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tokens: (1) perturb the previous step to propose a new set of parameters θ * drawn from the prior; (2) use fleck to compute the smoothed-amplitude distribution for a large sample of stars, (3) for use as a summary statistic, we compute the two-sample Anderson–Darling statistic A 2 for comparing how close the trial smoothed-amplitude distribution is to the observed one (Anderson Darling 1952 ; Scholz Stephens 1987 , see discussion in Appendix 6); (4) if , we accept the proposed step and add it to our chain; (5) go back to step (1), and repeat. We select , not far from the minimum value of the Anderson–Darling statistic . The approximate posterior distributions produced by ABC should approach the true posterior distributions in the limit that , provided that the Anderson–Darling statistic is a sufficient statistic. In practice it is difficult to prove that a statistic is sufficient, so we note that the posterior distributions shown here are valid given the hypothesis that the Anderson–Darling statistic is a sufficient one. The posterior distributions from the ABC analysis illustrate the three-way degeneracy between starspot latitudes, radii, and contrasts for stars with unknown inclinations. For a fixed number of spots, small spots spread randomly over all latitudes generate rotational modulations similar to larger spots concentrated near the poles. Similarly, small spots with extreme intensity contrasts () reproduce similar rotational modulations to larger spots with less extreme spot contrasts (). This exercise is a demonstration of why it is so difficult to invert light curves of rotational modulation and recover unique starspot properties—a wide range of spot parameters can produce similar light curves. Figure 6 shows the simulated smoothed-amplitude distributions (gray histograms) with spot parameters drawn randomly from the posterior distributions, compared with the observed smoothed-amplitude distribution for stars in each association (colored histograms). This figure illustrates how the ABC algorithm minimized the Anderson–Darling statistic between the simulated and observed smoothed-amplitude distributions. Most simulated and observed distributions are statistically indistinguishable according to the Anderson–Darling statistic. Figure 6. Observed smoothed light-curve amplitude distributions (colored histograms) compared with simulated smoothed-amplitude distributions (gray) drawn from the posterior distributions for the spot parameters from the ABC technique with fleck. The goal of the ABC technique is to search for starspot parameters that produce simulated smoothed-amplitude distributions that are statistically indistinguishable from the observations. The poorest “fit” is M67, the oldest cluster, for which the simulations produce a more strongly peaked smoothed-amplitude distribution near 0.5%. The lack of a peak in the observed smoothed-amplitude distribution for M67 is likely real; observational bias in favor of detecting large