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Storey's method also leads to a direct estimate of FDP.  If we reject at level \(\alpha\) we expect the number of false discoveries to be \(\alpha m_0\).  So the estimate of FDP is \(\alpha\hat{m}_0 / R\).

This leads directly to the Storey q-value [1] which is often interpreted as either an FDR-adjusted p-value or FDP(p) where p is any observed p-value in the experiment.

We start by sorting the p-values as we do for the BH or Holmes procedures.

Note that if we reject for \(p\leq p_{(i)}\) then the total rejections will be at least i (with equality unless two or more of the p-values are equal to \(p_{(i)}\)).  Let R(\(\alpha\)) be the number of rejections when we reject for all \(p\leq\alpha\).  Then define the q-values by:

\[q(1)= p_{(1)}\hat{m}_0/R(p_{(1)})\]

\[q(i+1)=max(q(i),p_{(i+1)}\hat{m}_0/R(p_{(i+1)})\]

This associates a q-value with each feature, which estimates the FDP if you reject the null hypothesis for this feature and all features which are this significant or more.  Often we pick a cut-off for the q-value and reject the null hypothesis for all features with q-value less than or equal to our cut-off.

[1] Storey, John D. "The positive false discovery rate: a Bayesian interpretation and the q-value." Annals of statistics(2003): 2013-2035. https://projecteuclid.org/download/pdf_1/euclid.aos/1074290335