We introduce a multiple testing procedure that controls the median of the proportion of false discoveries (FDP) in a flexible way. The procedure only requires a vector of p-values as input and is comparable to the Benjamini-Hochberg method, which controls the mean of the FDP. Our method allows freely choosing one or several values of alpha after seeing the data -- unlike Benjamini-Hochberg, which can be very liberal when alpha is chosen post hoc. We prove these claims and illustrate them with simulations. Our procedure is inspired by a popular estimator of the total number of true hypotheses. We adapt this estimator to provide simultaneously median unbiased estimators of the FDP, valid for finite samples. This simultaneity allows for the claimed flexibility. Our approach does not assume independence. The time complexity of our method is linear in the number of hypotheses, after sorting the p-values.

翻译：我们提出了一种多重检验程序，能够灵活控制错误发现比例（FDP）的中位数。该程序仅需一组p值作为输入，其性能可与控制FDP均值的Benjamini-Hochberg方法相媲美。与Benjamini-Hochberg方法在事后选择alpha值时可能过于宽松不同，我们的方法允许在观察数据后自由选择一个或多个alpha值。我们通过理论证明与模拟实验验证了这些结论。该程序受一种流行的真实假设总数估计量启发，我们对该估计量进行了改进，使其能同时提供有限样本下FDP的中位数无偏估计，这种同步性保证了所声称的灵活性。本方法无需假设独立性，在p值排序后时间复杂度与假设数量呈线性关系。