summaries of Bayesian Model Averaging objects from BAS CCH Generalized g-Prior Distribution for Coefficients in BMA Models EB.global Find the global Empirical Bayes estimates for BMA BAS BAS: Bayesian Model Averaging using Bayesian Adaptive Sampling Bernoulli Independent Bernoulli Prior Distribution for Models Bernoulli.heredity Independent Bernoulli prior on models that with constraints for model hierarchy induced by interactions IC.prior Information Criterion Families of Prior Distribution for Coefficients in BMA Models Jeffreys Jeffreys Prior Distribution for $g$ for Mixtures of g-Priors for Coefficients in BMA Models EB.local Empirical Bayes Prior Distribution for Coefficients in BMA Model Hald Hald Data No Results!