  In multiple hypotheses testing it has become widely popular to make inference
on the true discovery proportion (TDP) of a set $\mathcal{M}$ of null
hypotheses. This approach is useful for several application fields, such as
neuroimaging and genomics. Several procedures to compute simultaneous lower
confidence bounds for the TDP have been suggested in prior literature.
Simultaneity allows for post-hoc selection of $\mathcal{M}$. If sets of
interest are specified a priori, it is possible to gain power by removing the
simultaneity requirement. We present an approach to compute lower confidence
bounds for the TDP if the set of null hypotheses is defined a priori. The
proposed method determines the bounds using the exact distribution of the
number of rejections based on a step-up multiple testing procedure under
independence assumptions. We assess robustness properties of our procedure and
apply it to real data from the field of functional magnetic resonance imaging.
