For the measure of brain activation in functional MRI many methods compute a heuristically chosen metric. The statistic of the underlying metric which is implicitely derived from the original assumption about the noise in the data, provides only an indirect way to the statistical inference of brain activation. We propose an alternative procedure by presenting a binary hypothesis-testing approach. This approach treats the problem of detecting brain activation at its origin by directly deriving a test statistic based on the probabilistic model of the noise in the data. Thereby, deterministic or parameterized models for the hemodynamic response can be considered. Results show that time series models can be detected even if they are characterized by unknown parameters, associated with the unclear nature of the mechanisms that mediate between neuronal stimulation and hemodynamic brain response. The likelihood ratio tests proposed in this paper are very efficient and robust in making a statistical inference about detected regions of brain activation. To validate the usefulness of our approach we present a simulation environment for functional MRI. This environment also serves as a testbed for comparative study and systematic tests.