ON SPIKE AND SLAB EMPIRICAL BAYES MULTIPLE TESTING

• 成果类型: Article
• 署名作者: Castillo, Ismael; Roquain, Etienne
• 署名单位: Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1897
• 发表日期: 2020
• 页码: 2548-2574
• 关键词: false discovery rate; variable-selection; posterior concentration; unknown sparsity; needles; rates; CONVERGENCE; optimality; straw; slope

摘要

This paper explores a connection between empirical Bayes posterior distributions and false discovery rate (FDR) control. In the Gaussian sequence model this work shows that empirical Bayes-calibrated spike and slab posterior distributions allow a correct FDR control under sparsity. Doing so, it offers a frequentist theoretical validation of empirical Bayes methods in the context of multiple testing. Our theoretical results are illustrated with numerical experiments.