  The perturbation of a transcription factor should affect the expression
levels of its direct targets. However, not all genes showing changes in
expression are direct targets. To increase the chance of detecting direct
targets, we propose a modified two-group model where the null group corresponds
to genes which are not direct targets, but can have small non-zero effects. We
model the behaviour of genes from the null set by a Gaussian distribution with
unknown variance $\tau^2$, and we discuss and compare three methods which
adaptively estimate $\tau^2$ from the data: the iterated empirical Bayes
estimator, the truncated MLE and the central moment matching estimator. We
conduct a detailed analysis of the properties of the iterated EB estimate which
has the best performance in the simulations. In particular, we provide
theoretical guarantee of its good performance under mild conditions.
  We provide simulations comparing the new modeling approach with existing
methods, and the new approach shows more stable and better performance under
different situations. We also apply it to a real data set from gene knock-down
experiments and obtained better results compared with the original two-group
model testing for non-zero effects.
