James Scott (University of Texas at Austin)

False discovery rate smoothing

Many approaches for multiple testing begin with the assumption that all tests in a given study should be combined into a global false-discovery-rate analysis.  But this may be inappropriate for many of today’s large-scale screening problems, where test statistics have a natural spatial lattice structure (voxels in the brain, distance along the chromosome), and where a combined analysis can lead to poorly calibrated error rates.  To address this problem, we introduce an approach called false-discovery-rate smoothing.  FDR smoothing can, at modest computational cost, identify localized spatial regions of the underyling lattice structure where the frequency of signals is enriched versus the background.  We give background on the multiple-testing problem, introduce the method, describe a model-fitting algorithm based on an augmented-Lagrangian formulation of the problem, and show an application to fMRI data analysis in functional neuro-imaging.  The issue of scalability is essentially important in this context, as a single fMRI image may contain millions of voxels in a 3D lattice.  We show how recent results on algorithms for Laplacian linear systems can be exploited to address this challenge. Further applications of the method in genomics and environmental sensor networks are briefly discussed.

Joint work with Wesley Tansey (University of Texas at Austin).