  To interpret differentially expressed genes or other discovered features,
researchers conduct hypothesis tests to determine which biological categories
such as those of the Gene Ontology (GO) are enriched in the sense of having
differential representation among the discovered features. We study application
of better estimators of the local false discovery rate (LFDR), a probability
that the biological category has equivalent representation among the
preselected features.
  We identified three promising estimators of the LFDR for detecting
differential representation: a semiparametric estimator (SPE), a normalized
maximum likelihood estimator (NMLE), and a maximum likelihood estimator (MLE).
We found that the MLE performs at least as well as the SPE for on the order of
100 of GO categories even when the ideal number of components in its underlying
mixture model is unknown. However, the MLE is unreliable when the number of GO
categories is small compared to the number of PMM components. Thus, if the
number of categories is on the order of 10, the SPE is a more reliable LFDR
estimator. The NMLE depends not only on the data but also on a specified value
of the prior probability of differential representation. It is therefore an
appropriate LFDR estimator only when the number of GO categories is too small
for application of the other methods.
  For enrichment detection, we recommend estimating the LFDR by the MLE given
at least a medium number (~100) of GO categories, by the SPE given a small
number of GO categories (~10), and by the NMLE given a very small number (~1)
of GO categories.
