We present false discovery rate smoothing, an empirical-Bayes method for
exploiting spatial structure in large multiple-testing problems. FDR smoothing
automatically finds spatially localized regions of significant test statistics.
It then relaxes the threshold of statistical significance within these regions,
and tightens it elsewhere, in a manner that controls the overall
false-discovery rate at a given level. This results in increased power and
cleaner spatial separation of signals from noise. The approach requires solving
a non-standard high-dimensional optimization problem, for which an efficient
augmented-Lagrangian algorithm is presented. In simulation studies, FDR
smoothing exhibits state-of-the-art performance at modest computational cost.
In particular, it is shown to be far more robust than existing methods for
spatially dependent multiple testing. We also apply the method to a data set
from an fMRI experiment on spatial working memory, where it detects patterns
that are much more biologically plausible than those detected by standard
FDR-controlling methods. All code for FDR smoothing is publicly available in
Python and R.

该研究提出了一种基于经验贝叶斯方法的误发现率平滑技术，利用空间结构解决大规模多重检验问题，对显著性测试统计量的空间本地化区域自动降低统计显著性阈值，从而提高功率和减少噪声干扰。该方法需要解决非标准高维优化问题，但在模拟研究和 fMRI 实验数据上表现出了现有空间依赖多重检验方法所无法比拟的鲁棒性能优势，代码已公开在 Python 和 R 平台上。