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Two-sample multiple testing problems of sparse spatial data are frequentlyarising in a variety of scientific applications. In this article, we develop anovel neighborhood-assisted and posterior-adjusted (NAPA) approach toincorporate both the spatial smoothness and sparsity type side information toimprove the power of the test while controlling the false discovery of multipletesting. 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 thelocations, and the sparsity structure is encoded by a set of auxiliarycovariates. We establish the theoretical properties of the proposed test,including the guaranteed power improvement over some state-of-the-artalternative tests, and the asymptotic false discovery control. We demonstratethe efficacy of the test through intensive simulations and two neuroimagingapplications.

NAPA: Neighborhood-Assisted and Posterior-Adjusted Two-sample Inference