Journal article
Consistent high-dimensional Bayesian variable selection via penalized credible regions
HD Bondell, BJ Reich
Journal of the American Statistical Association | TAYLOR & FRANCIS INC | Published : 2012
Abstract
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 Markov chain Monte Carlo (MCMC) runs. The chosen model can depend heavily on various choices for priors and also posterior thresholds. ..
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Awarded by National Science Foundation
Funding Acknowledgements
Howard D. Bondell is Associate Professor (E-mail: bondell@stat.ncsu.edu) and Brian J. Reich is Associate Professor (E-mail: brian_reich@ncsu.edu), Department of Statistics, North Carolina State University, Raleigh, NC 27695. The authors are grateful to the editor, an associate editor, and three anonymous referees for their valuable comments. Bondell's research was partially supported by an NSF grant DMS 1005612 and NIH grants P01-CA-142538-01 and R01-MH-084022-01. Reich's research was partially supported by an NIH grant R01-ES-014843-02. The authors thank Gareth James for providing the DASSO code for the Dantzig selector.