ADDIS {onlineFDR} | R Documentation |
Implements the ADDIS algorithm for online FDR control, where ADDIS stands for an ADaptive algorithm that DIScards conservative nulls, as presented by Tian and Ramdas (2019). The algorithm compensates for the power loss of SAFFRON with conservative nulls, by including both adapativity in the fraction of null hypotheses (like SAFFRON) and the conservativeness of nulls (unlike SAFFRON).
ADDIS(pval, alpha = 0.05, gammai, w0, lambda = 0.5, tau = 0.5, async = FALSE, decision.times)
pval |
A vector of p-values. |
alpha |
Overall significance level of the procedure, the default is 0.05. |
gammai |
Optional vector of γ_i. A default is provided with γ_j proportional to 1/j^(1.6). |
w0 |
Initial ‘wealth’ of the procedure, defaults to τ λ α/2. |
lambda |
Optional parameter that sets the threshold for ‘candidate’ hypotheses. Must be between 0 and 1, defaults to 0.5. |
tau |
Optional threshold for hypotheses to be selected for testing. Must be between 0 and 1, defaults to 0.5. |
async |
Logical. If |
decision.times |
A vector of decision times for the hypothesis tests,
this is required if |
The function takes as its input a vector of p-values. Given an overall significance level α, ADDIS depends on constants w_0 λ and τ. w_0 represents the intial ‘wealth’ of the procedure and satisfies 0 ≤ w_0 ≤ τ λ α. τ \in (0,1) represents the threshold for a hypothesis to be selected for testing: p-values greater than τ are implicitly ‘discarded’ by the procedure. Finally, λ \in (0,1) sets the threshold for a p-value to be a candidate for rejection: ADDIS will never reject a p-value larger than τ λ. The algorithm also require a sequence of non-negative non-increasing numbers γ_i that sum to 1.
The ADDIS procedure provably controls the FDR for independent p-values. Tian
and Ramdas (2019) also presented a version for an asynchoronous testing
process, consisting of tests that start and finish at (potentially) random
times. The discretised finish times of the test correspond to the decision
times. These decision times are given as the input decision.times
.
Further details of the ADDIS algorithms can be found in Tian and Ramdas (2019).
d.out |
A dataframe with the original p-values |
Tian, J. and Ramdas, A. (2019). ADDIS: an adaptive discarding algorithm for online FDR control with conservative nulls. arXiv preprint, https://arxiv.org/abs/1905.11465.
ADDIS is identical to SAFFRON
with option discard=TRUE
.
ADDIS with option async=TRUE
is identical to SAFFRONstar
with option discard=TRUE
.
pval = c(2.90e-08, 0.06743, 3.51e-04, 0.0154, 0.04723, 3.60e-05, 0.79149, 0.27201, 0.28295, 7.59e-06, 0.69274, 0.30443, 0.00136, 0.82342, 0.54757) ADDIS(pval) ADDIS(pval, async=TRUE, decision.times=seq_len(15)) # Same as above ADDIS(pval, async=TRUE, decision.times=seq_len(15)+1) # Asynchronous