Suboptimal human inference can invert the bias-variance trade-off for decisions with asymmetric evidence
Fig 5
Increased bias and variance in asymmetric blocks corresponded to Bayesian subject model fits with mistuned parameters and heuristic subject model fits, respectively.
a. Left: Hard Asymmetric (HA) and Easy Asymmetric (EA) block bias-variance plots from Fig 3E and 3F, color-coded according to each subject’s best-fitting model described in Fig 4D. Triangles denote median values for the bias-variance fits for: 1) Nearly Ideal subjects (best fit by “Noisy Bayesian Set ρ” model), 2) Mistuned Bayesian subjects (best fit by “Noisy Bayesian” or “Prior Bayesian” models), 3) Heuristic subjects (best fit by “Variable Rare”, “Rare Ball”, or “Guess” models). Mistuned Bayesian and Heuristic groups that significantly (not significantly) differ from the Nearly Ideal group are denoted by filled (open) triangles based on a Wilcoxon rank-sum test with p < 0.05. Right: Group bootstrapped means (1000 iterations) and 95% confidence intervals for low-jar responses. Statistically significant differences between groups (two-sided t-test with unequal variance, p < 0.05) are noted with an asterisk. b. Estimated subject bias obtained from best–fit psychometric functions compared with the maximum-likelihood estimate (MLE) of the rare-ball weight, ρ, for subjects best fit by the Noisy Bayesian model in asymmetric blocks (dots, EA-grey, HA-black). Regression lines are shown for group-blocks with significant correlations (Spearman correlations, p < 0.05). Vertical lines indicating the rare-ball weights used by the ideal observer for each asymmetric block and symmetric blocks (orange) are included for reference. c. Estimated subject bias from fit psychometric functions compared with the MLE of the response bias (Prior) for subjects best fit to the Prior Bayesian model in the asymmetric block (marker legend as in b). Negative values correspond to a bias in favor of the low jar.