Default Variable Selection Using Shrinkage Priors

• Activity Number: 123
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Debdeep Pati*
• Companies: Florida State University
• Keywords: Bayesian ; horseshoe ; shrinkage ; variable selection

Abstract

Variable selection has received widespread attention over the last decade as we routinely encounter high-throughput datasets in complex biological and environment research. Most Bayesian variable selection methods are restricted to mixture priors having a distinct component each for characterizing the signal and the noise. However, such priors encounter computational problems in high dimensions unless careful algorithms are devised limiting their applicability in very high dimensional complex models. This has motivated continuous shrinkage priors, resembling the two-component priors facilitating computation and interpretability. While such priors are widely used for estimating high-dimensional sparse vectors, selecting a subset of variables remains a daunting task. In this article, we propose a default method for variable selection using continuous shrinkage priors. The absence of any tuning parameters make our method attractive in comparison to adhoc thresholding approaches. Theoretical properties of the proposed approach are investigated and the method is shown to have good performance in synthetic and real data examples. (Joint work with Hanning Li.)