Consistent high-dimensional Bayesian variable selection via penalized credible regions.

TitleConsistent high-dimensional Bayesian variable selection via penalized credible regions.
Publication TypeJournal Article
Year of Publication2012
AuthorsBondell, Howard D., and Brian J. Reich
JournalJ Am Stat Assoc
Date Published2012 Dec 21

For high-dimensional data, particularly when the number of predictors greatly exceeds the sample size, selection of relevant predictors for regression is a challenging problem. Methods such as sure screening, forward selection, or penalized regressions are commonly used. Bayesian variable selection methods place prior distributions on the parameters along with a prior over model space, or equivalently, a mixture prior on the parameters having mass at zero. Since exhaustive enumeration is not feasible, posterior model probabilities are often obtained via long MCMC runs. The chosen model can depend heavily on various choices for priors and also posterior thresholds. Alternatively, we propose a conjugate prior only on the full model parameters and use sparse solutions within posterior credible regions to perform selection. These posterior credible regions often have closed-form representations, and it is shown that these sparse solutions can be computed via existing algorithms. The approach is shown to outperform common methods in the high-dimensional setting, particularly under correlation. By searching for a sparse solution within a joint credible region, consistent model selection is established. Furthermore, it is shown that, under certain conditions, the use of marginal credible intervals can give consistent selection up to the case where the dimension grows exponentially in the sample size. The proposed approach successfully accomplishes variable selection in the high-dimensional setting, while avoiding pitfalls that plague typical Bayesian variable selection methods.

Alternate JournalJ Am Stat Assoc
Original PublicationConsistent high-dimensional Bayesian variable selection via penalized credible regions.
PubMed ID23482517
PubMed Central IDPMC3587767
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
R01 ES014843 / ES / NIEHS NIH HHS / United States
R01 MH084022 / MH / NIMH NIH HHS / United States