Simulated sample means and their errors as a function of sample size S (points) for the yearly sample. The last point (filled triangle) is the simulation for N points. The shaded areas mark the 68.3% (red), 95.4% (orange), and 99.7% (yellow) confidence intervals for IDC_sim (see Sect. 3) and from Eq. (7) (dark green, green, light green, respectively; see Table 1 in the case of a uninformative prior, a = b = 1).