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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 specifically, we calculate the p-values as the excursion probability of an inhomogeneous Gaussian random field on a two dimensional representation manifold that are dependent on the structure of error co variance 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.