  The Benjamini-Hochberg (BH) procedure is a celebrated method for multiple
testing with false discovery rate (FDR) control. In this paper, we consider
large-scale distributed networks where each node possesses a large number of
p-values and the goal is to achieve the global BH performance in a
communication-efficient manner. We propose that every node performs a local
test with an adjusted test size according to the (estimated) global proportion
of true null hypotheses. With suitable assumptions, our method is
asymptotically equivalent to the global BH procedure. Motivated by this, we
develop an algorithm for star networks where each node only needs to transmit
an estimate of the (local) proportion of nulls and the (local) number of
p-values to the center node; the center node then broadcasts a parameter
(computed based on the global estimate and test size) to the local nodes. In
the experiment section, we utilize existing estimators of the proportion of
true nulls and consider various settings to evaluate the performance and
robustness of our method.
