The plot at the left in Figure Suppl. I. 1 shows the Poisson distributions P (z| y) with mean and variance y= 0.1, 0.5, 1, 1.5, 2. At the right, we show the distributions P (λ− 2 i zi| y)(Equation 2 in the manuscript) of the data obtained after the convex combination with λ= 0.2. Note how the convex combination results in a shift of the distributions towards higher mean values and how the overlap between different distributions is reduced. Because of this reduced overlap, different distribution can benefit from the different slopes of the Anscombe transformation at the corresponding locations; this leads to a significantly more accurate stabilization. In particular, in the legends we report the standard deviations of the stabilized distributions, which for the combined data is much closer to the target value 1.