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December 2003 Rotation space random fields with an application to fMRI data
K. Shafie, D. Siegmund, B. Sigal, K.J. Worsley
Ann. Statist. 31(6): 1732-1771 (December 2003). DOI: 10.1214/aos/1074290326


Siegmund and Worsley considered the problem of testing for a signal with unknown location and scale in a Gaussian random field defined on~$\mathbb{R}^N$. The test statistic was the maximum of a Gaussian random field in an $(N+1)$-dimensional "scale space," N dimensions for location and one dimension for the scale of a smoothing kernel. Siegmund and Worsley used two methods, one involving the expected Euler characteristic of the excursion set and the other involving the volume of tubes, to derive an approximate null distribution. The purpose of this paper is to extend the scale space result to the rotation space random field when N=2, where the maximum is taken over all rotations of the filter as well as scales. We apply this result to the problem of searching for activation in brain images obtained by functional magnetic resonance imaging (fMRI).


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K. Shafie. D. Siegmund. B. Sigal. K.J. Worsley. "Rotation space random fields with an application to fMRI data." Ann. Statist. 31 (6) 1732 - 1771, December 2003.


Published: December 2003
First available in Project Euclid: 16 January 2004

zbMATH: 1043.92019
MathSciNet: MR2036389
Digital Object Identifier: 10.1214/aos/1074290326

Primary: 60G60 , 62M09
Secondary: 52A22 , 60D05

Keywords: differential topology , Euler characteristic , image analysis , integral geometry , nonstationary random fields

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 6 • December 2003
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