Empirical Bayes large-scale multiple testing for high-dimensional binary outcome data

Abstract: This paper explores the multiple testing problem for sparse high-dimensional data with binary outcomes. We propose novel empirical Bayes multiple testing procedures based on a spike-and-slab posterior and then evaluate their performance in controlling the false discovery rate (FDR). A surprising finding is that the procedure using the default conjugate prior (namely, the $\ell$-value procedure) can be overly conservative in estimating the FDR. To address this, we introduce two new procedures that provide accurate FDR control. Sharp frequentist theoretical results are established for these procedures, and numerical experiments are conducted to validate our theory in finite samples. To the best of our knowledge, we obtain the first {\it uniform} FDR control result in multiple testing for high-dimensional data with binary outcomes under the sparsity assumption.