Derandomised Knockoffs from E-values
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This note is for Wang, R., & Ramdas, A. (2022). False Discovery Rate Control with E-values. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84(3), 822–852. https://doi.org/10.1111/rssb.12489 and Aaditya’s talk at ISSI on October 25, 2023
e-values have gained attention as potential alternatives to p-values as measures of uncertainty, significance and evidence.
e-values are realized by random variables with expectation at most one under the null
examples:
- betting scores
- (point null) Bayes factors
- likelihood ratios
- stopped supermartingales
the paper designs a natural analog of the BH procedure for FDR control that utilizes e-values, called the e-BH procedure, and compare it with the standard procedure for p-values
one of the central results is that,
- unlike the usual BH procedure, the e-BH procedure controls the FDR at the desired level—with no correction—for any dependence structure between the e-values
BH procedure is a special case of the e-BH procedure through calibration between p-values and e-values