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.
