Scalar-on-image regression via the soft-thresholded Gaussian process

• 成果类型: Article
• 署名作者: Kang, Jian; Reich, Brian J.; Staicu, Ana-Maria
• 署名单位: University of Michigan System; University of Michigan; North Carolina State University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asx075
• 发表日期: 2018
• 页码: 165184
• 关键词: bayesian variable selection; posterior consistency; matrix; models; density; priors

摘要

This work concerns spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models and develop an efficient posterior computational algorithm. The proposed soft-thresholded Gaussian process provides large prior support over the class of piecewise-smooth, sparse, and continuous spatially varying regression coefficient functions. In addition, under some mild regularity conditions the soft-thresholded Gaussian process prior leads to the posterior consistency for parameter estimation and variable selection for scalar-on-image regression, even when the number of predictors is larger than the sample size. The proposed method is compared to alternatives via simulation and applied to an electroencephalography study of alcoholism.