Supplementary Figure 7: Evidence that the repulsion zone is located where the density of the prior is highest (adapted from Fig. 3c).

Empirical biases (points, n = 24) are color-coded as a function of the prior density resulting from our model predictions (see Supplementary Fig. 2). The repulsion zone corresponds to the area where the density is highest, with the bias crossing the x-axis at the highest-density point of the prior. This is line with the prediction of previous work (Wei and Stocker, 2015) that in the case of unimodal priors, repulsion should take place in the vicinity of the prior mode (note that we assume a logistic distribution in our study, which is in indeed a unimodal density function). We also show that the prior starts to exert attraction once the wider likelihood in the high noise regime is located away from the peak of the prior. This is a phenomenon expected based on classical Bayesian frameworks. This difference to the work by Wei & Stocker may reflect that their earlier studies did not consider (near-)boundary effects on non-circular scales, as we considered in our simulations. Error bars in this figure represent s.e.m. across participants. The data of each participant is shown in main text Fig. 3c. Wei, X.-X., and Stocker, A.A. (2015). A Bayesian observer model constrained by efficient coding can explain ’anti-Bayesian’ percepts. Nat. Neurosci. 18, 1509–1517.