False discovery control with p-value weighting

We present a method for multiple hypothesis testing that maintains control of the false discovery rate while incorporating prior information about the hypotheses. The prior information takes the form of p-value weights. If the assignment of weights is positively associated with the null hypotheses being false, the procedure improves power, except in cases where power is already near one. Even if the assignment of weights is poor, power is only reduced slightly, as long as the weights are not too large. We also provide a similar method for controlling false discovery exceedance.