Panel A depicts the raw difference \(D_{g}=Y_{g_{1}}-Y_{g_{2}}\) for \(20,000\) genes, suggesting that the variance of \(D_{g}\) increases as the mean \(\mu_{g}\) increases; hence, there is no uniform cutoff to differentiate DEGs and null genes. Panel B illustrates that, for null genes, VST makes the variance of \(D^{*}_{g}=h_{Pois}(Y_{g1})-h_{Pois}(Y_{g2})\) constant regardless of their expression mean \(\mu_{g}\). Panel C illustrates the marginal distribution and the empirical null distribution computed for calculating fdr; where the purple solid line represents marginal density of \(Z_{g}\), scaled to overlay the histogram; the orange dashed line displays the empirical null distribution of \(Z_{g}\), and the two triangles are located at the decision boundary for calling DEGs. Panel D represents the probability of a gene being null given \(z_{g}\) (the solid curve), and the red dashed line displays the cutoff (local \(\mbox{fdr}\leq 0.2\)) for defining a DEG.