Fig. 2: Model fitting and simulation of participants’ adaptive performances.

A Bayesian model comparison given participants’ choices across the third-/second-order volatility inference model, Weber-variability model, and best-fitting RL model (noisy RW-RL, Supplementary Fig. 2). Bars show exact model posterior probabilities over the n = 22 participants (“Methods” section). Model exceedance probabilities are shown in brackets. Error bars: Bayesian estimates of model posterior probability standard deviations. The Weber-variability model fitted decisively better than the other models. B Confusion matrices from the model recovery procedure across the same models. Large matrix: exact model posterior probability given models’ simulated performances; small matrix: model exceedance probability. Each model fitted its own simulated performance in the task decisively better than the other models. C simulations of fitted model performances compared to participants’ performances around reversals in high volatility episodes. Shaded areas: s.e.m. across participants. Statistically significant differences (two-sided T-tests over three consecutive trials, d.f. = 21) are shown. Left: *p = 0.029, ****p = 0.000051; middle left: **p = 0.0098, ****p = 0.000952; middle right: all ps > 0.09. Right: all ps < 0.000015. Only the Weber-variability model reproduced participants’ choices with no significant deviations. Note that the best RL model (noisy RW-RL) dramatically failed (see Supplementary Note 1 for explanation). Source data are provided as a Source Data file.