Figures and data in Regime shift detection and neurocomputational substrates for under and overreactions to change | eLife

Figures
Additional files

9 figures and 14 additional files

Figures

Figure 1

Download asset Open asset

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, that is 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 a $q = 0.01$ 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 ( $P_{t}$ ) 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 $P (C h a n g e)$ 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 $P (B l u e)$ , 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 us to rule out motor confounds.

Figure 2

Download asset Open asset

Behavioral results.

(A) Probability estimates ( $P_{t}$ ) from all subjects are plotted as histograms separately for each condition—a combination of transition probability and signal diagnosticity. The blue bars represent the actual probability estimates, while the orange bars correspond to the probability estimates predicted by the Bayesian model. (B) 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 ( $P_{t},$ solid line) and the normative Bayesian posterior probability ( $P_{t}^{B},$ dashed line). Bottom row: belief revision shown by the subject ( $Δ P_{t} = P_{t}, - P_{t - 1},$ solid line) and the Bayesian belief revision ( ${Δ P}_{t}^{B},$ dashed line). The orange bars represent $Δ P_{t} - Δ P_{t}^{B}$ , which we define as the Index of Overreaction ( $I O$ ; vertical axis in orange on the right). (C) Over- and underreactions to change (Experiment 1). The mean $I O$ (across all 30 subjects) is plotted as a function of transition probability and signal diagnosticity. Subjects overreacted to change if $I O > 0$ and underreacted if $I O < 0$ . (D) Parameter estimates of the system-neglect model (Experiment 1). Left graph: Weighting parameter (α) for transition probability. Right graph: Weighting parameter (β) for signal diagnosticity. Dashed lines indicate parameter values equal to 1, which is required for Bayesian updating. (E) Parameter estimates of the system-neglect model (Experiment 2). Weighting parameter (β) for signal diagnosticity in the system-neglect model. (F) Correlation between α and β estimates at different levels of transition probability ( $q_{1}$ to $q_{3}$ ) and signal diagnosticity ( $d_{1}$ to $d_{3}$ ). All pairwise Pearson correlation coefficients (indicated by the values on the table that were also color coded) were not significantly different from 0 (p > 0.05). (G) Pearson correlation coefficients of $α$ estimates between different levels of transition probability. All pairwise correlations were significantly different from 0 (p < 0.05). (H) Pearson correlation coefficients of β estimates between different levels of signal diagnosticity. All pairwise correlations were significantly different from 0 (p < 0.05). Error bars represent ±1 standard error of the mean (n=30).

Figure 3

Download asset Open asset

Parameter recovery analysis.

We simulated probability estimates according to the system-neglect model. We used each subject’s parameter estimates as our choice of parameter values used in the simulation. Using simulated data, we estimated the parameters ( $α a n d β$ ) in the system-neglect model. To examine parameter recovery, we plot the parameter values we used to simulate the data against the parameter estimates we obtained based on simulated data and computed their Pearson correlation. Further, we added different levels of Gaussian white noise with standard deviation $σ = [0.01, 0.05, 0.1, 0.2, 0.3]$ to the simulated data to examine parameter recovery. For each noise level, we show the parameter estimates in the left two graphs. In the right two graphs, we plot the parameter estimates based on simulated data against the parameter values used to simulate the data. (A) Noise $σ = 0.01$ . (B) Noise $σ = 0.05$ . (C) Noise $σ = 0.1$ . (D) Noise $σ = 0.2$ . (E) Noise $σ = 0.3$ . (F) Empirically estimated noise (σ) of each subject. Each bar represents a subject’s estimated noise level. (G–H) Impact of noise homoscedasticity on parameter estimation. (G) Empirically estimated residual standard deviation. Mean residual standard deviation (across subjects, black data points) in the five probability intervals, [0.0–0.2), [0.2–0.4), [0.4–0.6), [0.6–0.8), and [0.8–1.0], were 0.1015, 0.1296, 0.1987, 0.1929, and 0.2061, respectively. Error bars represent ±1 standard error of the mean. (H) Parameter recovery results assuming heteroscedastic noise. We performed parameter recovery using the empirically estimated, probability-dependent residual variance shown in (G) (the mean residual standard deviation estimates). Error bars represent ±1 standard error of the mean (n=30).

Figure 4

Download asset Open asset

Probability estimates from the actual and simulated data.

(A) Histogram of subjects’ probability estimates collapsed across all conditions (left graph) and model-simulated probability estimates (system-neglect model) under three different noise levels (Noise $σ = 0.01, 0.05, 0.1$ ). (B) Subjects’ data are plotted as histograms separately for each condition. (C) System-neglect model can well-describe subjects’ over- and underreactions to change. We fit the system-neglect model to each individual subject’ probability estimates and used the resulting parameter estimates to compute each subject’s probability estimates under the system-neglect model $(P_{t}^{S N})$ . We then used $P_{t}^{S N}$ to compute Index of Overreaction ( $I O$ ). Here, IO was computed by subtracting belief revision predicted by the Bayesian model $(Δ P_{t}^{B} = P_{t}^{B} - P_{t - 1}^{B})$ from belief revision estimated by system-neglect model $(Δ P_{t}^{S N} = P_{t}^{S N} - P_{t - 1}^{S N})$ . Formally, $I O = Δ P_{t}^{S N} - Δ P_{t}^{B}$ . The mean $I O$ (across all subjects; indicated by the bars) is plotted as a function of transition probability and signal diagnosticity. Data points in black represent individual subjects. Error bars represent ±1 standard error of the mean (n=30). The patterns of over- and underreactions here resembled those based on actual data (Figure 2C), suggesting that the system-neglect model can describe subjects’ over- and underreactions well.

Figure 5 with 1 supplement

Download asset Open asset

Neural representations for regime-shift probability estimates and belief revision.

(A) An example. Belief revision (updating) is captured by the difference in probability estimates between two adjacent periods ( $∆ P_{t}$ ). The blue bars reflect the period-by-period probability estimates ( $P_{t}$ ), while yellow bars depict $∆ P_{t}$ . (B) Whole-brain results (GLM-1) of the main experiment (Experiment 1) showing brain regions that significantly correlate with regime-shift probability estimates ( $P_{t}$ ; clusters in blue) and the updating of beliefs about change ( $∆ P_{t}$ ; clusters in orange). Clusters in magenta indicate brain areas that correlate with both $P_{t}$ and $∆ P_{t}$ . (C–D) Between-experiment comparison of $P_{t}$ . To rule out visual and motor confounds, we compared the $P_{t}$ contrast between the main experiment (Experiment 1) and two control experiments (Experiments 2 and 3). (C) Experiments 1 and 2 comparison. Whole-brain results of (Experiment 1 – Experiment 2) on the $P_{t}$ contrast. (D) Experiments 1 and 3 comparison. Whole-brain results of (Experiment 1 – Experiment 3) on the $P_{t}$ contrast. (E–F) Independent region-of-interest (ROI) analysis of vmPFC and ventral striatum on $P_{t}$ across the three experiments. For each subject and each ROI, we extracted the mean parameter estimates (PE) of the $P_{t}$ contrast from GLM-1. (E) vmPFC ROI. Experiment 1: One-sample t test, $t (29) = - 3.82, p < 0.01$ ; Experiment 2: One-sample t test, $t (29) = 0.36, p = 0.71$ ; Experiment 3: One-sample t test, $t (29) = - 1.11, p = 0.28$ ; Experiments 1 $-$ Experiment 2: two-sample t test, $t (58) = - 3.67, p < 0.01$ ; Experiments 1 $-$ and 3: two-sample t test, $t (58) = - 3.12, p < 0.01$ . (F) Ventral striatum ROI. Experiment 1: $(29) = - 3.06, p < 0.01$ ; Experiment 2: $t (29) = 0.44, p = 0.67$ ; Experiment 3: $t (29) = - 0.93, p = 0.36$ ; Experiments 1 $-$ and 2: $t (58) = - 2.55, p = 0.01$ ; Experiments 1 $-$ and 3: $t (58) = - 1.95, p = 0.06$ . The * symbol indicates p<0.05 (two-tailed), and ** symbol indicates p<0.01 (two-tailed). Error bars represent ±1 standard error of the mean (n=30).

Figure 5—figure supplement 1

Download asset Open asset

Whole-brain results of GLM-1 from the main experiment (Experiment 1) showing brain regions that significantly correlate with regime-shift probability estimates ( $P_{t}$ ; clusters in blue in Panel A) and belief revision ( $∆ P_{t}$ ; clusters in orange in Panel B).

Cluster-level inference using Gaussian random field theory (familywise error-corrected at p < 0.05 using a cluster-forming threshold $z > 3.1$ ).

Figure 6 with 1 supplement

Download asset Open asset

Robustness of neural representations for regime-shift probability estimates and belief revision in the vmPFC and ventral striatum.

(A) Whole-brain results (GLM-2) of the main experiment (Experiment 1) showing brain regions that correlate with regime-shift probability estimates ( $P_{t}$ ; clusters in blue) and the updating of beliefs about change ( $∆ P_{t}$ ; clusters in orange). Clusters in magenta represent brain areas that correlate with both $P_{t}$ and $∆ P_{t}$ . (B–C) Independent region-of-interest (ROI) analysis of vmPFC and ventral striatum. We compared the effect of $P_{t}$ and $∆ P_{t}$ estimated from GLM-1 with GLM-2, which differed on whether various task-related regressors contributing to $P_{t}$ , especially the intertemporal prior, were included in the model. For a given ROI and a given regressor ( $P_{t}$ , $∆ P_{t}$ , or the intertemporal prior), we extracted the corresponding mean parameter estimates (PEs; averaged across voxels within the ROI) from each subject separately and plotted them. The bar height represents the mean across subjects. Each data point in black represents a single subject. Error bars represent ±1 standard error of the mean (n=30). (B) vmPFC results. (C) Ventral striatum results. (D) Whole-brain results of activity that significantly correlated with the subjects’ log odds estimates of regime shift, $l n (P_{t} / (1 - P_{t}))$ . In this analysis, we replaced the parametric regressor of $P_{t}$ with the log odds of regime shifts in GLM-1. Familywise error-corrected at p < 0.05 using Gaussian random field theory with a cluster-forming threshold $z > 3.1$ . (E) Whole-brain results of $P_{t}$ at change-consistent and change-inconsistent signals. We estimated the effect of $P_{t}$ separately at change-consistent (blue) and change-inconsistent (red) signals. The model was identical to GLM-1 except that we implemented R1-R5 in GLM-1 separately for change-consistent and change-inconsistent signals. Familywise error-corrected at p < 0.05 using Gaussian random field theory with a cluster-forming threshold $z > 3.1$ .

Figure 6—figure supplement 1

Download asset Open asset

Whole-brain results of GLM-2 from the main experiment (Experiment 1) showing brain regions that significantly correlate with regime-shift probability estimates ( $P_{t}$ ; clusters in blue in Panel A) and belief revision ( $∆ P_{t}$ ; clusters in orange in Panel B).

Cluster-level inference using Gaussian random field theory (familywise error-corrected at $p < .05$ using with a cluster-forming threshold $z > 3.1$ ).

Figure 7

Download asset Open asset

A frontoparietal network represents key variables for regime-shift estimation.

(A) Variable 1: strength of change evidence measured by the interaction between signal diagnosticity and signal. Left: two examples of the interaction between signal diagnosticity (d) and signal (s), where a change-consistent (blue) signal is coded as 1 and a change-inconsistent (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, $l n (d) \times s$ . Right: whole-brain results showing brain regions in a frontoparietal network that significantly correlated with $l n (d) \times s$ . (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 change evidence. 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 < 0.05, ** indicates p < 0.01. dmPFC: dorsomedial prefrontal cortex; lIPS: left intraparietal sulcus; rIPS: right intraparietal sulcus; lIFG: left inferior frontal gyrus; rIFG: right inferior frontal gyrus. (C) Whole-brain results of the intertemporal prior of regime shift. (D) Using the intertemporal prior ROI (left graph: magenta indicates voxels shared by the LOSO ROI of all subjects; blue indicates voxels of LOSO ROI of at least one subject) to examine the regression coefficients of the strength of change evidence, $l n (d) \times$ signal. The mean parameter estimates (mean PE), i.e., regression coefficient, was not significantly different from 0 (one-sample t test, $t (29) = 0.54, p = 0.59$ , two-tailed). Error bars represent ±1 standard error of the mean.

Figure 8

Download asset Open asset

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 change-consistent signal periods (when the subject saw a blue signal) and change-inconsistent signal periods. We computed the Pearson correlation coefficient (r) 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 change-inconsistent signals; $r = - 0.37, p = 0.047$ for change-consistent signals), but not signal diagnosticity ( $r = 0.28, p = 0.13$ for change-inconsistent signals; $r = 0.26$ , $p = 0.17$ for change-consistent signals). The ventral striatum did not show selectivity to either transition probability or signal diagnosticity. Error bars represent ±1 standard error of the mean.

Figure 9

Download asset Open asset

Model comparison.

(A–E) Modeling results from five competing models. For each model, we plot subjects’ belief revision ( $Δ P_{t}$ ) and the model-estimated $Δ P_{t}$ . Light-colored dots and dashed lines, respectively, represent the model-estimated $Δ P_{t}$ at the individual and group levels. Dark-colored dots and solid lines indicate individual subjects’ $Δ P_{t}$ and group-averaged behavioral data, respectively. Blue indicates data and model estimates at change-consistent signals; Red indicates data and model estimates at change-inconsistent signals. (A) Bayesian model. (B) Original system-neglect model (SN-original). (C) Signal-dependent β system-neglect model (SN-SigDep-β). (D) Signal-dependent α system-neglect model (SN-SigDep-α). (E) Signal-dependent α and β system-neglect model (SN-SigDep-αβ). (F) Model comparison based on the Akaike Information Criterion (AIC). Lower AIC values indicate better models. The bars indicate group mean AIC (averaged across all subjects), while the black dots indicate individual subjects’ AIC values. Error bars represent ±1 standard error of the mean (n=30). The * symbol indicates p < 0.05, ** indicates p < 0.01 (paired t-test; see Supplementary file 11 for summary of statistical tests).

Additional files

Supplementary file 1 Experiment 1: Probability estimates ${(P}_{t})$ and belief revision $({∆ P}_{t})$ contrasts based on GLM-1. Cluster-level inference using Gaussian random field theory (familywise error corrected at p < 0.05 with a cluster-forming threshold $z > 3.1$ ).: https://cdn.elifesciences.org/articles/104684/elife-104684-supp1-v1.docx
Download elife-104684-supp1-v1.docx
Supplementary file 2 Experiment 1: Probability estimates ${(P}_{t})$ and belief revision $({∆ P}_{t})$ contrasts based on GLM-1. Permutation tests based on threshold-free-cluster-enhancement (TFCE) statistic.: https://cdn.elifesciences.org/articles/104684/elife-104684-supp2-v1.docx
Download elife-104684-supp2-v1.docx
Supplementary file 3 Experiment 1: Probability estimates ${(P}_{t})$ and belief revision $({∆ P}_{t})$ contrasts based on GLM-1. Permutation tests based on cluster extent.: https://cdn.elifesciences.org/articles/104684/elife-104684-supp3-v1.docx
Download elife-104684-supp3-v1.docx
Supplementary file 4 Experiment 3: Instructed number $(I N_{t})$ and difference in instructed number $(Δ I N_{t})$ contrasts based on GLM-1. For Experiment 3, ${IN}_{t}$ represents the two-digit number subjects were instructed to press at each period, and $Δ I N_{t}$ represents the difference in number between successive periods. ${IN}_{t}$ is the control for $P_{t}$ in Experiment 1, and $Δ I N_{t}$ is the control for ${∆ P}_{t}$ in Experiment 1. Cluster-level inference using Gaussian random field theory (familywise error corrected at p < 0.05 with a cluster-forming threshold $z > 3.1$ ).: https://cdn.elifesciences.org/articles/104684/elife-104684-supp4-v1.docx
Download elife-104684-supp4-v1.docx
Supplementary file 5 Experiment 1 $-$ and Experiment 2 based on the probability estimates ${(P}_{t})$ contrast in GLM-1. Cluster-level inference using Gaussian random field theory (familywise error corrected at p < 0.05 with a cluster-forming threshold $z > 3.1$ ).: https://cdn.elifesciences.org/articles/104684/elife-104684-supp5-v1.docx
Download elife-104684-supp5-v1.docx
Supplementary file 6 Experiment 1 $-$ and Experiment 3: based on the probability estimates ${(P}_{t})$ contrast in GLM-1. Cluster-level inference using Gaussian random field theory (familywise error corrected at p<0.05 with a cluster-forming threshold z>3.1).: https://cdn.elifesciences.org/articles/104684/elife-104684-supp6-v1.docx
Download elife-104684-supp6-v1.docx
Supplementary file 7 Experiment 1: GLM-2. Cluster-level inference using Gaussian random field theory (familywise error corrected at p < 0.05 with a cluster-forming threshold $z > 3.1$ ).: https://cdn.elifesciences.org/articles/104684/elife-104684-supp7-v1.docx
Download elife-104684-supp7-v1.docx
Supplementary file 8 Experiment 1: GLM-2. Permutation tests based on the threshold-free-cluster-enhancement (TFCE) statistic.: https://cdn.elifesciences.org/articles/104684/elife-104684-supp8-v1.docx
Download elife-104684-supp8-v1.docx
Supplementary file 9 Experiment 1: GLM-2. Permutation tests based on cluster extent.: https://cdn.elifesciences.org/articles/104684/elife-104684-supp9-v1.docx
Download elife-104684-supp9-v1.docx
Supplementary file 10 Model-fitting summary.: https://cdn.elifesciences.org/articles/104684/elife-104684-supp10-v1.docx
Download elife-104684-supp10-v1.docx
Supplementary file 11 Model comparison using paired t-test with Bonferroni correction.: https://cdn.elifesciences.org/articles/104684/elife-104684-supp11-v1.docx
Download elife-104684-supp11-v1.docx
Supplementary file 12 Experiment 1: GLM-1 without the action-handedness regressor. Cluster-level inference using Gaussian random field theory (familywise error corrected at $p < .05$ with a cluster-forming threshold $z > 3.1$ ).: https://cdn.elifesciences.org/articles/104684/elife-104684-supp12-v1.docx
Download elife-104684-supp12-v1.docx
Supplementary file 13 Experiment 1: GLM-2 without $P_{t}$ and $Δ P_{t}$ regressors. Cluster-level inference using Gaussian random field theory (familywise error corrected at p < 0.05 with a cluster-forming threshold $z > 3.1$ ).: https://cdn.elifesciences.org/articles/104684/elife-104684-supp13-v1.docx
Download elife-104684-supp13-v1.docx
MDAR checklist: https://cdn.elifesciences.org/articles/104684/elife-104684-mdarchecklist1-v1.pdf
Download elife-104684-mdarchecklist1-v1.pdf

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Mendeley

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

Mu-Chen Wang
George Wu
Shih-Wei Wu

(2026)

Regime shift detection and neurocomputational substrates for under and overreactions to change

eLife 14:RP104684.

https://doi.org/10.7554/eLife.104684.5

Sign up for email alerts

Privacy notice