  We introduce a new class of methods for finite-sample false discovery rate
(FDR) control in multiple testing problems with dependent test statistics where
the dependence is fully or partially known. Our approach separately calibrates
a data-dependent p-value rejection threshold for each hypothesis, relaxing or
tightening the threshold as appropriate to target exact FDR control. In
addition to our general framework we propose a concrete algorithm, the
dependence-adjusted Benjamini-Hochberg (dBH) procedure, which adaptively
thresholds the q-value for each hypothesis. Under positive regression
dependence the dBH procedure uniformly dominates the standard BH procedure, and
in general it uniformly dominates the Benjamini-Yekutieli (BY) procedure (also
known as BH with log correction). Simulations and real data examples illustrate
power gains over competing approaches to FDR control under dependence.
