  Despite the popularity of the false discovery rate (FDR) as an error control
metric for large-scale multiple testing, its close Bayesian counterpart the
local false discovery rate (lfdr), defined as the posterior probability that a
particular null hypothesis is false, is a more directly relevant standard for
justifying and interpreting individual rejections. However, the lfdr is
difficult to work with in small samples, as the prior distribution is typically
unknown. We propose a simple multiple testing procedure and prove that it
controls the expectation of the maximum lfdr across all rejections;
equivalently, it controls the probability that the rejection with the largest
p-value is a false discovery. Our method operates without knowledge of the
prior, assuming only that the p-value density is uniform under the null and
decreasing under the alternative. We also show that our method asymptotically
implements the oracle Bayes procedure for a weighted classification risk,
optimally trading off between false positives and false negatives. We derive
the limiting distribution of the attained maximum lfdr over the rejections, and
the limiting empirical Bayes regret relative to the oracle procedure.
