Fig. 5: POMDP model explains the hard-easy effect and the opposing effect of a sudden change in stimulus variability on accuracy and confidence.
a The hard-easy effect. Uncertainty about the strength of observed evidence makes the model more confident than warranted by accuracy on hard trials and less confident than warranted by accuracy on easy trials (compare blue and red curves). The psychometric and predicted confidence functions for subjects M1 and M2 are adopted from Fig. 4a, b. Error bars indicate standard error of the mean (s.e.m.). Data points are the same as in the motion strength plots in Fig. 1b. b While the major reason for the hard-easy effect is marginalization over coherence by the decision maker, our POMDP model also predicts a small underconfidence bias (red curve) compared to using a generative model (black curve) that assumes the exact set of coherence levels in the experiment is given. c–e Sudden increase in stimulus variability following training with lower stimulus variability reduces accuracy (c) but boosts confidence (d) and decreases the probability of sure-bet selection (e), or equivalently, increases the probability of sure-bet rejection. This dissociation occurs because the model relies on the observation noise learned during the lower-variability training period to render choices on the subsequent higher variability trials. f The increase in the probability of sure-bet rejection after a sudden increase in stimulus variability is illustrated here for two trials with the same coherence and duration but different stimulus variability. Distributions of the sum of observations for low (black Gaussian curve) and high variability (gray Gaussian curve) intersect at two points (red dotted lines). A high sure-bet rejection threshold on confidence (e.g., 85% in this example) learned during training with low variability stimuli maps to two thresholds (dotted black lines) on the sum of observations that fall outside of the intersection points. Given these fixed thresholds, the probability of sure-bet rejection is higher (larger blue filled areas under the curve) when stimulus variability is suddenly increased. This explanation is consistent with ideas presented in previous work16,28,53.
