Let ˜ π$_{0}$ ( λ ) with a tuning parameter λ ∈ [0 , 1) be an estimator of π$_{0}$ such that ˜ π$_{0}$ ( λ ) ranges in [0 , 1]. We define a “Storey-type FDR estimator” as For α ∈ [0 , 1], let and the decision rule based on ˜ F DR$_{λ}$ The procedure defined by (1) and (3) is called a “Storey-type FDR procedure”. A Storey-type FDR procedure allows the use of various estimators of π$_{0}$ and is very versatile. For example, (i) it is Storey’s procedure when ˜ π$_{0}$ ( λ ) in (1) is the estimator in Storey et al. (2004); (ii) it is the generalized FDR procedure in Chen and Doerge (2014), designed for multiple testing based on discrete p-values, when ˜ π$_{0}$ ( λ ) is the estimator of π$_{0}$ proposed there and further studied in Chen and Doerge (2015); (iii) it is the BH procedure in Benjamini and Hochberg (1995) when λ = 0 is set in (4) in Storey’s procedure or ˜ π$_{0}$ ( λ ) ≡ 1 is set; (iv) it is a “dynamic adaptive FDR procedure” studied in Liang and Nettleton (2012) when λ in (4) is determined from the p-values and can be a random variable. For notational simplicity, we will from now on write t$_{α}$ ( ˜ F DR$_{λ}$ ) as ˜ t$_{α}$ ( λ ). Define the backward filtration 3 3 Stopping time property of the rejection threshold ˜ F DR$_{λ}$ ( t ) = min { 1 , ˜ π$_{0}$ ( λ ) t m − $^{1}$max { R ( t ) , 1 } } for t ∈ [0 , 1] . (1) t$_{α}$ ( ˜ F DR$_{λ}$ ) = sup { t ∈ [0 , 1] : ˜ F DR$_{λ}$ ( t ) ≤ α } (2) claim H$_{i}$ as a false null ⇐⇒ p$_{i}$ ≤ t$_{α}$ ( ˜ F DR$_{λ}$ ) . (3) ˆ π$_{0}$ ( λ ) = min { 1 , (1 − λ ) − 1 m − 1 ∑ m i $_{=1}$1$_{{}$$_{p}$$_{i}$$_{>λ}$$_{}}$ } (4) F$_{t}$ = σ ( 1$_{{}$$_{p}$$_{i}$$_{≤}$$_{s}$$_{}}$ , t ≤ s ≤ 1 , i = 1 , ..., m ) (5)