Bayesian Model Selection in High-Dimensional Settings

• 成果类型: Article
• 署名作者: Johnson, Valen E.; Rossell, David
• 署名单位: University of Texas System; UTMD Anderson Cancer Center; Barcelona Institute of Science & Technology; Institute for Research in Biomedicine - IRB Barcelona
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.682536
• 发表日期: 2012
• 页码: 649-660
• 关键词: nonconcave penalized likelihood; variable-selection; Consistency; CONVERGENCE; moments

摘要

Standard assumptions incorporated into Bayesian model selection procedures result in procedures that are not competitive with commonly used penalized likelihood methods. We propose modifications of these methods by imposing nonlocal prior densities on model parameters. We show that the resulting model selection procedures are consistent in linear model settings when the number of possible covariates p is bounded by the number of observations n, a property that has not been extended to other model selection procedures. In addition to consistently identifying the true model, the proposed procedures provide accurate estimates of the posterior probability that each identified model is correct. Through simulation studies, we demonstrate that these model selection procedures perform as well or better than commonly used penalized likelihood methods in a range of simulation settings. Proofs of the primary theorems are provided in the Supplementary Material that is available online.