Detecting activation in fMRI data.

We present a simple approach to the analysis of fMRI data collected from several runs, sessions and subjects. We take advantage of the spatial nature of the data to reduce the noise in certain key parameters, achieving an increase in degrees of freedom for a mixed effects analysis. Our main interest is the analysis of the resulting images of test statistics using the geometry of random fields. We show how the Euler characteristic of the excursion set plays a key role in setting the threshold of the image to detect regions of the brain activated by a stimulus.