  The ability to identify reliably a positive or negative partial correlation
between the expression levels of two genes is influenced by the number $p$ of
genes, the number $n$ of analyzed samples, and the statistical properties of
the measurements. Classical statistical theory teaches that the product of the
root sample size multiplied by the size of the partial correlation is the
crucial quantity. But this has to be combined with some adjustment for
multiplicity depending on $p$, which makes the classical analysis somewhat
arbitrary. We investigate this problem through the lens of the Kullback-Leibler
divergence, which is a measure of the average information for detecting an
effect. We conclude that commonly sized studies in genetical epidemiology are
not able to reliably detect moderately strong links.
