Fast sampling with Gaussian scale mixture priors in high-dimensional regression

• 成果类型: Article
• 署名作者: Bhattacharya, Anirban; Chakraborty, Antik; Mallick, Bani K.
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw042
• 发表日期: 2016
• 页码: 985991
• 关键词: variable-selection; posterior concentration; geometric ergodicity; confidence-intervals; horseshoe estimator; binary; models

摘要

We propose an efficient way to sample from a class of structured multivariate Gaussian distributions. The proposed algorithm only requires matrix multiplications and linear system solutions. Its computational complexity grows linearly with the dimension, unlike existing algorithms that rely on Cholesky factorizations with cubic complexity. The algorithm is broadly applicable in settings where Gaussian scale mixture priors are used on high-dimensional parameters. Its effectiveness is illustrated through a high-dimensional regression problem with a horseshoe prior on the regression coefficients. Other potential applications are outlined.