Shrinkage estimation of dispersion. Plot of dispersion estimates over the average expression strength (A) for the Bottomly et al.  dataset with six samples across two groups and (B) for five samples from the Pickrell et al.  dataset, fitting only an intercept term. First, gene-wise MLEs are obtained using only the respective gene’s data (black dots). Then, a curve (red) is fit to the MLEs to capture the overall trend of dispersion-mean dependence. This fit is used as a prior mean for a second estimation round, which results in the final MAP estimates of dispersion (arrow heads). This can be understood as a shrinkage (along the blue arrows) of the noisy gene-wise estimates toward the consensus represented by the red line. The black points circled in blue are detected as dispersion outliers and not shrunk toward the prior (shrinkage would follow the dotted line). For clarity, only a subset of genes is shown, which is enriched for dispersion outliers. Additional file 1: Figure S1 displays the same data but with dispersions of all genes shown. MAP, maximum a posteriori; MLE, maximum-likelihood estimate.