  Functional Magnetic Resonance Imaging~(fMRI) is widely used to study
activation in the human brain. In most cases, data are commonly used to
construct activation maps corresponding to a given paradigm. Results can be
very variable, hence quantifying certainty of identified activation and
inactivation over studies is important. This paper provides a model-based
approach to certainty estimation from data acquired over several replicates of
the same experimental paradigm. Specifically, the $p$-values derived from the
statistical analysis of the data are explicitly modeled as a mixture of their
underlying distributions; thus, unlike methodology currently in use, there is
no subjective thresholding required in the estimation process. The parameters
governing the mixture model are easily obtained by the principle of maximum
likelihood. Further, the estimates can also be used to optimally identify
voxel-specific activation regions along with their corresponding certainty
measures. The methodology is applied to a study involving a motor paradigm
performed on a single subject several times over a period of two months.
Simulation experiments used to calibrate performance of the method are
promising. The methodology is also seen to be robust in determining areas of
activation and their corresponding certainties.
