Suboptimal human inference can invert the bias-variance trade-off for decisions with asymmetric evidence
Fig 6
More complex but suboptimal human strategies exhibited more bias.
a. Mutual information (MI) between the number of rare balls in a sample (|ξ|), the sample length (n), and the response (r) for each subject and block. b. Accuracy versus MI (computed as bootstrapped means from 1000 iterations per subject) for the Hard Asymmetric (HA) and Easy Asymmetric (EA) blocks. Dots represent data from individual subjects, color coded by subject’s best-fitting model described in Fig 4D. Black line represents the accuracy bound (the maximum accuracy attainable by the idea observer for a fixed MI in the limit of many trials). The dashed horizontal lines indicate the accuracy bound for maximum MI values. Note that points could exceed the asymptotic accuracy bound because the number of trials for each subject was finite. Median values for the Nearly Ideal, Mistuned Bayesian and Heuristic subject groups are indicated with triangles. In each case, filled Mistuned Bayesian and Heuristic triangles denote statistically significant differences in MI from the nearly ideal group (p < 0.05) based on a Wilcoxon rank-sum test. Median values for all 3 groups showed increase in both accuracy and MI ranking from lowest (Heuristic), middle (Mistuned Bayesian), highest (Nearly Ideal). c- d. Relationship between estimated bias (c) and variance (d) from the fit psychometric function for each subject and MI, triangles represented as in b based on statistically significant differences in bias or variance. e. Algorithmic complexity for each model. Bayesian models shown as the mean algorithmic complexity across sample lengths.