Bayesian Multiple Testing Under Dependence with Application to Functional Magnetic Resonance Imaging

• Activity Number: 508
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): D. Andrew Brown*+ and Nicole Lazar and Gauri Sankar Datta
• Companies: University of Georgia and University of Georgia and University of Georgia
• Keywords: simultaneous inference ; spatially correlated data ; conditional autoregressive model ; syndromic surveillance

Abstract

In the analysis of high-throughput data, a massive number of hypotheses are tested simultaneously. Correcting for multiple testing becomes problematic because relatively simple procedures such as the Bonferroni correction are overly conservative, whereas ignoring the problem altogether leads to a very high number of false rejections. This is especially true when trying to identify sparse signals. Many multiple testing procedures, both Bayesian and frequentist, rely on the assumption of independence of the data. One particular Bayesian procedure for the simultaneous testing of independent data was given in Scott and Berger (2006). We extend this method by introducing a conditional autoregressive (CAR) model to account for spatial dependence. The model is applied to data from a functional magnetic resonance imaging (fMRI) study and compared to results obtained under the independence assumption.