Perhaps the most controversial and impactful contribution of this paper is the concept of the Empirical Null.
Efron argues that in real-world large-scale testing, the theoretical null distribution (often $N(0,1)$) is often wrong.
Possible intended references:
This is a crucial distinction from the standard FDR.
Efron defines the local FDR as: $$fdr(z) = \fracp_0 f_0(z)f(z)$$ Efa Licgen 2011.64
In plain English: It is the ratio of the null curve height to the observed data curve height at point $z$. If the null curve is much higher than the observed mixture curve, the $fdr$ is high, meaning that z-score is likely just noise. If the observed curve is much higher, the $fdr$ is low, indicating a likely discovery.
Traditional statistics (like the t-test or p-value) were designed for single hypothesis testing. However, in the era of genomics (microarrays, RNA-seq) and large-scale data mining, researchers often test thousands of hypotheses simultaneously. Perhaps the most controversial and impactful contribution of
The paper essentially created the field of Large-Scale Inference.