期刊
COMPUTATIONAL STATISTICS & DATA ANALYSIS
卷 107, 期 -, 页码 107-119出版社
ELSEVIER
DOI: 10.1016/j.csda.2016.10.008
关键词
Bayesian; Horseshoe; Markov chain Monte Carlo; Shrinkage priors; Variable selection
资金
- Office of Naval Research (ONR) [BAA 14-0001]
- National Science Foundation (NSF) [DMS 1613156]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1613156] Funding Source: National Science Foundation
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 separate components for characterizing the signal and the noise. However, such priors encounter computational issues in high dimensions. 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. A general approach for variable selection with shrinkage priors is proposed. The presence of very few tuning parameters makes our method attractive in comparison to ad hoc thresholding approaches. The applicability of the approach is not limited to continuous shrinkage priors, but can be used along with any shrinkage prior. Theoretical properties for near-collinear design matrices are investigated and the method is shown to have good performance in a wide range of synthetic data examples and in a real data example on selecting genes affecting survival due to lymphoma. (C) 2016 Elsevier B.V. All rights reserved.
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