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

Judging whether the world has changed is ubiquitous, from public health officials grappling with whether a pandemic surge has peaked, central banks figuring out whether inflation is easing, investors discerning whether the electric car market is getting traction, or romantic partners divining whether a relationship has soured. In all of these examples, individuals must update their beliefs that the world has changed based on a noisy signal, such as a drop in positive pandemic cases or a romantic partner’s suddenly mysterious behavior. In some cases, epidemiological or statistical models provide guidance. However, in many, if not most cases, the determination of whether a regime shift has occurred is made intuitively (Sanders and Manrodt, 2003).

We investigate intuitive judgments of regime-shift detection using a simple empirical paradigm (Massey and Wu, 2005; Seifert et al., 2023). Although this paradigm abstracts away some complications of real-world change detection, it maintains the most central features of the problem: normatively, regime-shift judgments reflect the signals from the environment as well as knowledge about the system that produces the signals. The most recent time series of inflation rates, pandemic cases, and sales of electric cars are all examples of signals. When pandemic cases continue to decline in recent weeks, one might infer a shift from pandemic to non-pandemic regime, only to learn a few weeks later that pandemic has resurged. Indeed, signals such as the latest pandemic cases are seldom precise indications of the true state of the world. Put differently, signals are, by and large, noisy. The noisier the signals are, the less diagnostic they are of the underlying regime.

In addition, signals are affected by how likely the regime shifts from one to another (transition probability). These two fundamental features or system parameters—the diagnosticity of the signals and transition probability—can be conceptualized as two independent aspects of the system that generates the signals. Previous works on regime-shift detection have found that people tend to overreact to change when they receive noisy signals (low signal diagnosticity) but nonetheless are in a stable environment (small transition probability). By contrast, precise signals (high signal diagnosticity) in an unstable environment (large transition probability) typically result in underreaction (Benjamin, 2019; Brown and Steyvers, 2009; Massey and Wu, 2005).

Massey and Wu, 2005 proposed that over- and underreactions reflect system neglect—the tendency to respond primarily to signals and secondarily to the system parameters that produce the signals. The system-neglect hypothesis was derived from theoretical accounts of the determinants of confidence by Griffin and Tversky, 1992. To explain system neglect, consider someone who is making judgments on whether a stock market had shifted from the bear to the bull market regime and has been given information about recent stock returns (signals), how frequent regime shifts happen (transition probability), and how similar the two regimes are (signal diagnosticity). If her judgments are solely based on the signals and not affected by transition probability and signal diagnosticity, she shows a complete neglect of the system parameters. Broadly, system neglect describes a lack of sensitivity—compared with normative Bayesian updating—to the system parameters. In the case of regime-shift detection, this leads to insufficient belief revision (i.e. underreaction) in diagnostic and unstable environments, where Bayesian updating requires a larger change in beliefs, and excessive belief change in noisy and stable environments (i.e. overreaction), where Bayesian updating calls for less pronounced belief revision. Empirical patterns akin to system neglect are not only observed in regime-shift detection, but also in other domains such as confidence judgments (Griffin and Tversky, 1992; Kraemer and Weber, 2004), demand forecasting (Kremer et al., 2011), and pricing decisions (Seifert et al., 2023). Under- and overreactions have been an active research topic in financial economics, often measured as reactions to stock market changes or firm news (Baker and Wurgler, 2007; Barberis et al., 1998; Daniel et al., 1998; De Bondt and Thaler, 1985; Nelson et al., 2001).

At the neurobiological level, change detection has been investigated in the context of reinforcement learning in dynamic environments where changes in the state of the world, such as reward distributions, take place during the experiments (Soltani and Izquierdo, 2019). Different behavioral paradigms, most notably reversal learning, and computational models were developed to investigate its neurocomputational substrates (Behrens et al., 2007; Izquierdo et al., 2017; McGuire et al., 2014; Muller et al., 2019; Nassar et al., 2010; Payzan-LeNestour and Bossaerts, 2011; Payzan-LeNestour et al., 2013). Key findings on the neural implementations for such learning include identifying brain areas and networks that track volatility in the environment (rate of change; Behrens et al., 2007), the uncertainty or entropy of the current state of the environment (Muller et al., 2019), participants’ beliefs about change (Kao et al., 2020; McGuire et al., 2014; Payzan-LeNestour and Bossaerts, 2011), and their uncertainty about whether a change had occurred (Kao et al., 2020; McGuire et al., 2014). Evidence from several of the aforementioned studies (Behrens et al., 2007; Kao et al., 2020; McGuire et al., 2014) suggests that the dorsomedial frontal cortex (DMFC) is critical to learning in dynamic environments, as information about volatility, subjective beliefs, and uncertainty about change converge in this brain region.

But how do biases in change detection arise in the brain? Although reinforcement learning studies provide valuable insights into change detection in the learning process, it remains unclear how biases in change detection—under- and overreactions to change—arise at the neural algorithmic and implementation levels. For example, it is unclear how a certain brain area, such as DMFC, that had been shown to represent environmental volatility, would contribute to under- and overreactions to change. In order to systematically characterize under- and overreactions, it would be critical to (1) adopt a well-established behavioral paradigm that robustly elicits these behavioral phenomena and (2) have computational frameworks suitable for developing neural hypotheses regarding under- and overreactions. To address these issues, in this study, we adopted the regime-shift detection task from Massey and Wu, 2005 and their system-neglect computational framework. At the behavioral level, the regime-shift task is a well-established paradigm that robustly elicits under- and overreactions to change. At the algorithmic and implementation levels, the system-neglect framework provides a straightforward neurocomputational hypothesis regarding under- and overreactions. It predicts that for brain areas involved in regime-shift detection, under- and overreactions arise from their sensitivity or lack thereof in response to the system parameters.

We replicated previous behavioral findings on under- and overreactions (Massey and Wu, 2005). Using blood-oxygen-level-dependent (BOLD) functional magnetic resonance imaging (fMRI), we reported three key findings. First, we identified two distinct brain networks involved in regime-shift detection, with the ventromedial prefrontal cortex (vmPFC) and ventral striatum in representing subjects’ reported beliefs about change and a frontoparietal network in evaluating the strength of change evidence. Second, we found that these two networks selectively respond to different system parameters: while the frontoparietal network represents individual subjects’ sensitivity to signal diagnosticity but not transition probability, the vmPFC shows the opposite pattern. Third, the neural sensitivity profiles were signal-dependent: the frontoparietal network only represented individuals’ sensitivity to signal diagnosticity when signals consistent with change appeared. By contrast, vmPFC represented individuals’ sensitivity to transition probability regardless of whether subjects received signals consistent or inconsistent with change. Such signal-dependent representations led us to further examine and subsequently verify that they are indeed key properties of our system-neglect computational model. Together, these results suggest that regime-shift detection is implemented jointly by a belief-updating network (vmPFC-striatum) and evidence evaluation network (frontoparietal network) and that their sensitivity in response to different environmental parameters contributes to under- and overreactions to change. More broadly, we showed that neural data can reveal important properties of computational models that are overlooked in theoretical treatments and behavioral analyses.

In our regime-shift detection task (Figure 1A), in each trial, subjects saw a series of sequentially presented sensory signals (red or blue balls). They were told that the signals came from one of two regimes, the red regime or the blue regime (Figure 1B). Regimes were symmetric, for example, with a red regime consisting of 60 red balls and 40 blue balls and the corresponding blue regime consisting of 60 blue balls and 40 red balls. Each trial started with the red regime but could shift to the blue regime before each of the 10 periods in a trial. After seeing a new signal in each period, subjects provided a probability estimate that the current regime was the blue regime, that is a posterior probability of a regime shift. They were also instructed that once the regime has shifted from the red to the blue during a trial, the regime would remain in the blue regime until the end of the trial, that is the blue regime was a trapping or absorbing state. Our experimental paradigm hence follows Massey and Wu, 2005. Note that, during a trial, subjects did not receive feedback—after making probability estimates in each period—on whether the regime had shifted and the monetary bonus earned as a result of accuracy in probability estimates (see Materials and methods for details). Hence, subjects had no access to information about accuracy and rewards as she or he was making probability estimates.

Figure 1

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We manipulated two system parameters, transition probability and signal diagnosticity (Figure 1BC). Transition probability, q, with possible values of 0.01, 0.05, and 0.1, specified the probability that the regime would shift from the red to the blue regime in any period. Signal diagnosticity, d, with possible values of 1.5, 3, and 9, captured the degree to which the two regimes differed. For example, an environment with high signal diagnosticity (e.g. $d\text{=}9$) indicated that there were nine times more red balls than blue balls in the red regime (a 90:10 Red to Blue ratio) and nine times more blue balls than the red balls in the blue regime (a 90:10 Blue to Red ratio). Therefore, the weight that a signal (blue or red ball) carried was captured by the signal diagnosticity: in a low diagnostic environment, a blue signal most likely reflects no change in regime ($d\text{=}1.5$, example on the top of Figure 1D). By contrast, in a highly diagnostic environment, a blue signal very likely reveals a shift in regime ($d\text{=}9$, example on the bottom of Figure 1D). At the beginning of each trial, subjects were informed about the transition probability and signal diagnosticity in that trial. In the example trial sequence (Figure 1A), the transition probability (indicated by ‘switch probability’ in Figure 1A) is 0.1 while the signal diagnosticity (indicated by ‘color ratio’ in Figure 1A) is 1.5, with the red regime consisting of 60 red balls and 40 blue balls and the blue regime consisting of 40 red balls and 60 blue balls.

To establish the neural representations for regime-shift estimation, we performed three fMRI experiments ($n\text{=}30$ subjects for each experiment, 90 subjects in total). Experiment 1 was the main experiment, while Experiments 2–3 were control experiments that ruled out two important confounds (Figure 1E). The control experiments were designed to clarify whether any effect of subjects’ probability estimates of a regime shift, $P_t$, in brain activity can be uniquely attributed to change detection. Here we considered two major confounds that can contribute to the effect of $P_t$. First, since subjects in Experiment 1 made judgments about the probability that the current regime is the blue regime (which corresponded to the probability of regime change), the effect of $P_t$ did not particularly have to do with change detection. To address this issue, in Experiment 2 subjects made exactly the same judgments as in Experiment 1 except that the environments were stationary (no transition from one regime to another was possible), as in Edwards, 1968 classic ‘bookbag-and-poker chip’ studies. Subjects in both experiments had to estimate the probability that the current regime is the blue regime, but this estimation corresponded to the estimates of regime change only in Experiment 1. Therefore, activity that correlated with probability estimates in Experiment 1 but not in Experiment 2 can be uniquely attributed to representing regime-shift judgments. Second, the effect of $P_t$ can be due to motor preparation and/or execution, as subjects in Experiment 1 entered two-digit numbers with button presses to indicate their probability estimates. To address this issue, in Experiment 3, subjects performed a task where they were presented with two-digit numbers and were instructed to enter the numbers with button presses. By comparing the fMRI results of these experiments, we were therefore able to establish the neural representations that can be uniquely attributed to the probability estimates of regime-shift.

Behavioral evidence for over- and underreactions to change

Our analyses used subjects’ probability estimates of a regime shift, $P_t$, for each period, $t\text{=}1,\dots ,10$. We found that subjects were in general responsive to the system parameters, with higher $P_t$ when the transition probability was larger (Figure 2A). We also found that subjects tended to give more extreme $P_t$ under high signal diagnosticity than low diagnosticity (Figure 2A). In addition, we used a measure of belief revision, $\mathrm{\Delta }{P}_t\text{=}{P}_t-P_{t-1}$. In Figure 2B, we show examples of $P_t$ and $\Delta P_t$ from a subject. On the left, the subject was in a stable environment (small transition probability, $q\text{=}0.01$) and faced two regimes that were very similar to each other (low signal diagnosticity, $d\text{=}1.5$). The red and blue signals (10 periods) were what the subject encountered during a trial. On the right, the subject was in an unstable environment ($q\text{=}0.1$) and faced two regimes that were very different ($d\text{=}9$).

Figure 2

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To examine over- and underreactions to change, we compared subjects’ belief revision, $\mathrm{\Delta }{P}_t\text{=}{P}_t-P_{t-1},t\text{=}2,\dots ,10$, with belief revision predicted by the Bayesian model, $\mathrm{\Delta }{P}_t^B\text{=}{P}_t^B-P_{t-1}^B$ (see Figure 2B for illustrations). $\Delta P_t$ and ${\Delta P}_t^B$, respectively, capture how much subjects and a normative Bayesian change probability estimates in response to a new signal. When $\mathrm{\Delta }{P}_t>\mathrm{\Delta }{P}_t^B$, it indicates larger belief revision than the normative Bayesian, that is an overreaction. By contrast, $\mathrm{\Delta }{P}_t<\mathrm{\Delta }{P}_t^B$ indicates smaller belief revision, that is an underreaction. We therefore use $IO\text{=}\mathrm{\Delta }{P}_t-\mathrm{\Delta }{P}_t^B$ as an Index of Overreaction $\left(IO\right)$. We found that subjects tended to overreact to change ($IO>0$) when they received noisy signals (i.e. low signal diagnosticity, $d\text{=}1.5$) and when the environment was stable (small transition probability, $q\text{=}0.01$). By contrast, underreaction ($IO<0$) was most commonly observed when they were in unstable environments (large transition probability, $q\text{=}0.1$) and with clear signals (i.e. high signal diagnosticity, $d\text{=}9$; Figure 2C). These patterns of over- and underreactions were consistent with findings in Massey and Wu, 2005 and the system-neglect hypothesis, which posits a tendency to respond primarily to the signals and secondarily to the system that generates the signals (Massey and Wu, 2005; Seifert et al., 2023). According to the system-neglect hypothesis, responding secondarily to the system is synonymous with a lack of sensitivity to the system parameters, which leads to underreactions in unstable environments with precise signals and overreactions in stable environments with noisy signals.

Following Massey and Wu, 2005, we quantitatively model these belief revisions using the system-neglect model (see System-neglect model in Methods). The model is a parameterized version of the normative Bayesian model that allows for distortion of the system parameters via weighting parameters for transition probability (α) and signal diagnosticity (β). In short, α reflects distortion of transition probability, with $\alpha \times q$ in the system-neglect model capturing a decision maker’s effective transition probability (q). For example, if $\alpha \text{=}4$ when $q\text{=}0.01$, the decision maker effectively treats a 0.01 transition probability as if it were 0.04. By contrast, β captures the extent to which the decision maker overweighs or underweighs signal diagnosticity ($d^{\beta }$) when faced with a signal. For example, if $\beta \text{=}2$ when $d\text{=}1.5$, subjects would treat a blue signal by updating the odds ratio for change by ${1.5}^2$, or 2.25 rather than 1.5.

In the system-neglect model, we estimated the weighting parameters separately for each level of transition probability and signal diagnosticity, that is ${\alpha }_i\times q_i$ and ${d_j}^{{\beta }_j}$, where ${\alpha }_1,{\alpha }_2$, and ${\alpha }_3$ correspond to transition probabilities of 0.01, 0.05, and 0.1, respectively, and ${\beta }_1,{\beta }_2$, and ${\beta }_3$ correspond to signal diagnosticity of 1.5, 3, and 9, respectively. In contrast to the Bayesian model which implies ${\alpha }_i\text{=}{\beta }_j\text{=}1$ for all $i,j$, the system-neglect model requires that ${\alpha }_i>{\alpha }_{i\text{+}1}$ and ${\beta }_j>{\beta }_{j\text{+}1}$ because it would effectively capture a lack of sensitivity to the system parameters.

We fit the model to $P_t$ for each subject separately and found parameter estimates consistent with system neglect (Figure 2D). The mean estimates of α were 3.69, 1.04, and 0.65 for $q\text{=}0.01,0.05$ and 0.10, respectively. The parameters indicated that, on average, when $q\text{=}0.01$, subjects treated as if it were 0.0369. By contrast, when $q\text{=}0.10$, the subjects treated it as if it were 0.065. Thus, a factor of 10 in actual transition probability (0.01 vs 0.1) was reduced to a factor of less than 2 (0.0369 vs 0.065) in effective transition probability. For signal diagnosticity, the mean parameter estimates of β were 1.69, 0.77, and 0.57 for $d\text{=}1.5,3$, and 9, respectively. Thus, subjects updated their beliefs ${1.5}^{1.69}\text{=}1.98$ when $d_1\text{=}1.5$ and $9^{0.57}\text{=}3.50$ when $d_3\text{=}9$. Normatively, the change in odds ratio between the two conditions should have been $d_3\text{/}{d}_1\text{=}6$ but, consistent with system neglect, was considerably smaller, $3.50\text{/}1.98\text{=}1.76$. Together, large parameter estimates ($\alpha >1,\beta >1$) at low signal diagnosticity (noisy signals) and low transition probability (stable environments) capture overreactions to changes, while small parameter estimates ($\alpha <1,\beta <1$) at large signal diagnosticity (precise signals) and large transition probability (unstable environments) reflect underreactions to change. These results replicate the findings by Massey and Wu, 2005, with the pattern of over- and underreactions as predicted by the system neglect hypothesis. Critically, the degree of system neglect can be captured by the negative trend of the parameter estimate as a function of the system parameter levels (Figure 2D): the steeper the slope, the larger the system neglect. We found a similar pattern on β in Experiment 2 (one of the control experiments) where environments were stationary (no transition probability) and signal diagnosticity was manipulated (Figure 2E; Benjamin, 2019; Tversky et al., 1990).

We next examined whether the way subjects respond to different system parameters is similar. It is possible, for example, that subjects who showed stronger (or weaker) distortion of transition probability (captured by α parameter) also showed stronger (or weaker) distortion of signal diagnosticity (captured by β parameter). There was no significant correlation between α and β parameters (Figure 2F). However, we did find within-parameter correlation: subjects who had a higher ${\alpha }_i$ for a transition probability level $i$ also tended to have a higher ${\alpha }_{i`}$ for a second transition probability level $i`$ (Figure 2G), with the same pattern also holding for signal diagnosticity parameter β (Figure 2H). Together, these results suggested that the way an individual decision maker responds to information about the probability of change in the environment (transition probability) has little to do with how she or he responds to information about the similarity between different regimes (signal diagnosticity). But individuals are consistent in responding to a particular system parameter (transition probability or signal diagnosticity) across different levels of the parameter.

We performed parameter recovery analysis to examine whether the fitting procedure gave reasonable parameter estimates (Wilson and Collins, 2019). First, we simulated each subject’s probability estimation data based on the system-neglect model by using that subject’s parameter estimates. Second, we fitted the system-neglect model to the simulated data. Third, we computed the correlation across subjects between the estimated parameters and the parameter values we used to simulate data. Fourth, we repeated the above steps by adding independent white noise to the simulated data. Across different levels of noise, we found good parameter recovery (Pearson’s r for transition probability $r\ge 0.9533$ across different noise levels, Pearson’s $r$ for signal diagnosticity $r\ge 0.9515$ across different noise levels; Figure 3). In addition, we found that the empirical results (Figure 2C) can be reproduced by the system-neglect model (Figure 4). That is, we used each subject’s parameter estimates to compute the period-wise probability estimates according to the system-neglect model and used these probability estimates to compute and plot index of overreaction (IO). The patterns of IO based on the system-neglect model (Figure 4C) were very similar to those based on subjects’ actual data (Figure 2C).

Figure 3

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Figure 4

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Ventromedial prefrontal cortex and ventral striatum represent regime-shift probability estimates and belief revision

Our first analysis is aimed at identifying brain regions that represented our subjects’ regime-shift estimation. To address this question, we used two behavioral measures, namely the period-by-period probability estimates of regime shift, $P_t$, and the change in $P_t$ between successive periods, ${\Delta P}_t$. $P_t$ can be regarded as the subjects’ posterior probability estimates of regime shift, whereas ${\Delta P}_t$ captures the change in belief (belief revision) about regime shift in the presence of a new signal (see Figure 5A for an example of $P_t$ and ${\Delta P}_t$).

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For $P_t$, we found that the ventromedial prefrontal cortex (vmPFC) and ventral striatum correlated with this behavioral measure of subjects’ belief about change. In addition, many other brain regions, including the motor cortex, central opercular cortex, insula, occipital cortex, and the cerebellum also significantly correlated with $P_t$. (Figure 5B; clusters in blue). For ${\Delta P}_t$, we also found that the vmPFC and ventral striatum were associated with regime shift belief revision (Figure 5B; clusters in orange). See GLM-1 in Materials and methods, Figure 5—figure supplement 1, and Supplementary file 1, Supplementary file 2, Supplementary file 3, respectively, for significant clusters of activation using Gaussian random field theory, permutation test on threshold-free-cluster-enhancement statistic, and permutations test on cluster-extent statistic. While many brain regions correlated with regime-shift probability estimates ${(P}_t)$, only the vmPFC and ventral striatum also correlated with belief revisions, ${\Delta P}_t$ (magenta clusters in Figure 5B).

Brain regions shown to correlate with regime-shift probability estimates, $P_t,$ could be driven by motor response because larger estimates predominantly involved right-hand finger presses (see Materials and methods for details). To rule out motor confounds, we conducted two control experiments (Experiments 2 and 3) and performed two analyses. First, we examined the neural correlates of probability estimates ($P_t$ in GLM-1) in the control experiments (Experiments 2 and 3). Second, we compared the effect of $P_t$ (GLM-1) between the main experiment (Experiment 1) and the control experiments. In the first analysis, we found that in both control experiments, vmPFC and ventral striatum did not significantly correlate with probability estimates $P_t$ at the whole-brain level (in Experiment 2, no significant clusters of activation at the whole-brain level; see Supplementary file 4 for Experiment 3). In the second analysis, we found that for both vmPFC and ventral striatum, the regression coefficient of $P_t$ was significantly different between Experiment 1 and Experiment 2 (Figure 5C) and between Experiment 1 and Experiment 3 (Figure 5D; also see Supplementary file 5 and Supplementary file 6). In a separate, independent ROI analysis on vmPFC and ventral striatum, we also found the same results (Figure 5EF; see Independent regions-of-interest (ROIs) analysis in Materials and methods for details). Finally, we note that in GLM-1, we implemented an ‘action-handedness’ regressor to directly address the motor-confound issue, that higher probability estimates preferentially involved right-handed responses for entering higher digits. The action-handedness regressor was parametric, coding –1 if both finger presses involved the left hand (e.g. a subject pressed ‘23’ as her probability estimate when seeing a signal), 0 if using one left finger and one right finger (e.g. ‘75’), and 1 if both finger presses involved the right hand (e.g. ‘90’). Taken together, these results ruled out motor confounds and suggested that vmPFC and ventral striatum represent subjects’ probability estimates of change (regime shifts) and belief revision.

We further examined the robustness of $P_t$ and ${\Delta P}_t$ representations in vmPFC and ventral striatum in three follow-up analyses. In the first analysis, we implemented a GLM (GLM-2 in Materials and methods) that, in addition to $P_t$ and ${\Delta P}_t$, included various task-related variables contributing to $P_t$ as regressors. Specifically, to account for the fact that the probability of regime change increased over time, we included the intertemporal prior as a regressor in GLM-2. The intertemporal prior is the natural logarithm of the odds in favor of regime shift in the t-th period,$\mathrm{l}\mathrm{n}\left(\frac{1-{\left(1-q\right)}^t}{{\left(1-q\right)}^t}\right)$, where q is transition probability and $t\text{=}1,\dots ,10$ is the period (Equation 1 in Materials and methods). It describes normatively how the prior probability of change increased over time regardless of the signals (blue and red balls) the subjects saw during a trial. Including it along with $P_t$ would clarify whether any effect of $P_t$ can otherwise be attributed to the intertemporal prior. We found that the results of $P_t$ and ${\Delta P}_t$ in the vmPFC and ventral striatum in GLM-2 were identical to those in GLM-1 (Figure 6): Figure 6A was meant to depict the results in slices identical to those shown in Figure 5B for results based on GLM-1. For slice-by-slice results, see Figure 5—figure supplement 1 for results based on GLM-1 and Figure 6—figure supplement 1 for GLM-2. For Tables of activations, see Supplementary file 1, Supplementary file 2, Supplementary file 3 for GLM-1 and Supplementary file 7, Supplementary file 8, Supplementary file 9 for GLM-2. In a separate, independent region-of-interest (ROI) analysis of vmPFC and ventral striatum (Figure 6BC; see Independent regions-of-interest (ROIs) analysis in Materials and methods for details), we further compared the effect of both $P_t$ and ${\Delta P}_t$ between GLM-1 and GLM-2. For $P_t$, the difference between GLM-1 and GLM-2 was significant in vmPFC but not in ventral striatum (paired t-test, $t\left(29\right)\text{=}-2.21,p\text{=}0.04$ in vmPFC, $t\left(29\right)\text{=}-0.85,p\text{=}0.40$ in ventral striatum), while the effect of $P_t$ from GLM-1 (one-sample t-test, $t\left(29\right)\text{=}-3.82,p<.01$ in vmPFC; $t\left(29\right)\text{=}-3.06,p<.01$ in ventral striatum) and GLM-2 was significant (one-sample t-test, $t\left(29\right)\text{=}-2.69,p\text{=}.01$ in vmPFC; $t\left(29\right)\text{=}-2.50,p\text{=}.02$ in ventral striatum). The significant difference in vmPFC between GLM-1 and GLM-2 suggested that the inclusion of intertemporal prior and other task-related regressors in GLM-2 did change the result of $P_t$ in vmPFC. However, vmPFC activity in both GLMs significantly correlated with $P_t$, suggesting that $P_t$ representations in vmPFC were present with and without the inclusion of intertemporal prior and other task-related regressors. For $∆P_t$, the difference between GLM-1 and GLM-2 was not significant (paired t-test, $t\left(29\right)\text{=}-0.22,p\text{=}0.83$ in vmPFC; $t\left(29\right)\text{=}0.51,p\text{=}0.61$ in ventral striatum), while the effect of $∆P_t$ from GLM-1 (one-sample t-test, $t\left(29\right)\text{=}3.12,p<.01$ in vmPFC; $t\left(29\right)\text{=}4.17,p<.01$ in ventral striatum) and GLM-2 was significant (one-sample t-test, $t\left(29\right)\text{=}2.92,p<.01$ in vmPFC; $t\left(29\right)\text{=}3.59,p<.01$ in ventral striatum). For the intertemporal prior, activity in both vmPFC and ventral striatum did not correlate significantly with the intertemporal prior (one-sample t-test, $t\left(29\right)\text{=}0.07,p\text{=}0.95$ in vmPFC; $t\left(29\right)\text{=}-0.53,p\text{=}0.60$ in ventral striatum). All the t-tests described above were two-tailed. Taken together, these results suggest that vmPFC and ventral striatum represented $P_t$ and ${\Delta P}_t$ regardless of whether the intertemporal prior and other task-related regressors contributing to $P_t$ were included in the GLM. We also did not find that vmPFC and ventral striatum to represent the intertemporal prior. In the second analysis, we implemented a GLM that replaced $P_t$ with the log odds of $P_t,\mathrm{l}\mathrm{n}\left(P_t\text{/}\left(1-P_t\right)\right)$ (Figure 6D). In the third analysis, we implemented a GLM that examined $P_t$ separately on periods when change-consistent (blue balls) and change-inconsistent (red balls) signals appeared (Figure 6E). Each of these analyses showed significant correlation with $P_t$ in vmPFC and ventral striatum, further establishing the robustness of the $P_t$ findings.

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A frontoparietal network represents key variables for estimating regime shifts

Our second analysis is aimed at identifying brain regions that represented key variables contributing to regime-shift estimation. Guided by our theoretical framework and computational models, we focused on two variables, the interaction between signals and signal diagnosticity and intertemporal prior probability of change (GLM-2 in Materials and methods) to examine these effects.

Our theoretical framework makes two fundamental predictions. First, a signal should be weighted differently depending on signal diagnosticity, that is a blue ball is stronger evidence for change in a highly diagnostic environment (e.g. $d\text{=}9$) than a system in which the red and blue regimes are very similar (e.g. $d\text{=}1.5$). To capture the interaction between signals and signal diagnosticity, we code a blue signal as 1 and a red signal as –1 and multiply the signal code (s=1 or –1) by the natural logarithm of signal diagnosticity, $\mathrm{l}\mathrm{n}\left(d\right)$ (two examples are shown in Figure 7A). We term this interaction, $s\times \mathrm{l}\mathrm{n}\left(d\right)$, the strength of evidence in favor of change or strength of change evidence for short. The Bayesian model, as described in Materials and methods, critically depends on $d^s$, computing posterior odds by multiplying prior odds by the likelihood ratio. Thus, the log posterior odds were calculated from both the prior odds and $s\times \mathrm{l}\mathrm{n}\left(d\right).$. At the whole-brain level, we found that a frontoparietal network including the dorsal medial prefrontal cortex (dmPFC), lateral prefrontal cortex (bilateral inferior frontal gyrus, IFG), and the posterior parietal cortex (bilateral intraparietal sulcus, IPS) represented $s\times \mathrm{l}\mathrm{n}\left(d\right)$ (Figure 7A). These brain regions overlap with what is commonly referred to as the frontoparietal control network (Buckner et al., 2013; Seeley et al., 2007; Yeo et al., 2011). Among them, dmPFC sits in the vicinity of the dorsomedial frontal cortex (DMFC) shown to represent change probability and uncertainty about change in reinforcement learning (McGuire et al., 2014).

Figure 7

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The second prediction our theoretical framework offers concerns the prior probability of a regime shift over time. Specifically, the Bayesian model predicts that the prior probability should increase over time (see two examples in Figure 7B), with the intertemporal prior, in log odds terms, defined as the natural logarithm of the odds in favor of regime shift in the t-th period,$\mathrm{l}\mathrm{n}\left(\frac{1-{\left(1-q\right)}^t}{{\left(1-q\right)}^t}\right)$, where q is transition probability and $t\text{=}1,\dots ,10$ is the period (Equation 1 in Materials and methods). With independent (leave-one-subject-out, LOSO) ROI analysis, we examined whether brain regions in the frontoparietal network (shown to represent strength of change evidence) correlated with intertemporal prior and found that all brain regions, with the exception of dmPFC, in the frontoparietal network correlated with the intertemporal prior (Figure 7B; dmPFC: $t\left(29\right)\text{=}-1.69,p\text{=}0.10$; left IFG: $t\left(29\right)\text{=}2.20,p\text{=}0.04;$ right IFG: $t\left(29\right)\text{=}-2.64,p\text{=}0.01;$ left IPS: $t\left(29\right)\text{=}-2.35,p\text{=}0.03;$ right IPS: $t\left(29\right)\text{=}-2.07,p\text{=}0.05$). By contrast, brain regions that represented the intertemporal prior, which we found to be in the right fusiform cortex in the occipitotemporal regions, did not correlate with the strength of change evidence (Figure 7C and D).

Finally, we emphasize that these effects—the strength of change evidence and intertemporal prior—cannot be otherwise attributed to probability estimates $\left(P_t\right)$ or belief revision ${(\Delta P}_t)$ because both $P_t$ and ${\Delta P}_t$ were included in GLM-2 where these effects were examined. Taken together, these results suggest that the frontoparietal network is critically involved in representing the two key variables for estimating regime shifts, strength of change evidence and intertemporal prior. See Supplementary file 7, Supplementary file 8, Supplementary file 9 for information about significant clusters of activation for the strength of change evidence, intertemporal prior, $P_t$, and ${\Delta P}_t$ from GLM-2 using Gaussian random field theory (Supplementary file 7), permutation test on threshold-free-cluster-enhancement (TFCE) statistic (Supplementary file 8), and permutation test on cluster-extent statistic (Supplementary file 9).

Under- and overreactions are associated with selectivity and sensitivity of neural responses to system parameters

The system-neglect hypothesis posits that under- and overreactions arise from a lack of sensitivity to the system parameters. We can measure individual subjects’ sensitivity to system parameters using behavioral data (subjects’ probability estimates). Meanwhile, we can also measure sensitivity using neural data. In the following analysis, we examined whether there is a match between the behavioral and neural measures of sensitivity to the system parameters. This would allow us to examine, through the system-neglect framework, whether sensitivity in neural responses to the system parameters are associated with under- and overreactions to change.

We focused on the vmPFC-striatum network and frontoparietal network, as they were shown to be involved in regime-shift detection (Figures 5—7). We examined whether these brain networks show selective preference for a particular system parameter, which we refer to as parameter selectivity. We also asked whether parameter selectivity is signal-dependent, i.e., different for signals consistent with change (blue signals) or inconsistent with change (red signals).

We started by defining a behavioral measure of sensitivity to the system parameter. To visualize this measure, we consider two extreme decision makers, a Bayesian and someone who reacts to signals identically across all systems, which we term complete neglect. In Figure 8A (left graph), we use signal diagnosticity (d) to illustrate the pattern of these two decision makers. The vertical axis is $\beta \mathrm{l}\mathrm{n}\left(d\right)$ and the horizontal axis is the signal-diagnosticity level (d), where β is the weighting parameter on signal diagnosticity in the system-neglect model. A Bayesian (open circles) does not overweight or underweight d, and thus $\beta \text{=}1$. We can then define the Bayesian slope by regressing ${\beta }_i\mathrm{l}\mathrm{n}\left(d_i\right)$ against $\mathrm{l}\mathrm{n}\left(d_i\right).$ In this formulation, the Bayesian slope is 1 and it reflects the sensitivity of a Bayesian decision maker to signal diagnosticity. On the other hand, a complete-neglect decision maker is unresponsive to signal diagnosticity, that is ${\beta }_1\mathrm{l}\mathrm{n}\left(d_1\right)\text{=}{\beta }_2\mathrm{l}\mathrm{n}\left(d_2\right)\text{=}{\beta }_3\mathrm{l}\mathrm{n}\left(d_3\right)$. Hence, the complete-neglect slope should be 0. These two slopes, the Bayesian slope and the complete-neglect slope, provide the boundaries for system neglect. For each subject, we computed ${\beta }_i\mathrm{l}\mathrm{n}\left(d_i\right)$ at each $d_i$ level, where ${\beta }_i$ is the estimate for diagnosticity $d_i$ fitted to the system-neglect model (see ${\beta }_i$ in Figure 2D). We then estimated each subject’s behavioral slope (to distinguish it from the neural slope reported later) and used it as a behavioral measure of sensitivity to signal diagnosticity.

Figure 8

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For each subject, we estimated two behavioral slopes, one for d, the signal diagnosticity (top row in Figure 8A), and the other for q, the transition probability (bottom row in Figure 8A). The right graphs in Figure 8A show the behavioral slope for each of the 30 subjects (top: signal diagnosticity; bottom: transition probability). For signal diagnosticity, 28 out of 30 subjects’ behavioral slopes were within the boundaries. For transition probability, 27 out of 30 subjects’ behavioral slopes were within the boundaries (between complete neglect and Bayesian). One subject’s (subject 6) behavioral slope for q (transition probability) was approximately 2 and clearly outside the boundaries. This subject’s data were excluded for further analysis of q (the right two columns in Figure 8C and D).

We found that, across subjects, system neglect was unique from either Bayesian or complete neglect. Subjects’ sensitivity to transition probability, as captured by the behavioral slope in Figure 8A, deviated significantly from the Bayesian slope (comparing subjects’ slope with 1, $t\left(29\right)\text{=}-10.8$, $p<.01$, two-tailed) and from complete neglect slope (comparing subjects’ slope with 0, $t\left(29\right)\text{=}4.8$, $p<.01$, two-tailed). For signal diagnosticity, subjects’ sensitivity to signal diagnosticity was also significantly different from both Bayesian ($t\left(29\right)\text{=}-12.5$, $p<.01$, two-tailed) and complete neglect ($t\left(29\right)\text{=}6.1$, $p<.01$, two-tailed).

However, subjects were closer to complete neglect than to the Bayesian. We tested this by examining whether the behavioral slope, γ, was significantly greater or smaller than 0.5, the midpoint between complete neglect (slope of 0) and Bayesian (slope of 1). $\gamma -.5>0$ indicates that subjects’ behavior was in closer alignment with Bayesian. By contrast, $\gamma -.5<0$ implies behavior closer to complete neglect. We found that, for both transition probability and signal diagnosticity, the behavioral slope was closer to complete neglect than to Bayesian (transition probability: $t\left(29\right)\text{=}-2.97$, p < 0.01; signal diagnosticity: $t\left(29\right)\text{=}-3.23$, p < 0.01, two-tailed). Together, these results suggested that, while subjects did respond to the system parameters in regime-shift estimation in the correct direction predicted by the Bayesian model, their sensitivity to the system parameters was closer to complete neglect than to normative Bayesian.

For the neural data, we defined a neural measure of sensitivity to the system parameters by estimating how neural responses change as a function of those parameters. Using the signal diagnosticity parameter as an example, for each subject and each ROI separately, we regressed average brain activity at each diagnosticity level against $\mathrm{l}\mathrm{n}\left(d\right)$. The slope estimate, termed the neural slope, from the linear regression gave us a neural measure of sensitivity to signal diagnosticity. To investigate whether the neural sensitivity was signal-dependent, that is neural sensitivity in response to the change-consistent signals (blue signals) was different from the change-inconsistent signals (red signals), we separately estimated the neural slope in response to blue and red signals.

After obtaining both the behavioral and neural measures of sensitivity to the system parameters, we then computed the Pearson correlation coefficient between them. We found that the vmPFC-striatum network and frontoparietal network showed clear dissociations in how they corresponded with the system parameters. First, the frontoparietal network represented individual subjects’ sensitivity to signal diagnosticity (left two columns in Figure 8C), but not transition probability (right two columns in Figure 8C). Notably, patterns of parameter selectivity were remarkably consistent across brain regions in the frontoparietal network: when change-consistent signals (blue signals) appeared, the neural measure of sensitivity from all brain regions in the frontoparietal network except the right IPS significantly correlated with the behavioral measure of sensitivity (second column from the left in Figure 8C; dmPFC: $r\text{=}0.48,p\text{=}0.007$; lIFG: $r\text{=}0.5,p\text{=}0.009$; rIFG: $r\text{=}0.4,p\text{=}0.027$; lIPS: $r\text{=}0.58,p\text{=}0.001$; rIPS108143: $r\text{=}0.32,p\text{=}0.082$). By contrast, when change-inconsistent signals (red signals) appeared, all regions within the frontoparietal network did not significantly correlate with the behavioral measure of sensitivity (first column from the left in Figure 8C; dmPFC: $r\text{=}0.32,p\text{=}0.083$; lIFG: $r\text{=}0.04,p\text{=}0.848$; rIFG: $r\text{=}0.19,p\text{=}0.312$; lIPS: $r\text{=}0.05,p\text{=}0.787$; rIPS: $r\text{=}-0.02,p\text{=}0.914$). We further tested, for each brain region, whether the difference in correlation was significant using both parametric and nonparametric tests (see Parametric and nonparametric tests for difference in correlation coefficients in Materials and methods). The results were identical. In the parametric test, we used the Fisher $z$ transformation to transform the correlation coefficients to the $z$ statistic. Since these correlation coefficients were not independent, we compared them using the test developed in Meng et al., 1992 (see Materials and methods). We found that among the five ROIs in the frontoparietal network, two of them, namely the left IFG and left IPS, the difference in correlation was significant (one-tailed z test; left IFG: $z\text{=}1.8908,p\text{=}0.0293$; left IPS: $z\text{=}2.2584,p\text{=}0.0049$). For the remaining three ROIs, the difference in correlation was not significant (dmPFC: $z\text{=}0.9522,p\text{=}0.1705$; right IFG: $z\text{=}0.9860,p\text{=}0.1621$; right IPS: $z\text{=}1.4833,p\text{=}0.0690$). We chose one-tailed test because we already know the correlation under change-consistent signals was significantly greater than 0. In the nonparametric test, we performed nonparametric bootstrapping to test for the difference in correlation. We referred to the correlation between neural and behavioral sensitivity at change-consistent (blue) signals as $r_{blue}$, and that at change-inconsistent (red) signals as $r_{red}$. Consistent with the parametric tests, we also found that the difference in correlation was significant in left IFG and left IPS (left IFG: $r_{blue}-r_{red}\text{=}0.46,p\text{=}0.0496$; left IPS: $r_{blue}-r_{red}\text{=}0.5306,p\text{=}0.0041$), but was not significant in dmPFC, right IFG, and right IPS (dmPFC: $r_{blue}-r_{red}\text{=}0.1634,p\text{=}0.1919$; right IFG: $r_{blue}-r_{red}\text{=}0.2123,p\text{=}0.1681$; right IPS: $r_{blue}-r_{red}\text{=}0.3434,p\text{=}0.0631$). In summary, we found that neural sensitivity to signal diagnosticity measured at change-consistent signals significantly correlated with individual subjects’ behavioral sensitivity to signal diagnosticity. By contrast, neural sensitivity to signal diagnosticity measured at change-inconsistent signals did not significantly correlate with behavioral sensitivity. The difference in correlation, however, was statistically significant in some (left IPS and left IFG) but not all brain regions within the frontoparietal network.

Second, in contrast to the frontoparietal network, vmPFC in the vmPFC-striatum network showed the opposite pattern of parameter selectivity: vmPFC selectively represented individual subjects’ sensitivity to transition probability (right two columns in Figure 8D), but not to signal diagnosticity (left two columns in Figure 8D). Selectivity in vmPFC was not signal-dependent: regardless of change-consistent (blue) or change-inconsistent (red) signals, neural sensitivity to transition probability in vmPFC represented individual subjects’ sensitivity to transition probability ($r\text{=}-0.38,p\text{=}0.043$ for change-inconsistent signals; $r\text{=}-0.37,p\text{=}0.047$ for change-consistent signals). By contrast, the ventral striatum did not show selectivity to either the transition probability or signal diagnosticity (transition probability: $r\text{=}-0.26,p\text{=}0.175$ for change-inconsistent signals; $r\text{=}0.03,p\text{=}0.870$ for change-consistent signals; signal diagnosticity: $r\text{=}0.33,p\text{=}0.077$ for change-inconsistent signals; $r\text{=}0.27,p\text{=}0.150$ for change-consistent signals). In summary, these results suggest that vmPFC selectively represented individuals’ sensitivity to transition probability, whereas the frontoparietal network selectively represented individuals’ sensitivity to signal diagnosticity.

Incorporating signal dependency into system-neglect model led to better models for regime-shift detection

The neural findings on signal dependency (Figure 8) point to the possibility that participants might respond to the system parameters differently when facing change-consistent and change-inconsistent signals. This led us to ask whether building signal dependency into the system-neglect model would be a better model choice for subjects’ behavioral data (probability estimates of regime shift) than the original system-neglect model. To examine this question, we built and fit three new versions of the system-neglect (SN) model (see Supplementary file 10 for model-fitting summary) and compared them with the original model (SN-original; see Supplementary file 11 for summary of statistical tests for model comparison). In the signal-dependent β system-neglect model (SN-SigDep-β model), we estimated the β parameters separately at change-consistent and change-inconsistent signals. As a result, in this model there were 6 β parameters—three for change-consistent signals to model each of the three levels of signal diagnosticity and three for change-inconsistent signals—and three α parameters that modeled each of the three levels of transition probability without distinguishing between change-consistent and change-inconsistent signals. In the signal-dependent α system-neglect model (SN-SigDep-α model), we estimated the α parameters separately at change-consistent and change-inconsistent signals. As a result, in this model there were 6 α parameters (three for change-consistent signals and three for change-inconsistent signals) and three β parameters. In the signal-dependent α and β system-neglect model (SN-SigDep-αβ model), we estimated both α and β parameters separately at change-consistent and change-inconsistent signals (12 total parameters). Compared with SN-original, we found that SN-SigDep-β, SN-SigDep-α, and SN-SigDep-αβ qualitatively described subjects’ behavioral data (belief revision, $\Delta P_t$) better (Figure 9B–E). Further, we found that estimating α separately at change-consistent and change-inconsistent signals (SN-SigDep-α, Figure 9D) model improved model fits than estimating β separately (SN-SigDep-β, Figure 9C), suggesting that subjects responded to transition probability differently when facing change-consistent and change-inconsistent signals more than to signal diagnosticity. Model comparison using Akaike Information Criterion (AIC) revealed that SN-SigDep-αβ is the best model, followed by SN-SigDep-α, SN-SigDep-β, and SN-original (Figure 9F). Together, these results suggest that participants showed system-neglect to both transition probability and signal diagnosticity and that they responded to these system parameters differently when facing change-consistent and change-inconsistent signals. In summary, signal dependency in response to system parameters is a new behavioral finding not reported in the original Massey and Wu, 2005 study and is largely inspired by the neural sensitivity findings in the current study.

Figure 9

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In this study, we investigated how humans detect changes in the environments and the neural mechanisms that contribute to how we might under- and overreact in our judgments. Combining a novel behavioral paradigm with computational modeling and fMRI, we discovered that sensitivity to environmental parameters that directly impact change detection is a key mechanism for under- and overreactions. This mechanism is implemented by distinct brain networks in the frontal and parietal cortices and in accordance with the computational roles they played in change detection. By introducing the framework in system neglect and providing evidence for its neural implementations, this study offered both theoretical and empirical insights into how systematic judgment biases arise in dynamic environments.

Regime shifts—the transition from one state of the world to another—are present in many daily situations, from the stock market (a change from the bull to the bear market) to the state of a pandemic. Detecting regime shifts can be challenging for at least two reasons. First, the signals we receive from the environments are often noisy. A signal in favor of potential change, for example a drop in pandemic cases, can either inform a true shift in regime or simply reflect noisy fluctuations. Second, the signals we receive reflect the volatility of the environment: while some environments are more prone to changes, others are not. To capture these two key features in regime-shift detection, we designed an fMRI task based on Massey and Wu, 2005 where subjects made probability judgments about regime shifts and where we manipulated the signal diagnosticity and transition probability. Signal diagnosticity captures the level of noise inherent in the signals, while transition probability reflects the volatility of the environment. Replicating Massey and Wu, 2005, we found that overreactions to regime shifts take place when participants received noisy signals (low signal diagnosticity) but when the environments were stable (low transition probability). By contrast, when the signals are more precise but the environments were unstable, participants tended to underreact to changes. These results suggest system neglect—people respond primarily to signals and secondarily to the system that generates the signals (Massey and Wu, 2005).

At the neurobiological level, we found that regime-shift detection is jointly implemented by two networks, the vmPFC-striatum network and a frontoparietal network. The vmPFC-striatum network represented subjects’ probability estimates of change and the revision of probability estimates in the presence of new signals (belief revision). By contrast, the frontoparietal network represented the strength of change evidence and intertemporal prior probability of change—two key variables contributing to probability estimation. Guided by the system-neglect framework, we found that under- and overreactions to change are closely associated with the sensitivity of these networks in response to the system parameters—transition probability and signal diagnosticity—that impact regime changes. In particular, the vmPFC represented individual subjects’ sensitivity to transition probability, whereas the frontoparietal network represented sensitivity to signal diagnosticity. Together, these findings suggest that selectivity and sensitivity of neural responses to system parameters are key mechanisms that give rise to under- and overreactions.

Our work is closely related to the reversal-learning paradigm—the standard paradigm in neuroscience and psychology to study change detection (Fellows and Farah, 2003; Izquierdo et al., 2017; O’Doherty et al., 2001; Schoenbaum et al., 2000; Walton et al., 2010). In a typical reversal-learning task, human or animal subjects choose between two options that differ in the reward magnitude or probability of receiving a reward. Through reward feedback, the participants gradually learn the reward contingencies associated with the options and have to update knowledge about reward contingencies when contingencies are switched in order to maximize rewards. While a switch in reward contingencies can be regarded as a kind of regime shift, there are three major differences between the reversal-learning paradigm and our regime-shift task. The first difference is about learning. In the reversal-learning paradigm, the subjects must learn both the reward contingencies and the switches through experience. By contrast, in the regime-shift task, the subjects were explicitly informed about the makeup of different regimes and the transition probability. Therefore, participants do not need to learn about the different regimes and the transition probability through experience. The second difference is the kind of behavioral data collected. In our task, we asked the subjects to estimate the probability of change, whereas in the reversal-learning task, the subjects indicate their choice preferences. The third difference is on reward contingency. In the reversal-learning task, a change is specifically about change in reward contingencies, which is not the case in our task.

We believe that these major differences in task design led to three key insights into change detection from our study. The first insight is on over- and underreactions to change. At the behavioral level, we were able to identify situations that led to over- and underreactions. At the theoretical level, we were able to provide a systematic account for these over- and underreactions in the system-neglect hypothesis. Finally, at the neurobiological level, we were able to quantify the degree to which individual subjects neglected the system parameters and use these behavioral measures to unravel the neural mechanisms that give rise to over- and underreactions to change.

The second insight is on the brain networks associated with change detection. In particular, we were able to clarify whether the neural systems involved in change detection in the reversal-learning tasks are contingent on whether rewards are involved. Since the reversal-learning tasks are about learning the reward contingencies and the change in reward contingencies, it would be challenging to infer whether the neural implementations of change detection are dissociable from reward processing. Indeed, brain regions shown to be involved in the reversal-learning tasks, the OFC, mPFC, striatum, and amygdala, were also found to be highly involved in reward-related learning and value-based decision making. In the current study, unlike in reversal-learning paradigms, regimes were not defined by rewards (e.g. high reward-probability regime vs. low reward-probability regime in reversal learning paradigm). Therefore, estimating the probability of regime shifts in our task did not require considerations for change in reward contingencies. Our findings that vmPFC and ventral striatum represent probability estimates of change and belief revision therefore suggest that these brain regions might be part of a common pathway for change detection in general where changes in the state of the world do not have to be about changes in reward contingencies.

The third insight has to do with the impact of learning on change detection. Under the reversal-learning paradigm, it has been challenging to infer whether there exists a unique change-detection mechanism that is dissociable from reinforcement learning mechanisms. The way to make such inference is through theory, such as implementing a prior for state changes (Bartolo and Averbeck, 2020; Costa et al., 2015). Unlike the reversal-learning task, participants in our task did not have to learn about the different regimes through experience. Without the confound of reinforcement learning, our results help clarify the roles of change detection on choice behavior by suggesting that independent of learning, there exists a specialized change-detection mechanism in the brain that impacts decision making. This mechanism involves the participation of the vmPFC-striatum network and the frontoparietal network, which partially overlap with the brain regions involved in reversal learning. However, it remains to be seen how learning interacts with change detection. Future investigations can address this question by combining the key features of both the reversal-learning paradigm and regime-shift paradigm.

Outside of the reversal-learning paradigm, previous fMRI studies that investigated learning and belief updating in dynamic environments where change takes place regularly had identified brain regions that represent perceived likelihood of change inferred from participants’ choice behavior. Payzan-LeNestour et al., 2013 identified that the posterior cingulate cortex, postcentral gyrus, middle temporal gyrus, hippocampus, and insula correlated with subjects’ perceived likelihood of change in a multi-arm bandit task. McGuire et al., 2014 found that subjective change-point probability was represented in a large posterior cluster including occipital, inferior temporal, and posterior parietal cortex. In addition, activity in dorsomedial frontal cortex, posterior cingulate cortex, superior frontal cortex, and anterior insula also positively correlated with change probability. Interestingly, both McGuire et al., 2014 and our results found that the ventral striatum negatively correlated with probability estimates of change. This result suggested that the ventral striatum represents probability estimates of change irrespective of whether the task was based on a learning-based paradigm (McGuire et al., 2014) or a non-learning paradigm where information about task-related variables was explicitly revealed to the participants. Further, both McGuire et al. and our results found the involvement of the dorsomedial prefrontal cortex (dmPFC; or dorsomedial frontal cortex in McGuire et al.) in change detection. Our results further suggest that dmPFC is specialized in weighing the strength of change evidence and represents individual subjects’ sensitivity to signal diagnosticity, both of which played important roles in contributing to the over- and underreactions to change.

How might our results relate to value-based decision making? In previous studies, vmPFC had been implicated to dynamically track financial risks that carry potential monetary gains or losses. To understand dynamic computations of risk, Schonberg et al., 2012 used a Balloon Analog Risk Task (BART) where subjects decide whether to inflate a simulated balloon through successive pumps for the potential to win larger gains or incur larger losses (if the balloon explodes), or to cash out before the balloon explodes. They found that vmPFC activity decreased as subjects pumped and expanded the balloon, suggesting its involvement in estimating the risk of potential losses. Since the explosion of the balloon can be regarded as a change in the state of the balloon, as the balloon expands, the possibility of such a change in state (regime shift) also increases. In this view, the vmPFC result from Schonberg et al., 2012 was consistent with our finding in that vmPFC negatively correlated with probability estimates of regime shift. Together, these results add to the existing literature by suggesting that vmPFC is involved in estimating and updating the state of the world in dynamic environments where changes take place regularly.

Related to OFC function in decision making and reinforcement learning, Wilson et al., 2014 proposed that OFC is involved in inferring the current state of the environment. For example, medial OFC had been shown to represent probability distribution on possible states of the environment (Chan et al., 2016), the current task state (Schuck et al., 2016), and uncertainty or entropy associated with the state of the environment (Muller et al., 2019). In the context of regime-shift detection, regimes can be regarded as states of the environment and therefore a change in regime indicates a change in the state of the environment. Muller et al., 2019 found that in dynamic environments where changes in the state of the environment happen regularly, medial OFC represented the level of uncertainty in the current state of the environment. Our finding that vmPFC represented individual participants’ probability estimates of regime shifts suggests that vmPFC and/or OFC are involved in inferring the current state of the environment through estimating whether the state has changed. Our finding that vmPFC represented individual participants’ sensitivity to transition probability further suggests that vmPFC and/or OFC contribute to individual participants’ biases in state inference (over- and underreactions to change) in how these brain areas respond to the volatility of the environment.

Our results are also closely related to the literature on the neural mechanisms for evidence accumulation in decision making (Gold and Shadlen, 2007; Mante et al., 2013; Philiastides et al., 2010; Roitman and Shadlen, 2002; Yates et al., 2017). In our task, evaluating the signals (red or blue balls) and, in particular, the strength of change evidence associated with the signals is central to performing the task. Normatively, such evaluation should depend on the signal diagnosticity. In a highly diagnostic environment, seeing a red ball should signal a strong possibility of being in the red regime, while seeing a blue ball should signal otherwise. By contrast, in a low diagnostic environment, a red (resp. blue) ball is not strongly indicative of a red (resp. blue) regime. Hence, the evaluation of signals should reflect the interaction between the signals and the diagnosticity of the signals.

We found that this key computation was implemented in a frontoparietal network commonly referred to as the frontoparietal control network (Buckner et al., 2013; Dosenbach et al., 2007; Seeley et al., 2007; Vincent et al., 2008; Yeo et al., 2011). This network was proposed to support adaptive control functions, including initiating control and providing flexibility to adjust the level of control through feedback (Dosenbach et al., 2007). The IPS and dlPFC, part of this network, have also been found to play a major role in the top-down control of attention (Corbetta and Shulman, 2002; Woldorff et al., 2004). In perceptual decision making, the IPS and dlPFC were also shown to represent the accumulation of sensory evidence that leads to the formation of a perceptual decision (Heekeren et al., 2004; Heekeren et al., 2006). Our findings—that activity in this network does not reflect just the sensory signals (red or blue balls) but how these signals should be interpreted through the lens of their diagnosticity—highlights the involvement of the frontoparietal control network in computing the strength of evidence through combining information about signals and knowledge about the precision of those signals.

For the frontoparietal network, we identified its involvement in our task through finding that its activity correlated with the strength of change evidence (Figure 7) and individual subjects’ sensitivity to signal diagnosticity (Figure 8). Conceptually, these two findings reflect how individuals interpret the signals (signals consistent or inconsistent with change) in light of signal diagnosticity. This is because (1) strength of change evidence is defined as signals (+1 for signal consistent with change, and -1 for signal inconsistent with change) multiplied by signal diagnosticity and (2) sensitivity to signal diagnosticity reflects how individuals subjectively evaluate signal diagnosticity. At the theoretical level, these two findings can be interpreted through our computational framework in that both the strength of change evidence and sensitivity to signal diagnosticity contribute to estimating the likelihood of change (Equations 1; 2 in Materials and methods).

Our result on the intraparietal sulcus (IPS) being part of the brain network that represents diagnosticity-weighted sensory signals is consistent with previous studies showing that IPS is involved in accumulating sensory evidence over time (Gold and Shadlen, 2007). There are three interesting aspects of our data that add to the current literature on evidence accumulation. First, IPS representations for sensory evidence need not be in the space of actions. Unlike previous studies showing that IPS represents sensory evidence for potential motor actions, we found that IPS represents the strength of evidence in favor of or against regime shifts. This result points to a more general role of the IPS in estimating the strength of sensory evidence. In fact, our result suggests that it depends on the task goal, which in the current study is to estimate whether a change has taken place. Second, although evidence accumulation is important and necessary for a wide array of cognitive functions, it is not a central requirement for the regime-shift task. Bayesian updating—the framework in which our system-neglect model was built upon—only requires the computation of the strength of change evidence associated with the signal shown in the latest period. By showing that IPS represents this quantity, this suggests that IPS is involved in evaluating the latest piece of evidence necessary for belief updating.

In the current study, the central opercular cortex—in addition to the vmPFC—is another brain region that represented the probability estimates of change. Like the vmPFC, activity in this region negatively correlated with the probability estimates of change. This finding is associated with previous findings on change detection using the oddball paradigm. Using the oddball paradigm, it was found that the central opercular cortex is involved in the detection of change, showing stronger activation in blocks containing only the standard stimulus than blocks containing both the standard and deviant stimulus (Hedge et al., 2015) and correlating with ERP P3 signals at the trial-level that reflected differences between standard and deviant stimuli (Warbrick et al., 2009). There are two implications here. First, our findings suggest that the central opercular cortex is not only involved in the detection of change—as revealed by the oddball tasks—but also is involved in the estimation of change where there is uncertainty regarding whether the state of the world had changed. Second, the central opercular cortex may be part of a common pathway for the detection of change across very different tasks such as the oddball paradigm and our regime-shift detection task.

In the current study, our psychometric-neurometric analysis focused on comparing behavioral sensitivity with neural sensitivity to the system parameters (transition probability and signal diagnosticity). We measured sensitivity by estimating the slope of behavioral data (behavioral slope) and neural data (neural slope) in response to the system parameters. Previous studies had adopted a similar approach (Ting et al., 2015; Vilares et al., 2012; Yang and Wu, 2020). For example, Vilares et al., 2012 found that sensitivity to prior information (uncertainty in prior distribution) in the orbitofrontal cortex (OFC) and putamen correlated with behavioral measures of sensitivity to the prior. In the current study, transition probability acts as prior in the system-neglect framework (Equation 2 in Materials and methods), and we found that the ventromedial prefrontal cortex represents subjects’ sensitivity to transition probability. Together, these results suggest that OFC (with vmPFC being part of OFC, see Wallis, 2012) is involved in the subjective evaluation of prior information in both static (Vilares et al., 2012) and dynamic environments (current study). In addition, distinct from vmPFC in representing sensitivity to transition probability or prior, we found through the behavioral-neural slope comparison that the frontoparietal network represents how sensitive individual decision makers are to the diagnosticity of signals in revealing the true state (regime) of the environment. Interestingly, such sensitivity to signal diagnosticity was only present in the frontoparietal network when participants encountered change-consistent signals. However, while most brain areas within this network responded in this fashion, only the left IPS and left IFG showed a significant difference in coding individual participants’ sensitivity to signal diagnosticity between change-consistent and change-inconsistent signals. Unlike the left IPS and left IFG, we observed in dmPFC a marginally significant correlation with behavioral sensitivity at change-inconsistent signals as well. Together, these results indicate that while different brain areas in the frontoparietal network responded similarly to change-consistent signals, there was a greater degree of heterogeneity in responding to change-inconsistent signals.

In summary, our results suggest that an important mechanism for under- and overreactions to change has to do with neural sensitivity to system parameters that impact regime shifts. Importantly, different system parameters appear to recruit distinct brain networks according to their unique computational specializations. Given that under- and overreactions underlie a wide array of human judgments, our findings indicate that network-level computational specificity and parameter selectivity are two key building blocks that give rise to human judgment biases.

The data and analysis code are available at https://osf.io/xh7dy/.

We performed three fMRI experiments (90 subjects in total, 30 subjects for each experiment). Experiment 1 was the main experiment where we investigated the neurocomputational substrates for regime shifts. Experiments 2 and 3 were control experiments. Experiment 2 was designed to rule out brain activity that correlated with probability estimates but was not specifically about regime shifts. Experiment 3 attempted to rule out brain activity that correlated with entering numbers through button presses. In the main text, we only presented the results from Experiment 1. The procedure and results of Experiments 2 and 3 were presented in Supplementary Materials.

All data, including behavioral and fMRI, and analysis code are available at Open Science Framework: https://osf.io/xh7dy/.

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Author details

1. Mu-Chen Wang

   Institute of Neuroscience, National Yang Ming Chiao Tung University, Taipei, Taiwan

   Contribution

   Conceptualization, Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   For correspondence

   raccoon65.y@nycu.edu.tw

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0009-0004-9451-2193

2. George Wu

   Booth School of Business, University of Chicago, Chicago, United States

   Contribution

   Conceptualization, Formal analysis, Supervision, Visualization, Methodology, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

3. Shih-Wei Wu

   1. Institute of Neuroscience, National Yang Ming Chiao Tung University, Taipei, Taiwan
   2. Brain Research Center, National Yang Ming Chiao Tung University, Taipei, Taiwan

   Contribution

   Conceptualization, Resources, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   For correspondence

   swwu@nycu.edu.tw

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-2728-9620

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