Detecting Sparse Cone Alternatives for Gaussian Random Fields

• Activity Number: 323
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Jonathan Taylor*+
• Companies: Stanford University

Abstract

I will talk about Keith Worsley's last paper, that we were working on the month he passed away. The problem we were considering is to find a good approximation to the P-value of the maximum of a random field of test statistics for a cone alternative at each point in a sample of Gaussian random fields. These test statistics had been proposed in the neuroscience literature for the analysis of fMRI data allowing for unknown delay in the hemodynamic response. However the null distribution of the maximum of this 3D random field of test statistics, and hence the threshold used to detect brain activation, was unsolved. To find a solution, we use Keith's favorite trick: we approximate the P-value by the expected Euler characteristic (EC) of the excursion set of the test statistic random field.