Figures and data
The regime-shift detection task. A. Trial sequence. In each trial, the subjects saw a sequence of red and/or blue signals and were told that these signals were drawn from one of the two regimes, a Red regime and a Blue regime. Both regimes were described as urns containing red and blue balls. The Red regime contained more red balls, while the Blue regime contained more blue balls. Each trial always started at the Red regime but could shift to the Blue regime in any of the 10 periods according to some transition probability (q). At the beginning of a trial, information about transition probability (shown as “switch” probability in the illustration) and signal diagnosticity (shown as “color ratio”) were revealed to the subjects. In this example, the transition probability is 0.1 and signal diagnosticity is 1.5. See main text for more detailed descriptions. B. Manipulation of the system parameters, i.e., transition probability (q) and signal diagnosticity (d). We independently manipulated the q (3 levels) and d (3 levels), resulting in a 3×3 factorial design. C. An example of a particular combination of the system parameters from the 3×3 design. Here the system that produces the signals has q = 0.01 transition probability and d = 1.5 signal diagnosticity. Signals were sequentially presented to subjects. After each new signal appeared (a period), subjects provided a probability estimate (Pt) of a regime shift. D. Two example trials sequences. The example on the left shows the sequence of 10 periods of blue and red signals where d = 1.5 and q = 0.01. In this example, the regime was never shifted. The example on the right shows the sequence of periods where d = 9 and q = .1. In this example, the regime was shifted from the Red to the Blue regime in Period 3 such that the signals shown starting at this period were drawn from the Blue regime. E. We performed three fMRI experiments (30 subjects in each experiment) to investigate the neural basis of regime-shift judgments. Experiment 1 was the main experiment looking at regime shift—which corresponds to P(Change) in the Venn diagram—while Experiments 2 and 3 were the control experiments that ruled out additional confounds. In both Experiments 1 and 2, the subjects had to estimate the probability that signals came from the blue regime. But unlike Experiment 1, in Experiment 2, which corresponds to P(Blue), no regime shift was possible. In Experiment 3, the subjects were simply asked to enter a number with a button-press setup identical to Experiments 1 and 2. Therefore, Experiment 3 (Motor) allowed to rule out motor confounds.
Behavioral results for Experiment 1. A. Illustrations of Over- and underreactions. Left column: stable environment (q = 0.01) with noisy signals (d = 1.5) and the 10 periods of red and blue signals a subject encountered. Right column: unstable environment (q = 0.1) with precise signals (d = 9). Top row: we plot a subject’s actual probability estimates (Pt, solid line) and the normative Bayesian posterior probability (
Neural representations for the updating of beliefs about regime shift. A. An example. Updating is captured by the difference in probability estimates between two adjacent periods (ΔPt). The Blue bars reflect the period probability estimates (Pt), while yellow bars depict ΔPt. B. Whole-brain results on the main experiment (Experiment 1) showing significant brain regions that correlate with the updating of beliefs about change (ΔPt). The clusters in orange represent activity correlated with ΔPt. The blue clusters represent activity correlated with the regime-shift probability estimates (Pt). The magenta clusters represent the overlap between the Pt and ΔPt clusters. C-D. Comparison between experiments. To rule out visual and motor confounds on the Pt results described in B, we compared the Pt contrast between the main experiment (Experiment 1) and two control experiments (Experiments 2 and 3). C. Whole-brain results on the effect of Pt between Experiments 1 and 2 (Experiment 1 – Experiment 2 on the negative Pt contrast). D. Whole-brain results on the effect of Pt between Experiments 1 and 3 (Experiment 1 – Experiment 3 on the negative Pt contrast).
A frontoparietal network represented key variables for regime-shift estimation. A. Variable 1: strength of evidence in favor of/against regime shifts (strength of change evidence), as measured by the interaction between signal diagnosticity and signal. Left: two examples of the interaction between signal diagnosticity (d) and sensory signal (s), where a blue signal is coded as 1 and a red signal is coded as -1. The x-axis represents the time periods, from the first to the last period, in a trial. The y-axis represents the interaction, ln(d) × A. Right: whole-brain results showing brain regions in a frontoparietal network that significantly correlated with ln(d) × A. B. Variable 2: intertemporal prior probability of change. Two examples of intertemporal prior are shown on the left graphs. To examine the effect of the intertemporal prior, we performed independent region-of-interest analysis (leave-one-subject-out, LOSO) on the brain regions identified to represent strength of evidence (5A). Due to the LOSO procedure, individual subjects’ ROIs (a cluster of contiguous voxels) would be slightly different from one another. To visualize such differences, we used the red color to indicate voxels shared by all individual subjects’ ROIs, and orange to indicate voxels by at least one subject’s ROI. The ROI analysis examined the regression coefficients (mean PE) of intertemporal prior. The * symbol indicates p < .05, ** indicates p < .01. dmPFC: dorsomedial prefrontal cortex; lIPS: left intraparietal sulcus; rIPS: right intraparietal sulcus; lIFG: left inferior frontal gyrus; rIFG: right inferior frontal gyrus.
Estimating and comparing neural measures of sensitivity to system parameters with behavioral measures of sensitivity. A. Behavioral measures of sensitivity to system parameters. For each system parameter, we plot the subjectively weighted system parameter against the system parameter level (top row: signal diagnosticity; bottom row: transition probability). For each subject and each system parameter, we estimated the slope (how the subjectively weighted system parameter changes as a function of the system parameter level) and used it as a behavioral measure of sensitivity to the system parameter (behavioral slope). We also show a Bayesian (no system neglect) decision maker’s slope (dark green) and the slope of a decision maker who completely neglects the system parameter (in light green; the slope would be 0). A subject with stronger neglect would have a behavioral slope closer to complete neglect. B. Comparison of behavioral and neural measures of sensitivity to the system parameters. To estimate neural sensitivity, for each subject and each system parameter, we regressed neural activity of a ROI against the parameter level and used the slope estimate as a neural measure of sensitivity to that system parameter (neural slope). We also estimated the neural slope separately for blue-signal periods (when the subject saw a blue signal) and red-signal periods. We computed the Pearson correlation coefficient (B) between the behavioral slope and the neural slope and used it to statistically test whether there is a match between the behavioral and neural slopes. C. The frontoparietal network selectively represented individuals’ sensitivity to signal diagnosticity (left two columns), but not transition probability (right two columns). Further, neural sensitivity to signal diagnosticity (neural slope) correlated with behavioral sensitivity (behavioral slope) only when a signal in favor of potential change (blue) appeared: all the regions except the right IPS showed statistically significant match between the behavioral and neural slopes. By contrast, sensitivity to transition probability was not represented in the frontoparietal network. D. The vmPFC selectively represented individuals’ sensitivity to transition probability (r = −0.38, p = 0.043 for red signals; r = −0.37, p = 0.047 for blue signals), but not signal diagnosticity (r = 0.28, p = 0.13 for red signals; r = 0.26, p = 0.17 for blue signals). The ventral striatum did not show selectivity to either transition probability or signal diagnosticity. Error bars represent ±1 standard error of the mean.
fMRI results revealed hidden properties of the system-neglect model: sensitivity to signal diagnosticity was signal-dependent, but sensitivity to transition probability was not. A. Signal diagnosticity parameter. Pearson correlation coefficient (r) between model-based behavioral slopes and model-free behavioral slopes estimated in response to red signals (left graph) and blue signals (right graph). Each data point represents a single subject. B. Transition probability parameter. Pearson correlation (r) between model-based behavioral slopes and model-free behavioral slopes estimated at the red signals (left graph) and blue signals (right graph). Each data point in the graph represents a single subject. C-D. Same analysis as in Fig. 6AB but using simulated probability estimation data. C. Signal diagnosticity parameter. D. Transition probability parameter.
