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For large-scale testing with graph-associated data, we present an empiricalBayes mixture technique to score local false discovery rates. Compared toempirical Bayes procedures that ignore the graph, the proposed method gainspower in settings where non-null cases form connected subgraphs, and it does soby regularizing parameter contrasts between testing units. Simulations showthat GraphMM controls the false discovery rate in a variety of settings. Onmagnetic resonance imaging data from a study of brain changes associated withthe onset of Alzheimer's disease, GraphMM produces substantially greater yieldthan conventional large-scale testing procedures.

Dimension constraints improve hypothesis testing for large-scale, graph-associated, brain-image data