Fig 4. Behavioral results, quantitative analysis across participants (n = 12).

To analyze the relation between these behavioral data with the predictions made by models, we first looked at the variability of all these measures conditioned on the predicted probability and gathered over 5 equal partitions of the [0, 1] probability segment. For the 12 participants, we collected an estimate of (A) the amplitude of anticipatory pursuit (aSPEM) and (B) the bet score value. As a regressor, we have used the true probability ($P_{\mathrm{\text{true}}}=x_1^t$, blue color), and the probability bias estimates obtained with a leaky integrator (P_leaky, orange color) and by the BBCP model (P_BBCP, green color). We display these functional relations using an error-bar plot showing the median with .25 and .75 quantiles over the 5 partitions. This shows a monotonous dependency for both behavioral measures with respect to the probability, close to a linear regression, but with different strengths. Second, we summarize in insets quantitative measures of the strength of this dependence for each participant individually, by computing the squared Pearson correlation coefficient r² and the mutual information (MI). Dots correspond to these measures for each individual observer, while the bar gives the median value over the population. This confirms quantitatively that for both experimental measures, there is a strong statistical dependency between the behavioral results and the prediction of the BBCP model, but also that this dependency is significantly stronger than that obtained with the true probability and with the estimates obtained with the leaky integrator (stars denote significative differences, see text for details).