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Title: Error control in fMRI using the (nonstationary) Gaussian kinematic formula Authors:  Armin Schwartzman - University of California, San Diego (United States) [presenting]
Dan Cheng - Texas Tech University (United States)
Fabian Telschow - University of California, San Diego (United States)
Robert Adler - Technion - Israel Institute of Technology (Israel)
Abstract: In fMRI, activation maps are typically excursion sets of a regression coefficient map, seen as a smooth Gaussian random field. The Euler Characteristic (EC) heuristic connects the error control to the expected EC, given by the Gaussian kinematic formula (GKF). While the GKF is remarkably simple, equal to a linear function of the Lipschitz-Killing curvatures (LKCs) of the field over the domain, the use of the GKF has been limited because the LKCs are difficult to compute or estimate for nonstationary fields. Given repeated observations of a field, a consistent estimator of the LKCs is proposed as a simple affine function of the observed EC curves. The estimator is easy to implement and shown to be consistent as the number of repeated observations increases, regardless of the underlying covariance structure. The proposed estimator is used to determine activation in fMRI and establish spatial error control, using central limit theorems to determine the accuracy in the inference.