  The use of weights provides an effective strategy to incorporate prior domain
knowledge in large-scale inference. This paper studies weighted multiple
testing in a decision-theoretic framework. We develop oracle and data-driven
procedures that aim to maximize the expected number of true positives subject
to a constraint on the weighted false discovery rate. The asymptotic validity
and optimality of the proposed methods are established. The results demonstrate
that incorporating informative domain knowledge enhances the interpretability
of results and precision of inference. Simulation studies show that the
proposed method controls the error rate at the nominal level, and the gain in
power over existing methods is substantial in many settings. An application to
genome-wide association study is discussed.
