A sequential algorithm for false discovery rate control on directed acyclic graphs

&NA; We propose a linear‐time, single‐pass, top‐down algorithm for multiple testing on directed acyclic graphs, where nodes represent hypotheses and edges specify a partial ordering in which the hypotheses must be tested. The procedure is guaranteed to reject a sub‐directed acyclic graph with bounded false discovery rate while satisfying the logical constraint that a rejected node's parents must also be rejected. It is designed for sequential testing settings where the directed acyclic graph structure is known a priori but the p‐values are obtained selectively, such as in a sequence of experiments; however, the algorithm is also applicable in nonsequential settings where all p‐values can be calculated in advance, such as in model selection. Our algorithm provably controls the false discovery rate under independence, positive dependence or arbitrary dependence of the p‐values and specializes to known algorithms in the special cases of trees and line graphs; it simplifies to the classical Benjamini‐Hochberg procedure when the directed acyclic graph has no edges. We explore the empirical performance of our algorithm through simulations and analysis of a real dataset corresponding to a gene ontology, and we demonstrate its favourable performance in terms of computational time and power.