Suppose one chose a single SNP at random, tested for association to a trait and obtained a P–value of exactly 0.05. As one test was performed, no correction for multiplicity is required, and from the frequentist perspective one may reject the hypothesis that no SNP is associated and invoke the closure principle to claim that the tested SNP is associated [Hochberg and Tamhane, 1987]. However, this is clearly absurd, as there was almost no prior reason to expect an association. In fact at standard error rates of α = 0.05 and Beta = 0.2, one would require prior odds of 2:1 against to obtain posterior odds of 8:1 in favor of association, or prior odds of evens to obtain posterior odds of 16:1. Usage of standard frequentist thresholds is only justified when the prior odds are in this order of magnitude, say between evens and 10:1 against.
