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.
Licgen tools are historically used to generate product keys, license files, or activation tokens. Version identifiers like “2011.64” often indicate:
Based on naming patterns, “Efa” may refer to: Efa Licgen 2011.64
Short-term:
Long-term:
This is a crucial distinction from the standard FDR.
Efron defines the local FDR as: $$fdr(z) = \fracp_0 f_0(z)f(z)$$ Traditional statistics (like the t-test or p-value) were
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.
Based on the name similarity and the date format (which resembles a standard citation format like volume.year or year.volume), it is highly probable that you are looking for the paper: Based on naming patterns, “Efa” may refer to:
"Size, Power, and False Discovery Rates" by Bradley Efron. Published in The Annals of Applied Statistics, 2007, Vol. 1, No. 1, 1-28. (Note: "2011.64" might be a specific repository ID, a typo for the volume/year, or a reference to a later follow-up, but the phonetic similarity "Efa" -> "Efron" is the strongest lead).
Here is a deep analysis of the core concepts found in Efron’s work on this topic, specifically focusing on the False Discovery Rate methodologies that defined his work in that era.