Abstract
This chapter presents a unified P-value for assessing the significance of peaks in statistical fields searched over regions of any shape or size. This is extended to 4D scale space searches over smoothing filter width as well as location. The results are usable in a wide range of applications, including positron emission tomography (PET) and fMRI, but are discussed with particular reference to PET images that represent changes in cerebral blood flow elicited by a specific cognitive or sensorimotor task. The first result, derived by Worsley, is an estimate of the P-value for local maxima of Gaussian fields over search regions of any shape or size in any number of dimensions. This unifies the P-values for large search areas in 2D, large search regions in 3D, and the usual uncorrected p-value at a single pixel or voxel. This makes it possible to restrict the search to small anatomical regions, such as the cingulate gyrus or caudate nucleus, or two-dimensional regions, such as a slice or the cortical surface, or even single voxels. The results are also generalizable to 4D searches in time as well as space, which may be useful for fMRI. The second result is an extension to searches over smoothing filter width or scale space.
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