  The mitigation of false positives is an important issue when conducting
multiple hypothesis testing. The most popular paradigm for false positives
mitigation in high-dimensional applications is via the control of the false
discovery rate (FDR). Multiple testing data from neuroimaging experiments can
be very large, and reduced precision storage of such data is often required.
Reduced precision computation is often a problem in the analysis of legacy data
and data arising from legacy pipelines. We present a method for FDR control
that is applicable in cases where only p\text{-values} or test statistics (with
common and known null distribution) are available, and when those
p\text{-values} or test statistics are encoded in a reduced precision format.
Our method is based on an empirical-Bayes paradigm where the probit
transformation of the p\text{-values} (called the z\text{-scores}) are modeled
as a two-component mixture of normal distributions. Due to the reduced
precision of the p\text{-values} or test statistics, the usual approach for
fitting mixture models may not be feasible. We instead use a binned-data
technique, which can be proved to consistently estimate the z\text{-score}
distribution parameters under mild correlation assumptions, as is often the
case in neuroimaging data. A simulation study shows that our methodology is
competitive when compared with popular alternatives, especially with data in
the presence of misspecification. We demonstrate the applicability of our
methodology in practice via a brain imaging study of mice.
