Posterior consistency in linear models under shrinkage priors

• 成果类型: Article
• 署名作者: Armagan, A.; Dunson, D. B.; Lee, J.; Bajwa, W. U.; Strawn, N.
• 署名单位: SAS Institute Inc; Duke University; Seoul National University (SNU); Rutgers University System; Rutgers University New Brunswick; Duke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast028
• 发表日期: 2013
• 页码: 10111018
• 关键词: selection

摘要

We investigate the asymptotic behaviour of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution concentrates in neighbourhoods of the true parameter under simple sufficient conditions. These conditions hold under popular shrinkage priors given some sparsity assumptions.