Near infared spectroscopy (NIRS) is a non-invasive method to measure the brain activity as the changes of hemoglobin oxygenation through the intact skull. In this paper, we statistically analyze the NIRS data based on general linear model (GLM) and propose a new theory for making inference using Sun’s tube formula. More speci cally, we calculate the p-values as the excursion probability of an inhomogeneous Gaussian random eld on a two dimensional representation manifold that are dependent on the structure of error covariance matrix and the interpolating kernels. These powerful tools for excursion probability allows us the super-resolution localization of the brain activation which is not possible using the conventional NIRS analysis. ©2008 IEEE.