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SUMMARY:Connecting the False Discovery Rate to shrunk estimates - Nick W G
 alwey (Former Statistics Leader\, Research Statistics\, at GlaxoSmithKline
  Research and Development (Retired))
DTSTART:20260203T191500Z
DTEND:20260203T210000Z
UID:TALK225970@talks.cam.ac.uk
CONTACT:Peter Watson
DESCRIPTION:Science is currently facing a ‘replication crisis’ – a c
 oncern that many scientific findings reported are difficult or impossible 
 to reproduce.   A major cause of this is the availability of technology th
 at permits the exploration and testing of very large numbers of hypotheses
 \, some of which will almost certainly show large or significant effects b
 y chance\, even when no real effects are present: this is the ‘multiplic
 ity’ or ‘multiple testing’ problem.   The statistical tools availabl
 e to address this problem include:\n•	the False Discovery Rate (FDR)\, w
 hich is specified in relation to the subset of the m hypotheses tested for
  which the discovery of an effect is reported\, and which indicates the pr
 oportion of these ‘discoveries’ that is expected to be false\; and\n
 •	shrunk estimates\, which reduce the estimated effect\, in relation to 
 every individual hypothesis\, from the observed value towards the null val
 ue.\nThis talk will first examine the conceptual basis for each of these t
 ools\, then consider how they are connected.   Though the FDR and shrunk e
 stimates are both conventionally presented in the frequentist statistical 
 framework\, they can both also be presented in empirical-Bayesian terms\, 
 the prior probability distribution being calculated from the data relating
  to the m hypotheses tested\, as follows:\n•	in the case of the FDR\, fr
 om the proportion of the m significance tests conducted that give a p-valu
 e at or below the specified significance threshold\, and that are therefor
 e announced as ‘discoveries’\; and\n•	in the case of shrunk estimate
 s\, from the distribution of the observed effect sizes over the m hypothes
 es.\nBased on this connection\, a formal relationship between FDR values a
 nd shrunk estimates will be presented.   It will be argued that these two 
 tools can profitably be used in conjunction\, and their combined applicati
 on\, both to real (human gene expression) data and to simulated data\, wil
 l be illustrated.   \n
LOCATION:MRC Cognition and Brain Sciences Unit\, 15 Chaucer Road\, Cambrid
 ge CB2 7EF
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