False Discovery Rate Smoothing

• Activity Number: 629
• Type: Invited
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): James Scott* and Wesley Tansey
• Companies: The University of Texas at Austin and The University of Texas at Austin
• Keywords: multiple testing ; false discovery rate ; spatial smoothing ; fMRI

Abstract

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 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.