Fig. 3: Empirical characteristics of Weber variability.

A Bayesian model comparison given participants’ choices (computed over the n = 22 participants) when models comprise no choice history accounts (left, same data as in Fig. 2A), comprise repetition biases (middle) and choice trace biases (right). Bars show exact model posterior probabilities. Model exceedance probabilities are shown in brackets. Error bars: Bayesian estimates of model posterior probability standard deviations. In every case, the Weber-variability model fitted decisively better than the other models, indicating that fitted Weber variability was unrelated to such choice history effects. B One-way ANOVA of best-fitting realizations \({U}_{{fit}}^{t}\) of Weber variability stochastic component \({u}_{t}\) over the n = 22 participants and factoring choice history from trial t-3 to t-1 (Switch vs. Repeat responses relative to preceding trials) into an 8-level fixed-effect factor. Bars show the means over participants. Error bars are s.d. across trials within participants. The choice history factor accounted for only η² = 17% of \({U}_{{fit}}^{t}\) total variance, indicating that 83% of \({U}_{{fit}}^{t}\) total variance was unrelated to any three-fold choice history. C autocorrelations of best-fitting realizations \({U}_{{fit}}^{t}\) of Weber variability stochastic components \({u}_{t}\) across successive trials averaged over participants (n = 22). These realizations \({U}_{{fit}}^{t}\) showed virtually no autocorrelations (all R² < 0.005). Bars and error bars are mean ± s.e.m. over the n = 22 participants. D Empirical distribution of best-fitting realizations \({U}_{{fit}}^{t}\) across trials and participants. Prior generative distribution \({u}_{t}\) is uninformative, i.e., uniform over [0;1]. The posterior distribution is obtained from marginalizing over parameter spaces and particle trajectories from particle filters (see “Methods” section). Note that this empirical posterior distribution is approximately Gaussian, centered on its mean 0.5, as expected from averaging over a series of independent random variables. E Mean ± s.d. (over the n = 22 participants) of empirical best-fitting realizations \({U}_{{fit}}^{t}\) distributions along experimental blocks (scanning runs) and fMRI sessions. Note the lack of any temporal order effects (F(5,105) = 1.737, p = 0.1544). Source data are provided as a Source Data file.