# SAFFRON and LORD Ensure Online Control of the False Discovery Rate Under Positive Dependence

@inproceedings{Fisher2021SAFFRONAL, title={SAFFRON and LORD Ensure Online Control of the False Discovery Rate Under Positive Dependence}, author={Aaron J. Fisher}, year={2021} }

Online testing procedures assume that hypotheses are observed in sequence, and allow the significance thresholds for upcoming tests to depend on the test statistics observed so far. Some of the most popular online methods include alpha investing, LORD++ (hereafter, LORD), and SAFFRON. These three methods have been shown to provide online control of the “modified” false discovery rate (mFDR). However, to our knowledge, they have only been shown to control the traditional false discovery rate…

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## References

SHOWING 1-10 OF 23 REFERENCES

Online control of the false discovery rate with decaying memory

- Computer Science, MathematicsNIPS
- 2017

A new quantity called the decaying memory false discovery rate (mem-FDR) is defined that may be more meaningful for truly temporal applications, and which alleviates problems that are described and refer to as "piggybacking" and "alpha-death".

On Online Control of False Discovery Rate

- Mathematics, Computer ScienceArXiv
- 2015

This work is the first that controls FDR in this setting and develops lower bounds on the total discovery rate under the mixture model and proves that both LOND and LORD have nearly linear number of discoveries.

THE CONTROL OF THE FALSE DISCOVERY RATE IN MULTIPLE TESTING UNDER DEPENDENCY

- Mathematics
- 2001

Benjamini and Hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems. A simple procedure was given there as an FDR…

Online Rules for Control of False Discovery Rate and False Discovery Exceedance

- Mathematics, Computer ScienceArXiv
- 2016

A class of "generalized alpha-investing" procedures are studied and it is proved that any rule in this class controls online FDR, provided $p-values corresponding to true nulls are independent from the other $p$-values, as well as a modified set of procedures that also allow to control the false discovery exceedance.

Controlling the Proportion of False Positives in Multiple Dependent Tests

- Biology, MedicineGenetics
- 2004

An approach based on controlling the proportion of false positives (PFP) among all positive test results and estimated PFP, FDR, pFDR, and GWER through simulation under a variety of models to illustrate practical and philosophical similarities and differences among the methods.

Online control of the familywise error rate

- Mathematics, MedicineStatistical methods in medical research
- 2021

The main contribution is the design of new, powerful, adaptive online algorithms that control the familywise error rate when the p-values are independent or locally dependent in time.

Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach

- Mathematics
- 2004

Summary. The false discovery rate (FDR) is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses. Benjamini and…

Contextual Online False Discovery Rate Control

- Computer Science, MathematicsAISTATS
- 2020

A new class of powerful online testing procedures are proposed, where the rejections thresholds are learnt sequentially by incorporating contextual information and previous results, and it is proved that any rule in this class controls online FDR under some standard assumptions.

SAFFRON: an adaptive algorithm for online control of the false discovery rate

- Mathematics, Computer ScienceICML
- 2018

This work presents a powerful new framework for online FDR control that is seen as an online analogue of the famous offline Storey-BH adaptive procedure, and demonstrates that SAFFRON is also more powerful than its non-adaptive counterparts, such as LORD and other generalized alpha-investing algorithms.

α-investing: a procedure for sequential control of expected false discoveries

- Mathematics
- 2008

"a"-investing is an adaptive sequential methodology that encompasses a large family of procedures for testing multiple hypotheses. All control mFDR, which is the ratio of the expected number of false…