  Random Effects analysis has been introduced into fMRI research in order to
generalize findings from the study group to the whole population. Generalizing
findings is obviously harder than detecting activation in the study group since
in order to be significant, an activation has to be larger than the
inter-subject variability. Indeed, detected regions are smaller when using
random effect analysis versus fixed effects. The statistical assumptions behind
the classic random effects model are that the effect in each location is
normally distributed over subjects, and "activation" refers to a non-null mean
effect. We argue this model is unrealistic compared to the true population
variability, where, due to functional plasticity and registration anomalies, at
each brain location some of the subjects are active and some are not. We
propose a finite-Gaussian--mixture--random-effect. A model that amortizes
between-subject spatial disagreement and quantifies it using the "prevalence"
of activation at each location. This measure has several desirable properties:
(a) It is more informative than the typical active/inactive paradigm. (b) In
contrast to the hypothesis testing approach (thus t-maps) which are trivially
rejected for large sample sizes, the larger the sample size, the more
informative the prevalence statistic becomes.
  In this work we present a formal definition and an estimation procedure of
this prevalence. The end result of the proposed analysis is a map of the
prevalence at locations with significant activation, highlighting activations
regions that are common over many brains.
