## a Bayesian interpretation of FDRs?

**T**his week, I happened to re-read John Storey’ 2003 “The positive discovery rate: a Bayesian interpretation and the q-value”, because I wanted to check a connection with our testing by mixture [still in limbo] paper. I however failed to find what I was looking for because I could not find any Bayesian flavour in the paper apart from an FRD expressed as a “posterior probability” of the null, in the sense that the setting was one of opposing two simple hypotheses. When there is an unknown parameter common to the multiple hypotheses being tested, a prior distribution on the parameter makes these multiple hypotheses connected. What makes the connection puzzling is the assumption that the observed statistics defining the significance region are *independent* (Theorem 1). And it seems to depend on the choice of the significance region, which should be induced by the Bayesian modelling, not the opposite. (This alternative explanation does not help either, maybe because it is on baseball… Or maybe because the sentence “If a player’s [posterior mean] is above .3, it’s more likely than not that their true average is as well” does not seem to appear naturally from a Bayesian formulation.) *[Disclaimer: I am not hinting at anything wrong or objectionable in Storey’s paper, just being puzzled by the Bayesian tag!]*

April 13, 2018 at 6:23 pm

You might want to look at Jon Wakefield’s 2007 paper on the Bayesian probability of false discovery (BFDP).

https://dx.doi.org/10.1086%2F519024