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

TL;DR

The paper introduces NAPA, a novel statistical method that leverages spatial smoothness and sparsity information to enhance two-sample testing power while controlling false discoveries in high-dimensional spatial data.

Contribution

NAPA is a new approach that incorporates neighborhood and posterior adjustments to improve multiple testing in spatial data analysis.

Findings

Guaranteed power improvement over existing tests.

Asymptotic false discovery control established.

Effective in neuroimaging applications.

Abstract

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.