Two-sample multiple testing problems of sparse spatial data are frequently arising in a variety of scientific applications. In this article, we develop a novel neighborhood-assisted and posterior-adjusted (NAPA) approach to incorporate both the spatial smoothness and sparsity type side information to improve the power of the test while controlling the false discovery of multiple testing. We translate the side information into a set of weights to adjust the $p$-values, where the spatial pattern is encoded by the ordering of the locations, and the sparsity structure is encoded by a set of auxiliary covariates. We establish the theoretical properties of the proposed test, including the guaranteed power improvement over some state-of-the-art alternative tests, and the asymptotic false discovery control. We demonstrate the efficacy of the test through intensive simulations and two neuroimaging applications.

翻译：稀疏空间数据的两样本多重检验问题在各类科学应用中频繁出现。本文提出了一种新颖的邻域辅助与后验调整（NAPA）方法，通过融合空间平滑性和稀疏性类型的辅助信息，在控制多重检验错误发现率的同时提升检验效能。我们将辅助信息转化为一组权重以调整$p$值，其中空间模式通过位置排序进行编码，稀疏结构则通过一组辅助协变量进行编码。我们建立了所提检验方法的理论性质，包括相较于若干先进替代检验方法具有保证的效能提升，以及渐近错误发现控制。通过大量模拟实验和两项神经影像学应用案例，我们验证了该检验方法的使用效果。