  General linear models (GLM) are often constructed and used in statistical
inference at the voxel level in brain imaging. In this paper, we explore the
basics of random fields and the multiple comparisons on the random fields,
which are necessary to properly threshold statistical maps for the whole image
at specific statistical significance level. The multiple comparisons are
crucial in determining overall statistical significance in correlated test
statistics over the whole brain. In practice, t- or F-statistics in adjacent
voxels are correlated. So there is the problem of multiple comparisons, which
we have simply neglected up to now. For multiple comparisons that account for
spatially correlated test statistics, various methods were proposed: Bonferroni
correction, random field theory, false discovery rates and permutation tests.
Among them, we will explore the random field approach.
