Fig. 4. Predicting reaction times for individual subjects.

a–f Estimated parameters and accuracy analysis for our maximum entropy model across 358 random walk sequences (across 286 subjects; Methods). a For the inverse temperature β, 40 sequences corresponded to the limit β → ∞, 73 corresponded to the limit β → 0. Among the remaining 245 sequences, the average value of β was 0.30. b Distributions of the intercept r₀ (left) and slope r₁ (right). c Predicted reaction time as a function of a subject’s internal anticipation. Gray lines indicate 20 randomly selected sequences, and the red line shows the average prediction over all sequences. d Linear parameters for the third-order competing model; data points represent individual sequences and bars represent averages. e, f Comparing the performance of our maximum entropy model with the hierarchy of competing models up to third-order. Root mean squared error (RMSE; e) and Bayesian information criterion (BIC; f) of our model averaged over all sequences (dashed lines) compared to the competing models (solid lines); our model provides the best description of the data across all models considered. g–j Estimated parameters and accuracy analysis for our maximum entropy model across all Hamiltonian walk sequences (120 subjects). g For the inverse temperature β, 20 subjects were best described as performing maximum likelihood estimation (β → ∞), 19 lacked any notion of the transition structure (β → 0), and the remaining 81 subjects had an average value of β = 0.61. h Distributions of the intercept r₀ (left) and slope r₁ (right). i Average RMSE of our model (dashed line) compared to that of the competing models (solid line); our model maintains higher accuracy than the competing hierarchy up to the second-order model. j Average BIC of the maximum entropy model (dashed line) compared to that of the competing models (solid line); our model provides a better description of the data than the second- or third-order models. Source data are provided as a Source Data file.