We present analyses to address two key hypotheses in this experiment: First, that observers are prematurely committing to their perceptual decisions whilst continuing to monitor additional evidence for evaluating their confidence. And second, that there are separable neural signatures of the evaluation of confidence during perceptual decision-making. To address the first hypothesis, we use a combination of behavioural analyses and computational modelling, and in addition, show that the EEG signatures of response preparation are triggered from the time of decision commitment, even when this occurs seconds prior to the response cue. To address the second hypothesis, we use the stimulus evoked responses in EEG to trace the representation of the presented evidence throughout each trial. We show that these neural representations of the optimal accumulated decision evidence are less precise when the observers’ behavioural responses were also less precise relative to optimal. We use this to isolate clusters of activity that specifically reflect the internal evidence used for observers’ confidence evaluations beyond the presented evidence. We then localise the sources of this activity, and relate these processes back to observers’ eventual confidence ratings.

Human observers (N = 20) performed two versions of the task whilst EEG was recorded. Across the two tasks, 100 predefined sequences of oriented Gabors were repeated for each observer, with stimuli presented as described in Figure 1a. In the Free task, the sequence continued until observers entered their perceptual decision (Figure 1b), indicating which category (Figure 1d) they thought the orientations were sampled from. Observers were instructed to enter their response as soon as they ‘felt ready’, on three repeats of each predefined sequence (300 trials in total). In the Replay task (Figure 1c), observers were shown a specific number of samples and could only enter their response after the response cue. After entering their perceptual decision, they made a confidence evaluation, how confident they were that their perceptual decision was correct, on a four-point scale. Importantly, the number of samples shown in the Replay task was manipulated relative to the Free task, in three intermixed conditions: in the Less condition, they were shown two fewer than the minimum they had chosen to respond to over the three repeats of that predefined sequence in the Free task; in the Same condition, they were shown the median number of samples; and in the More condition, four more than the maximum. The variability across repeats in the Free task means that in the More condition, observers were show at least four additional stimuli, but often more than that. There is an optimal way to perform this task, in the sense of maximising perceptual decision accuracy across trials. The optimal computation takes as decision evidence the log probability of each orientation given the category distributions (Figure 1d) and accumulates the difference in this evidence for each category (Figure 1e, Drugowitsch et al., 2016). We refer to the accumulated difference in log probabilities as the optimal presented evidence, L. Human observers may have a suboptimal representation of this evidence, L*, and we estimate the contribution of different types of suboptimalites (specifically, inference noise, and a temporal integration bias) with the help of a computational model (full details in Materials and methods and Appendix 1).

Figure 1

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Based on our previous findings (Balsdon et al., 2020), we expected observers to prematurely commit to perceptual decisions in the More condition, whilst continuing to monitor sensory evidence for evaluating their confidence. Replicating these previous results (Balsdon et al., 2020), we found that perceptual decision sensitivity (d’) was significantly decreased with just two fewer stimuli in the Less condition compared to those same (p_min) trials in the Free task (Wilcoxon sign rank Z = 3.88, p < 0.001, Bonferroni corrected for three comparisons), but four additional stimuli in the More condition resulted in only a small but not significant increase compared to the p_max trials in the Free task (Z = -1.53, p = 0.13, uncorrected). There was also no significant difference for the Same condition (Z = 1.21, p = 0.23, uncorrected; Figure 2a).

Figure 2

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This lack of substantial increase in performance in the More condition could be the result of either a performance ceiling effect or a premature commitment to the perceptual decision. The former explanation reflects a limitation of the perceptual evidence accumulation process, whereas the latter refers to an active mechanism that ignores the final sensory evidence. We compared these two hypotheses using a computational modelling approach (Balsdon et al., 2020; see Materials and methods). Specifically, we compared a model in which performance in the More condition is limited by the suboptimalities evident from the Same and the Less conditions (inference noise, and temporal integration bias, see Materials and methods and Appendix 1), to a model in which performance could be impacted by a covert bound at which point observers commit to a decision irrespective of additional evidence. Cross-validated model comparison provided significant evidence that observers were implementing a covert bound (mean relative increase in model log-likelihood = 0.048, bootstrapped p = 0.001, Figure 2c). The winning model provided a good description of the data (red open markers in Figure 2a, and individual participants in Figure 2e).

In contrast to what we found for the perceptual decision, there was no evidence that observers were implementing a covert bound on confidence: Implementing the same bound as the perceptual decision did not improve the fit (relative improvement with bound = −0.007, bootstrapped p = 0.11, uncorrected) and an independent bound actually significantly reduced the fit compared to continued accumulation (relative improvement = −0.014, p = 0.022, Bonferroni corrected for two comparisons; Figure 2c). We obtained further distinctions between perceptual and confidence processes through computational modelling: additional noise was required to explain the confidence ratings, along with a separate temporal bias. The best description of both perceptual and confidence responses was provided by a partially dissociated computational architecture (full details in Appendix 1), where perceptual and confidence decisions are based on the same noisy representation of the sensory evidence, but confidence accumulation incurs additional noise and can continue after the completion of perceptual decision processes (Figure 2d, and the predictions of this model for individual participants are show in Figure 2e). These computational differences between perceptual decisions and confidence evaluations suggest deviations between the internal evidence on which observers base their perceptual and confidence decisions (see Appendix 2 for model simulations).

These modelling results are supported by an analysis using general linear models to examine the relationship between the optimal presented evidence, L, and observers’ behaviour in the perceptual decision and confidence evaluation. As stated above, L is the evidence that which maximises the probability of a correct response: the accumulated difference in the log probabilities of the presented orientations given the category distribution (Figure 1e). First, we find the presented evidence accumulated over all samples does explain substantial variance in observers’ perceptual decisions (average $\beta$ = 0.77, t(19) = 6.48, p < 0.001), and confidence evaluations (with the evidence signed by the perceptual response; $\beta$ = 0.24, t(19) = 6.46, p < 0.001). This suggests that the internal evidence that observers were using to make their responses, L*, correlated significantly with the optimal evidence L (as has been found previously; Drugowitsch et al., 2016). Second, the total accumulated evidence in the More condition was not a significantly better predictor of the observers’ perceptual decisions than the evidence up to four samples prior to the response (average difference in $\beta$ = 0.034, t(19) = 1.63, p = 0.12), while for the Same and Less conditions the total accumulated evidence was a significantly better predictor (Less: t(19) = 4.99, p < 0.001; Same: t(19) = 3.11, p = 0.006; causing a significant interaction between condition and sample accumulated to F(2,38) = 10.348, p = 0.001, Bonferroni corrected for three comparisons, Figure 2f, top). This supports the finding from model comparison and behaviour that observers implemented a covert bound on perceptual evidence accumulation. And finally, this interaction was not present when examining how the presented evidence affected confidence evaluations (F(2,38) = 3.124, p = 0.09, uncorrected, Figure 2f, bottom). Rather, the accumulated evidence up to the final sample in the More condition was a significantly better predictor of confidence than the evidence accumulated to four samples from the response (average difference in $\beta$ = 0.26, t(19) = 5.33, p < 0.001), supporting the prediction from the computational model analysis that observers integrated all the presented evidence for evaluating confidence.

The analysis of behaviour and computational modelling so far has suggested that observers were committing to their perceptual decisions early in the More condition and ignoring the additional evidence for their perceptual decision. We questioned the extent of this covert decision commitment, that is, whether observers were going as far as to plan their motor response before the response cue. We examined the neural signatures of the planning and execution of motor responses using a linear discriminant analysis of the spectral power of band-limited EEG oscillations (see Materials and methods). Initial analysis suggested the spectral power in the 8 to 32 Hz frequency range (the ‘alpha’ and ‘beta’ bands) could be used to classify perceptual decisions based on lateralised differences over motor cortex (Appendix 5). A classifier was trained to discriminate observers’ perceptual decisions at each time-point in a four second window around the response in the Free task (3 s prior to 1 s after). This classifier was then tested across time in each condition of the Replay task, to trace the progression of perceptual decision-making in comparison to the Free task (where decisions are directly followed by response execution). If covert decisions lead to early motor response preparation, we would expect asymmetries in cross-classification performance on trials where the observer was likely to have covertly committed to a decision (in the More condition) compared to those trials in which they were unlikely to have committed to their decision (in the Less condition). Indeed, there were opposite asymmetries in the cross-classification of the Less and the More conditions (Figure 3a). Statistical comparison revealed substantial clusters of significant differences (Figure 3b): Training around −0.78 to 0.44 s from the time of the response in the Free task led to significantly better accuracy testing in the More condition than in the Less condition, prior to when the response was entered (for the cluster testing at −2.5 to −1.6 s Z_ave = 2.04, p_cluster = 0.002; testing at −1.5 to −1 s, Z_ave = 1.95, p_cluster = 0.01; testing at −0.8 to −0.3, Z_ave = 2.32, p_cluster < 0.001). This pattern of findings suggests that observers were not only committing to their perceptual decision early, but already preparing their motor response.

Figure 3

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As an exploratory analysis, we took the strength of the classifier prediction trained and tested at the time of the response as a trial-wise measure of the decision variable used by the participant to enter a response. We reasoned that the amount of evidence in favour of the decision could influence the assiduity with which observers enter their response. We found that the optimal evidence L, accumulated over all samples, could predict the strength of the classifier prediction at response time (mean $\beta$ = 0.11, t(19) = 3.89, p < 0.001; Figure 3c). For the Same and Less conditions, the weight on the accumulated evidence appeared to decrease as evidence was accumulated to samples further prior from the response. But, in the More condition, the evidence accumulated up to four samples prior to the response still predicted the strength of the classifier prediction (t(19) = 3.81, p = 0.001). This difference between conditions over samples is evidenced by a significant interaction based on a repeated measures ANOVA (F(8,152) = 2.429, p = 0.05, after Bonferroni correction for three comparisons). Leading up to the response, the accumulated evidence becomes increasingly predictive of the strength of the classifier prediction, except in the More condition, where this prediction is already accurate up to four samples prior to the response: After committing to a perceptual decision, the observer’s perceptual response is no longer influenced by additional evidence.

Our main goal was to isolate the neural signatures of the computation of confidence. Observers’ behaviour varied with the optimal evidence L presented to them, but the internal evidence on which they based their perceptual decisions and confidence evaluations, L*, clearly deviated from L. In other words, the observers’ behavioural performance was not optimal. To identify the neural computations underlying human behaviour, we therefore began by isolating the neural signals which correlate with L. We then isolated where and when deviations in the neural representation of L covary with deviations in L* - the internal evidence reflected in observers’ behaviour.

To perform this task the optimal observer must encode the orientation of the stimulus, estimate the decision update based on the categories, and add this to the accumulated evidence for discriminating between the categories (Wyart et al., 2012; Wyart et al., 2015). We examined the neural representation of these optimal variables using a regression analysis with the EEG signals (evoked response, bandpass filtered between 1 and 8 Hz, see Materials and methods). At each time point, we used the relationship between the pattern of neural activity and the encoding variables on 90% of the data to predict the encoding variables on the remaining 10% of the data (10-fold cross validation). The precision of the neural representation was calculated as the correlation between the predicted encoding variable and actual encoding variable in the held-out data, across all 10 folds (see Materials and methods). Figure 4a shows the time course of the precision of the neural representation of stimulus orientation, momentary decision update, and accumulated evidence (L), locked to stimulus onset. The precision of the representations of these variables showed distinct time courses and relied on distinct patterns of EEG activity over scalp topography (Figure 4b). There was a transient representation of stimulus orientation localised over occipital electrodes. The representation of the momentary decision update was maintained for a longer duration, initially supported by occipital electrodes, then increasingly localised over central-parietal electrodes. The representation of the accumulated evidence was sustained even longer and relied on both frontal and occipital electrodes.

Figure 4

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The internal evidence on which observers base their response, L*, can differ from the optimal evidence, L. When the eventual behavioural response differs from that predicted by L, L* is likely to be more different from L. A neural representation of L that reflects L* (that is, reflecting the underlying processing responsible for behaviour) should also be less precise for samples in these trials. For each variable, we estimated the representation precision separately for epochs leading to behavioural responses that differed from the optimal response (based on L), and responses that matched those of the optimal observer (Replay task epochs only; Figure 4c; Appendix 3). For perceptual decisions, the optimal observer responds with the correct category. For confidence evaluations, the optimal observer gives high confidence on trials with greater than the median evidence (over all trials) for their perceptual response. The precision of the representation of stimulus orientation did not significantly vary based on whether behaviour matched the optimal response. The representation precision of the momentary decision update showed a significant effect for the perceptual decision from 380 to 468 ms (F_avg(1,19) = 7.97, p_cluster = 0.008) and a significant interaction between perceptual and confidence responses from 396 to 468 ms (F_avg(1,19) = 6.66, p_cluster = 0.022) and from 716 to 856 ms (F_avg(1,19) = 10.75, p_cluster < 0.001). The largest effects were seen in the representation precision of the accumulated evidence. Representation precision was significantly reduced in epochs leading to non-optimal perceptual decisions from 108 ms post stimulus onset to the end of the epoch (F_avg(1,19) = 13.65, p_cluster <0.001). In addition, there was a significant interaction with confidence from 696 to 836 ms (F_avg(1,19) = 8.72, p_cluster = 0.005). The precision of the EEG representations therefore showed distinct associations with behaviour.

The presence of a covert bound implies that, after the observer commits to a decision, they no longer incorporate additional evidence for that decision. We should therefore see significant decreases in the precision of representations that specifically contribute to perceptual evidence accumulation. Indeed, the precision of the early representation of accumulated evidence was significantly attenuated for the last four samples of the More condition (in which observers were likely to have already committed to a decision), compared to the last four samples of the Less condition (where observers were unlikely to have committed to a decision; from the start of the epoch to 424 ms, Figure 4d; t_avg(19) = −5.19, p_cluster<0.001). These differences in representation precision were not present for the encoding of stimulus orientation, nor the decision update, suggesting that these processes may reflect input to perceptual evidence accumulation, but not the accumulation process itself. As a control analysis, this decreased precision was not evident in a comparison of the first four samples (Appendix 6), suggesting this effect on the representation of accumulated evidence is specific to those samples likely to have occurred after perceptual decision commitment, as opposed to those samples in More condition trials per se. Together, these comparisons suggest that different aspects of these evolving EEG representations of decision variables are related to the neural processes for perception and confidence.

The analysis above shows that the EEG representation of accumulated evidence reflected greater differences from the optimal presented evidence L in trials where behaviour does not match the optimal response. This suggests that the corresponding neural signals reflect more closely L* (the internal evidence actually used by observers to decide) than L. To isolate the neural signals which reflect L*, we assume that L* approximates L with normally distributed errors, and that these errors have larger variance on trials leading to responses that do not match the optimal evidence L (a similar approach as in van Bergen et al., 2015). We used multivariate Bayesian scan statistics (Neill, 2011; Neill, 2019) to cluster signals in space (electrode location) and time where the variance from L in the neural representation corresponded to deviations in L*, based on behaviour. The statistic tested whether the variability in the neural representation was related to L* to a greater extent than could be explained by measurement noise alone (see Appendix 7 for further details). In this way, the statistic isolates signals more closely related to L* than can be explained by L, taking into account the noise affecting our measurement of these neural signals.

For perceptual decision-making, signals related to L* were initially clustered over posterior electrodes, becoming dispersed over more anterior electrodes late in the epoch (Figure 5a, top). For confidence, we found two co-temporal clusters in posterior and anterior electrodes emerging from 668 ms to 824 ms from stimulus onset (Figure 5a, bottom). In Figure 5a, we highlight an early posterior cluster of signals strongly related to L* for perceptual decisions, that was not diagnostic of confidence evaluations (in fact the evidence was in favour of the null hypothesis; summed log likelihood ratio = −1176). We obtained cluster-wide representations of L from the signals in this early posterior cluster and the two confidence related clusters. The precision of these representations is shown in Figure 5b, left. That the information from these clusters is not redundant is evident from the fact that combining the clusters improves the representation precision (Figure 5b). For simplicity, we combined the two confidence clusters for further analysis. Similar to the previous analysis (Figure 4d), the representation precision of the early posterior cluster was attenuated for the last four samples of the More condition. But, the representation precision of the confidence cluster was maintained (a repeated measures ANOVA revealed a significant interaction between cluster and condition for decoding precision in the last four samples, F(1,19) = 32.00, p = 0.001, Bonferroni corrected for three comparisons). These results are consistent with dissociable stages of neural processing for confidence evaluation and perceptual decision-making, and support the computational modelling in suggesting a partial dissociation between the internal evidence used for making perceptual decisions and confidence evaluations.

Figure 5

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We used the representation from the confidence cluster as an estimate of the internal evidence on which observers base their confidence ratings. We then took the difference from L in the estimate of L* from the cluster representation as an estimate of the single-sample inference error. This estimate of the single-sample inference error was significantly correlated with the single-sample inference error estimated from the computational model of confidence ratings (t(19) = 5.12, p < 0.001), and this correlation was significantly greater than the correlation with the error estimated from the model of perceptual decisions alone (t(19) = 2.62, p = 0.017; see Appendix 8). This suggests that this cluster representation is indeed reflecting activity specific to the computation of confidence.

We asked what processes were responsible for driving variability in the internal evidence for confidence beyond what could be explained by the evidence presented to the observer. We selected ‘Noise Min’ and ‘Noise Max’ epochs as the top and bottom quartile of epochs sorted by the estimate of the inference error from the cluster representation, and examined the source-localised EEG activity across these epochs. The presented sensory evidence was similar across Noise Min and Noise Max epochs (see Appendix 8), but the additional variability in the Noise Max epochs pushes the represented evidence further from the mean, and should therefore correspond to a greater absolute normalised signal. We estimated the sources of activity in the Noise Min and Noise Max epochs using a template brain (see Materials and methods) and tested for differences in the rectified normalised current density in ROIs defined based on the previous literature (Figure 5c; Graziano et al., 2015; Gherman and Philiastides, 2018; Herding et al., 2019, see Appendix 9). As expected, Noise Max epochs showed a greater increase in current density power over time. Significant differences first emerged in the superior parietal cortex (Figure 5d; 276 to 304 ms; t_avg(19) = 2.37, p_cluster = 0.016, re-emerging at 596 to 748 ms; t_avg(19) = 2.53, p_cluster = 0.016; and 912 ms; t_avg(19) = 2.50, p_cluster = 0.014), and then in the orbitofrontal cortex (OFC; 516 to 556 ms; t_avg(19) = 2.30, p_cluster = 0.022, re-emerging at 660 to 772 ms; t_avg(19) = 2.79, p_cluster = 0.032, and 824 to 1000 ms; t_avg(19) = 2.60, p_cluster = 0.022). No differences in the rostral middle frontal cortex nor lateral occipital cortex survived cluster correction.

Whilst the activity localised to the superior parietal cortex reflected stimulus driven computations (the consecutive peaks correspond temporally to the response to subsequent stimuli), the activity localised to the orbitofrontal cortex was more indicative of an accumulation process across samples (a smoother increase in signal over time). As an exploratory analysis, we tested whether the activity localised to the orbitofrontal cortex could predict observers’ confidence ratings, presumably by accumulating evidence for evaluating confidence up to the observers’ perceptual decision response. Indeed, the activity localised to the orbitofrontal cortex predicted observers’ confidence ratings, based on the predictions of a generalised linear model with 90/10 cross validation: the standardised regression coefficients increased up to and continued after the perceptual decision response (Figure 5e, a significant cluster was located from −300 to 520 ms around the time of the response; t_ave(19) = 3.46, cluster-corrected p < 0.001).

A total of 20 participants were recruited from the local cognitive science mailing list (RISC) and by word of mouth. No participant met the pre-registered (https://osf.io/346pe/) exclusion criteria of chance-level performance or excessive EEG noise. Written informed consent was provided prior to commencing the experiment. Participants were required to have normal or corrected to normal vision. Ethical approval was granted by the INSERM ethics committee (ID RCB: 2017-A01778-45 Protocol C15-98).

Stimuli were presented on a 24’ BenQ LCD monitor running at 60 Hz with resolution 1920 x 1080 pixels and mean luminance 45 cd/m². Stimulus generation and presentation was controlled by MATLAB (Mathworks) and the Psychophysics toolbox (Brainard, 1997; Pelli, 1997; Kleiner et al., 2007), run on a Dell Precision M4800 Laptop. Observers viewed the monitor from a distance of 57 cm, with their head supported by a chin rest. EEG data were collected using a 64-electrode BioSemi ActiveTwo system, run on a dedicated mac laptop (Apple Inc), with a sample rate of 512 Hz. Data were recorded within a shielded room.

Stimuli were oriented Gabor patches displayed at 70% contrast, subtending four dva and with spatial frequency two cyc/deg. On each trial a sequence of stimuli was presented, at an average rate of 3 Hz, with the stimulus presented at full 70% contrast for a variable duration between 50 and 83 ms, with a sudden onset, followed by an offset ramp over two flips, where the stimulus contrast decreased by 50% and 75% before complete offset. Stimulus onset timing was jittered within the stimulus presentation interval such that the timing of stimulus onset was irregular but with at least 216 ms between stimuli. These timings and stimulus examples are shown in Figure 1a.

On each trial the orientations of the presented Gabors were drawn from one of two circular Gaussian (Von Mises) distributions centred on +/- 45° from vertical (henceforth referred to as the ‘orange’ and ‘blue’ distributions, respectively), with concentration κ = 0.5 (shown in Figure 1d). Stimuli were displayed within an annular ‘colour-guide’ where the colour of the annulus corresponds to the probability of the orientation under each distribution, using the red and blue RGB channels to represent the probabilities of each orientation under each distribution. Stimuli were presented in the centre of the screen, with a black central fixation point to guide observers’ gaze.

The task was a modified version of the weather prediction task (Knowlton et al., 1996; Drugowitsch et al., 2016). Throughout the experiment, the observer’s perceptual task was to categorise which distribution the stimulus orientations were sampled from. They were instructed to press the ‘d’ key with their left hand (of a standard querty keyboard) for the blue distribution and the ‘k’ key with their right hand for the orange distribution. There were two variants of the task: The Free task and the Replay task. The trials were composed of three repetitions of 100 predefined sequences of up to 40 samples (50 trials from each distribution) for each observer (300 trials per task).

In the ‘Free’ task, observers were continually shown samples (up to 40) until they entered their response. They were instructed to enter their response as soon as they ‘feel ready’ to make a decision, with emphasis on both accuracy (they should make their decision when they feel they have a good chance of being correct) and on time (they shouldn’t take too long to complete each trial). A graphical description of this task is shown in Figure 1b.

After completing the Free task, observers then completed the Replay task. In this task they were shown a specific number of samples and could only enter their response after the sequence finished, signalled by the fixation point turning red. The number of samples was determined based on the number observers chose to respond to in the Free task. There were three intermixed conditions: In the Less condition observers were shown two fewer samples than the minimum they had chosen to respond to on that predefined sequence in the Free task; In the Same condition observers were shown the median number of samples from that predefined sequence; in the More condition observers were shown four additional samples compared to the maximum number they chose to respond to on that sequence in the Free task. After entering their perceptual response, observers were cued to give a confidence rating. The confidence rating was given on a four-point scale where 1 represents very low confidence that the perceptual decision was correct, and 4, certainty that the perceptual decision was correct. The rating was entered by pressing the ‘space bar’ when a presented dial reached the desired rating. The dial was composed of a black line which was rotated clockwise to each of 4 equidistant angles (marked 1–4) around a half circle, at a rate of 1.33 Hz. The dial started at a random confidence level on each trial and continued updating until a rating was chosen. A graphical description of this task is shown in Figure 1c.

Prior to commencing the experimental trials, participants were given the opportunity to practice the experiment and ask questions. They first performed 20 trials of a fixed number of samples with only the perceptual decision, with feedback after each response as to the true category. They then practiced the Replay task with the confidence rating (and an arbitrary number of samples). Finally, they practiced the Free task, before commencing the experiment with the Free task.

The computational model is described in full in the Materials and methods section. Briefly, the model is based on the Bayesian optimal observer with full knowledge of the category distributions (means ${\displaystyle {\mu }_1}$ and ${\displaystyle {\mu }_2}$, concentration ${\displaystyle \kappa }$), and takes as evidence the difference in the log posterior probability (${\displaystyle {\ell }_n}$) of each category given the orientation (${\displaystyle {\theta }_n}$)

where chosen values ($\kappa =0.5$, ${\mu }_1=-\pi /4$, and ${\mu }_2=\pi /4$) have been implemented in the last equation. Whilst the optimal observer perfectly sums the evidence over each sample, the suboptimal human observer accumulates evidence with some temporal integration bias, $\alpha$ (where ${\displaystyle \alpha >1}$ creates a primacy effect, and ${\displaystyle \alpha <1}$, a recency effect), and incurs inference error (noise in the estimate of the true evidence) parameterised by $\sigma$, the standard deviation of the Gaussian distribution from which each sample of noise, ${\epsilon }_n$, is drawn from. The human observer may also experience some response bias, c (the tendency to choose one category irrespective of the evidence), and incur lapses (pressing a random key), described by the lapse rate, l. The accumulated evidence, L*, up to sample n, is suboptimally accumulated by

The observer then chooses category one if L* > c, except on a proportion of trials, l, where the response is randomly selected.

These four parameters were used to capture the differences in the human observers’ responses (category choice and confidence rating) from the optimal observer who perfectly integrates all evidence presented.

In the Free task, the model was designed not only to describe the category choice, but at which sample the human observer chose to respond. This was achieved via a decision boundary, the nature of which has been addressed in previous work (Balsdon et al., 2020). The boundaries, ${\mathrm{\Lambda }}_{n+}$ and ${\mathrm{\Lambda }}_{n-}$, follow an exponential function on the average evidence over samples (which is a constant bound on the probability of a correct response), described by three parameters: the minimum, a, the scale, b, and the rate of decline, $\lambda$

There is an optimal combination of these parameters to achieve any particular proportion correct across the experiment, but the human observer may set their bound suboptimally. In addition, non-decision time (the time from the last sample integrated to pressing the response key) was described by a Normal distribution with mean ${\mu }_U$, and variance ${\sigma }_U^2$. Giving an additional five parameters for describing when the observer enters their response.

We followed the same procedure as in Balsdon et al., 2020, involving four stages:

1. Reduce the number of free parameters with a knock-out procedure.

2. Compare (covert) Bound and No-bound models of the perceptual decision in the Replay task.

3. Identify any systematic differences in the parameters required to describe the confidence ratings, compared to the perceptual decision, in order to discern the relationship between processes for perceptual decisions and confidence.

4. Apply the same Bound vs. No-bound comparison for describing the confidence ratings.

The average parameter values and fit metrics for Stage 1. are shown in Appendix 1—table 1. According to this analysis, the bias (c) and lapse rate (l) were fixed. There was some evidence the boundary minimum (a) could be fixed in the Replay task, but the preference in the Free task was to leave it free to vary.

To compare the Bound and No-bound models in Stage 2. we used five-fold cross validation. The No-bound model had two free parameters: $\alpha$ (temporal bias) and $\sigma$ (inference noise), which were fit to the Same and Less conditions of the Replay task, but tested across all conditions. The Bound model had three free parameters to describe the bound, with the inference noise and temporal bias parameters fixed to those fit to the Same and Less conditions only. In this way, the no-bound model must account for the lack of increased performance in the More condition with the suboptimalities present in the Same and Less conditions, whilst the bound model can limit performance in the More condition in particular by stopping further evidence accumulation. The results of this analysis are presented in the manuscript: the bound significantly improved the fit, mean relative increase in model log-likelihood = 0.048, bootstrapped = 0.001, Figure 2c in the main text.

Of additional interest is the pattern of parameters fit to each condition separately, when the model attempts to explain behaviour without a bound. There was little difference in parameters fit to the Same and Less conditions (mean ${\sigma }_S=0.48$, ${\sigma }_L=0.44$, Z(19) = -1.46, p = 0.15; ${\alpha }_S=0.86$, ${\alpha }_L=0.78$, Z(19) = 1.38, p = 0.17). The inference noise fit to the More condition significantly increased from the Less condition (${\sigma }_M=0.55$, Z(19) = -2.61, p_bonf*4 = 0.036), but there was significantly reduced temporal integration bias (${\alpha }_M=0.93$, Z(19) = -2.50, p_bonf*4 = 0. 0496) suggesting observers’ performance was worse than predicted by the Same and Less conditions, and they were putting less weight on the more recent evidence. These differences in parameters are consistent with the model trying to mimic bounded evidence accumulation without a bound, providing additional support for the comparison described above.

Stage 3. of the model procedure was to account for the confidence ratings. We compared three processing architectures that span the space from single-channel to dual-channel (Maniscalco and Lau, 2016). We took as the null hypothesis a serial processing (single-channel) architecture in which the confidence ratings (Type-II decisions) can be described by the exact same evidence as used to make the perceptual (Type-I) decision. A weaker version of this null hypothesis is that the same suboptimal inference process is used for both perception and confidence, but that the observer can commit to their perceptual decision whilst continuing to monitor additional evidence for evaluating their confidence (a schematic of these processes is shown in Appendix 1—figure 1). The average parameter values are shown in Appendix 1—table 2, labelled ‘Serial’ and ‘Serial continued’ respectively. Note the substantial increase in inference noise ($\sigma$) and reduction in temporal bias ($\alpha$ is closer to 1) when attempting to describe both the perceptual decision and the confidence rating compared to only the perceptual decision (Appendix 1—table 1, Replay task – bound, model c = 0; l = 0.001). This is indicative of the difficulty of describing both perception and confidence with the same suboptimalities.

At the other extreme is the parallel processing (dual-channel) architecture, in which perception and confidence are computed by independent resources, based on the same sensory input (Appendix 1—figure 1b, labelled ‘Parallel’ in Appendix 1—table 2). This is the most computationally expensive description, and provided a lack of parsimony that was only surpassed by a model that attempted to describe confidence ratings with only the inference noise evident from the perceptual decisions.

Appendix 1—figure 1

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The intermediate models in this architectural space are the partial dissociation models (Appendix 1—figure 1c), which suggest that confidence inherits the same noisy perceptual evidence as the perceptual decision, but may incur some independent suboptimalities. We compared four versions of these models: same $\sigma$ (no additional inference noise); accumulation noise (additional inference noise with each sample of evidence); read-out noise (one additional sample of noise before the confidence response); and same $\alpha$ (the temporal bias affecting the confidence accumulation is the same as that affecting the perceptual accumulation).

In all cases the models were fit to minimise the negative log-likelihood of both perceptual and confidence decisions. The model comparison overwhelmingly favoured the partial dissociation models, and of these, the best description was offered by a model with an independent temporal bias on the confidence evidence accumulation, and additional noise at the read-out stage. We caution against interpreting this result as meaning that there is no additional accumulation noise in the processing of confidence evidence, whilst the models are very similar, it is possible that the read-out noise in this case can additionally capture some noise in setting and maintaining bounds for assigning a rating to the confidence evidence.

The model comparison of Stage 3. just described mainly assumed continued, unbounded accumulation of confidence evidence (with the exception of the strictly serial processing architecture). Stage 4. was to formally compare bounded and unbounded accumulation for confidence evaluations in the same manner as with the perceptual decisions. This time, two versions of the bound were compared: the same bound as perceptual evidence accumulation (the participant could close their eyes after committing to their perceptual decisions and their responses would not change); or an independent bound (the participant can continue to accumulate evidence for confidence decisions after the committing to the perceptual decision, but will eventually stop). As reported in the manuscript, neither bound improved the fit, if anything, adding the bound decreased the log-likelihood of the model (same bound: relative improvement with bound = −0.007, bootstrapped p = 0.11, uncorrected; independent bound: relative improvement = −0.014, p = 0.022, Bonferroni corrected for two comparisons; Figure 2c, in the main text). This reflects the fact that even a very high bound affects the shape of the accumulation trace, which will harm the fit when behaviour is not affected by a bound.

In summary, this computational modelling procedure suggests a partial dissociation in the processing for perception and confidence. In the Replay task, perceptual decisions were best described by bounded evidence accumulation, enabling observers to commit to decisions before the sequence of presented samples finishes. The confidence ratings required additional noise and reduced temporal integration bias compared to the suboptimalities affected the perceptual decisions. These differences were best described by the partial dissociation architecture where confidence received the same noise samples of evidence as the perceptual decision, though they are accumulated differently. In addition, model comparison suggested confidence evidence accumulation continued to the end of the sequence, even in cases of premature commitment to the perceptual decision. The results of these comparisons replicate the results of Balsdon et al., 2020, with the exception of the confidence noise comparison: here we find evidence in favour of read-out noise, whereas the previous analysis found the models indistinguishable.

The computational model comparison suggested a partial dissociation in the evidence used to make perceptual decisions and confidence evaluations. We compared the evidence underlying the observers’ perceptual decisions and confidence ratings by simulating the winning computational model. For each trial, 10,000 samples of noise per decision update were randomly sampled from the Gaussian distribution describing the observer’s inference noise. These were combined to give 10,000 simulated evidence traces per trial. The first 1,000 simulated evidence traces that agreed with the observer’s response on that trial were taken to measure the median evidence trace (or, the process was repeated until 1,000 adequate simulated evidence traces were drawn, up to 100 repeats). Appendix 2—figure 1a demonstrates this process for one example trial of one observer. For the perceptual evidence (Appendix 2—figure 1a, left) simulated evidence traces that agreed with the observer’s response are those that reach the respective decision bound before the opposing decision bound, or reach no bound but show evidence in favour of the response by the final sample. It was assumed that once the evidence reaches the bound, that evidence is maintained until the response. For the confidence evaluation (in the example, a confidence rating of 3), the final evidence had to be between the confidence rating bounds to agree with the observer’s confidence decision (after the final sample of additional noise – which is why a few samples in Appendix 2—figure 1a, right, exceed the bounds). The median evidence was compared to the ideal evidence (green lines of Appendix 2—figure 1a).

Appendix 2—figure 1

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The estimated inference error (used in Appendix 7) scaled the difference between the median consistent evidence and the ideal evidence by the probability of the response given all samples, to estimate the relative deviation of the observers’ internal evidence from the optimal observer’s evidence. This estimate of the error is quite imprecise: the median trace tends to be quite close to the ideal, even though any one of the traces (which reflect much larger error) could have described the internal evidence of the observer. Appendix 2—figure 1b shows the predicted final accumulated evidence for the perceptual (Type-I) compared to the confidence (Type-II) decision for the same example observer. The evidence is strongly correlated but there are substantial deviations, because of the additional noise, different temporal bias, and continued accumulation for the confidence decision, especially in the More condition (light blue). The example observer is a more extreme case because of the relatively strong bound on perceptual evidence accumulation. The (Fisher transformed) correlation for each observer is shown in Appendix 2—figure 1c. For many observers there are substantial differences between the median simulated evidence consistent with the perceptual and confidence responses, meaning the simulated evidence could be useful in distinguishing representations important for perception vs. confidence.

Proportion correct increased with increasing confidence, reflecting the observers’ ability to use their confidence ratings to discriminate correct from incorrect responses (Appendix 3—figure 1a). Observers appeared to be monitoring the decision evidence to make their confidence ratings, as opposed to some proxy for confidence such as the number of samples they were shown (Appendix 3—figure 1b and c).

We required a single-trial measure of confidence precision for identifying the key neural processes underlying the computation of confidence. To do so, we compared observers’ responses to an optimal observer. The optimal observer perfectly accumulates all presented evidence and assigns ratings to equally partition the evidence for their perceptual decision. To simplify, we split trials by the median evidence for the chosen category, where the optimal observer gives a high confidence rating (3 or 4) to those trials with greater than the median evidence, and a low confidence rating (1 or 2) to those with less than the median evidence. We labelled trials as ‘suboptimal confidence’ when the observer’s confidence response disagreed with the response of this optimal observer. This trial labelling is demonstrated for two example observers in Appendix 3—figure 1d. We reasoned that on suboptimal confidence trials the internal evidence of the human observer was less likely to be close to the optimal presented evidence, and the neural representation of the optimal presented evidence should be less precise in neural circuits that actually represent this suboptimal confidence evidence. That this measure of confidence precision does capture the suboptimalities in confidence evaluation is confirmed by the significant increase in model estimated confidence error on suboptimal confidence trials (Wilcoxon sign rank test: Z(19) = 3.85, p < 0.001; Appendix 3—figure 1e).

Appendix 3—figure 1

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In this way, observers’ confidence is assessed relative to a “super-ideal” observer, who has perfect access to the presented evidence (Mamassian and de Gardelle, 2021). Theoretically, observers’ confidence should be assessed relative to the internal evidence for their perceptual decision, that is, relative to the evidence based on suboptimal inference (afflicted by noise and temporal integration biases). However, the single-trial estimates of the internal evidence for perceptual decisions, based on model simulations, were relatively imprecise (see Appendix 2), and could also introduce systematic errors from the model assumptions, making this estimate of the internal evidence unappealing for the purpose of assessing confidence. Moreover, the goal of this measure was to compare observers’ confidence ratings to the neural representation of the accumulated evidence, which was also assessed relative to the optimal evidence. We therefore chose to assess confidence ratings relative to the optimal observer in the same way that neural responses were assessed relative to optimal, though this ignores the fact that some suboptimality is actually inherited from perceptual decision processes.

A second important consideration with this measure is that it is affected by confidence bias. There are three types of biases that could affect confidence ratings: first, a response bias to enter a certain response irrespective of the evidence; second, a miscalibration bias such that ratings mean different things to different observers (the same value of evidence will be given a rating of 4 for one observer and 3 for another, for example); third, a miscalling bias such that perceptual evidence is relatively exaggerated or diminished in the assessment of confidence. All these biases mean that the same internal perceptual evidence could result in systematically different confidence ratings across observers, and observers could report on average higher or lower confidence despite similar perceptual performance and precision in representing the internal evidence for evaluating their confidence.

Taking an average proportion of suboptimal confidence ratings and comparing across observers would result in observers of similar ability having different scores simply because of biases in how they implement the confidence rating responses: greater biases will increase average proportion suboptimal. Importantly, this single-trial measure of confidence was not used for this purpose. Rather, it was compared to neural activity during the process of accumulating evidence for the perceptual decision and confidence evaluation. We expect that biases that are not of interest for the computation of confidence (in particular, response bias and miscalibration bias) are incorporated at a later stage, when the confidence evaluation is converted into a rating for executing the response. The biases will only reduce the sensitivity with which a trial labelled as suboptimal truly reflects internal evidence that differs from optimal, reducing our ability to identify neural processes underlying confidence computation. This is simulated in Appendix 3—figure 1f, where a relative bias is introduced by assessing human confidence ratings to a biased optimal observer (who responds on 65% of trials with high confidence – making the human observers relatively more liberal, or 35% high confidence – making the human observers more conservative). The general trend for the difference between confidence ratings that match the (biased) optimal observer and those that are suboptimal remains the same, though the bias reduces the difference.

To link back with the previous literature, we present here two more classical EEG analysis approaches, examining the modulations of EEG amplitude around the time of the response. In Appendix 4—figure 1a, we show the Lateralised Readiness Potential (LRP; difference in microvolts between the average of electrodes [C1, C3], and [C2, C4], signed by response hand; Deecke et al., 1976). The data are unfiltered with the exception of the pre-processing, and baselined using the 100 ms before the onset of the first stimulus of each trial. There was a significant difference in the LRP between the Less and More conditions of the Replay task from just after the response (the first cluster from 32 to 196 ms; t_ave(19) = −3.57, p_cluster < 0.002, Appendix 4—figure 1a, top). There were also differences based on perceptual decision accuracy (from −84 ms to 652 ms around the response, with the largest difference just after the response, t_ave(19) = 2.81, p_cluster < 0.002; Appendix 4—figure 1a, middle). There was no significant difference in the LRP between trials with high confidence (ratings of 3 and 4) and low confidence (ratings of 1 and 2; Appendix 4—figure 1a, bottom).

Appendix 4—figure 1

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We also computed the Central Parietal Positivity (CPP; O'Connell et al., 2012) which has previously been shown to reflect perceptual evidence accumulation. We followed the methods presented in Kelly and O'Connell, 2013: data were lowpass filtered at 45 Hz with no highpass filter, and converted to current source density (Kayser and Tenke, 2006). As with the LRP, a baseline was taken from the 100 ms before the onset of the first stimulus of each trial. The slopes of the CPP (a linear fit from −500 to −50 ms) showed no significant differences across all conditions (F(1,19) = 2.15, p = 0.14). We observed a significantly greater slope for correct compared to incorrect decisions (t(19) = −2.86, p = 0.01), and an even greater difference between high and low confidence trials (t(19) = −3.24, p = 0.004). This is consistent with the literature suggesting the CPP traces the internal evidence for the perceptual decision, however it is difficult to disambiguate how this signal may differentially contribute to perceptual decisions and confidence evaluations.

A linear discriminant analysis was used to classify the perceptual decision response based on the spectral power of band-limited EEG signals in epochs locked to the time of the response. The spectral power across frequency tapers from 1 to 64 Hz with 25% spectral smoothing was resolved using wavelet convolution implemented in FieldTrip (Oostenveld et al., 2011). The epochs were then clipped at −3 to 1 s around the time of entering the perceptual decision response. We first trained and tested at each frequency taper at each time point in the Free task (Appendix 5—figure 1a). Classifier performance was measured as the area under the curve (AUC). The power in frequency bands between 8 and 32 Hz yielded the most accurate classification performance. The difference in the average power across these frequency bands between −0.5 and 0.5 s around the time of the response for right- and left-handed responses showed a clear lateralisation over central and parietal electrodes (Appendix 5—figure 1b). Training and testing at each time point in each condition of the Replay task showed a similar pattern to the Free task, with reliable classifier performance from around −0.5 to 0.5 s around the response (Appendix 5—figure 1c). Training and testing within each condition of the Replay task resulted in a larger between-subject error, likely because there are only 100 trials per condition. In the main text, we present a cross-classification analysis where the classifier is trained on the Free task, and tested on each condition in the Replay task, which more directly examines when the signals relevant for entering a response (based on the Free task) emerge during the lead up to the response in each condition of the Replay task.

Appendix 5—figure 1

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Linear regression was used to examine the representation of encoding variables in the EEG signals. First, regression weights (${\displaystyle \hat{W}}$) were computed using ridge regression of the encoding variables (C, an n × 1 matrix) on the EEG signals (D, an n × m matrix, where m is the number of EEG signals, and n, the number of epochs)

The regularisation parameter, $\lambda$, was set to 1, where I is the identity matrix. Weights were computed on 90% of the epochs, and used to predict the encoding variables on the other 10% (10-fold cross validation) simply as: ${\displaystyle \hat{C}=D\ast \hat{W}}$. The precision of the prediction was calculated as the correlation between ${\displaystyle \hat{C}}$ and C, standardised using a Fisher transformation.

Three different encoding variables, $C_{\theta }$, ${\displaystyle C_{\ell }}$, and $C_z$, were examined (Appendix 6—figure 1a): the stimulus orientation ($C_{\theta }=\pi -\left|{\theta }_n\right|$), the momentary decision update (${\displaystyle C_{\ell }=\left|{\ell }_n\right|=\left|\kappa cos\left(2\left({\theta }_n-{\mu }_1\right)\right)-\kappa cos\left(2\left({\theta }_n-{\mu }_2\right)\right)\right|}$), and the accumulated evidence (${\displaystyle C_z=z_n=\sum _{N=1}^n{\ell }_N}$, signed by the response). These variables are not entirely independent: There is a weak correlation between the stimulus orientation and the momentary decision update (r = 0.03), and a weak correlation between the momentary decision update and the accumulated evidence (r = 0.09). In addition, the accumulated evidence is strongly correlated over samples (r = 0.92 at n+1, and r = 0.85 at n+2). The cross-correlations are shown in Appendix 6—figure 1c.

Appendix 6—figure 1

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The EEG signals in D were low-pass filtered and decomposed into real and imaginary parts using a Hilbert transform. Regression precision was first calculated using the signals from all electrodes (m = 128) separately for each time-point in the stimulus-locked epochs. Initial analysis showed a low-pass cut-off of 8 Hz was appropriate to decrease noise whilst maintaining precision (Appendix 6—figure 1b). The previous literature has shown similar results (Salvador et al., 2020).

Temporal generalisation of the representation of encoding variables was tested by computing weights at each time point and testing the predicted encoding variables across time (Appendix 6—figure 1d). Though the representation of the momentary decision update is maintained for a relatively longer duration than the representation of stimulus orientation, there is little temporal generalisation, suggesting the representation in the EEG signals evolves over time. This is also the case for the representation of accumulated evidence, however, there are also strong off-diagonals in the temporal generalisation matrix. This is likely because of the strong correlation across consecutive samples (Appendix 6—figure 1c).

The precision of the representation of accumulated evidence was compared across the Less and More conditions for the first four and the last four stimuli (Appendix 6—figure 1e). As reported in the main text, representation precision was substantially attenuated for the last four stimuli of the More condition. This was not the case for the first four samples, where decoding precision in the More condition was briefly (from 132 to 244 ms) greater than in the Less condition (t_ave(19) = 3.67, p_cluster < 0.001).

Given the sustained precision of decoding accumulated evidence over time, and the strong correlation between consecutive samples, it is curious that the measured precision does drop to baseline at the start of the epoch. That the same pattern is found when decoding sample n-1 and sample n+1 based on the epoch at sample n (Appendix 6—figure 1f) suggests that the onset of the stimulus is disrupting the ongoing representation (or at least, our ability to measure it). Furthermore, this decrease in performance is not seen in the temporal generalisation matrix, where the off-diagonal is not aligned with the onset of successive samples (due to the jitter in stimulus presentation timing). Comparing precision between groups of epochs where the timing of the subsequent sample is aligned (Appendix 6—figure 1g; red 317 ms, green 333 ms, blue 350 ms) suggests there could be an interaction between the timing of ongoing updates and the precision of the representation of the accumulated evidence (but not the momentary decision update). This could be of interest for future research.

Cluster modelling was used to isolate contiguous signals in space (electrode location) and time, where the precision of the representation of optimal accumulated evidence systematically varied how closely the internal representation of evidence matched optimal, based on whether behavioural responses matched the optimal observer. We assume that responses that do not match the optimal observer are based on evidence that deviates further from the optimal evidence. Neural signals that reflect the internal evidence of the observer should also deviate further from the optimal evidence used in the regression on these trials, and be closer to the optimal evidence on trials where the observers response matched the optimal observer. Clusters were isolated using a multivariate Bayesian scan statistic (Neill, 2011; Neill, 2019). This statistic was calculated based on the log-likelihood ratio of the alternative hypothesis (that representation precision depends on the internal evidence of the observer) against the null hypothesis (that any difference in representation precision is due to measurement noise alone, which is independent across epochs). It is assumed that the neural signals reflect the input (cumulative presented evidence) with added measurement noise ($N_m$) and, when the neural signals are relevant for behaviour, inference noise ($N_i$) that reflects the deviations from the optimal evidence in the internal representation of the observer

Where the two sources of noise are assumed to be gaussian distributed ($N(0,{\sigma }^2)$). The total measured correlation ($r_T)$ between $Y_{in}$ and $Y_{out}$ is a function of the additional noise (where Y_in is normalised)

When the observer’s decision does not match the optimal decision their internal representation of the accumulated evidence is likely to be further from the optimal value, resulting in a weaker correlation between the internal representation and the presented evidence. Therefore, when we split based on behaviour, we expect that on average there is greater inference noise on incorrect trials than correct trials. The correlation over all samples can be described as

where p(I) is the observed probability of a decision that does not match the optimal observer, and p(C), a decision that corresponds to that of the optimal observer. The null hypothesis is that the neural signal is not relevant for behaviour, specifically, signals on suboptimal trials do not reflect additional inference noise. Any difference in the correlation is due to variance in the measurement noise,

The alternative hypothesis is that the neural signals are relevant for behaviour, reflecting the greater variance from optimal on trials where the observer makes a decision that does not match the optimal decision,

The difference in the inference noise is limited by the total variance

Solving for ${\displaystyle {\sigma }_{iI}^2\left(\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{e}p\left(C\right)+p\left(I\right)=1\right)}$:

If we consider the correlation between the neural representation and the presented evidence on trials with optimal and non-optimal responses separately (for simplicity, let $R=\frac{1}{r_T^2}$),

Setting a uniform prior on the ratio of inference and measurement noise, results in a linearly descending prior on x

We actually measure the difference in the Fischer transform of the correlation

Since $r_c$ and $r_I$ are independent of the assumed measurement noise, there is one $x$ that corresponds to a measured difference $z_C-z_I$, given the overall correlation $r_T$.

For each participant, for each electrode, at each time-point, the prior on ${\sigma }_m^2$ for $H_0$ is calculated by permuting the data labels (accurate vs inaccurate behavioural responses). The probability of the data given $H_0$ and $H_1$ are calculated as above and used to compute the loglikelihood ratio

The clusters are identified using the Fast Subset Sums procedure: The loglikelihood ratios are summed across participants, for each electrode and time-point. We then find small clusters by thresholding the log posterior odds ratio

where the prior p($H_1$) is set to 0.05. The cluster with the largest LLR (summed across electrodes and time points) is then expanded by continuing to add the largest neighbour and the new log prior (p($H_1$) = 0.05/n), where n is the size of the cluster, whilst the POR remains in favour of $H_1$. This is repeated until all clusters with evidence in favour of $H_1$ have been identified.

We aimed to examine the neural processes that are important for the representation of the decision evidence for computing confidence. To do so, we explored the source(s) of the activity reflecting the neural representation of the accumulated evidence in the clusters of signals identified as relevant for confidence evaluations. We use the representation from the cluster as an estimate of the internal evidence the observer uses to make their confidence evaluations. The cluster inference error is the absolute difference between the predicted value (on each sample) and the optimal value given the presented evidence. We take this as an estimate of the inference error of the observer at the sample level. This estimate is likely substantially affected by measurement noise, however, we do not expect measurement noise to be systematically driven by a specific source, especially not across subjects. Noise Min and Noise Max epochs were selected by taking the top and bottom quartiles of epochs sorted by this estimate of inference error.

A separate estimate of the inference error was obtained by simulating the computational model (Appendix 8—figure 1a shows the process of obtaining these estimates and their mutual reliance on the input stimulus variables and the behavioural output). This computational model estimate also has its drawbacks: It is relatively imprecise, given the large range of errors that are consistent with the observers’ behavioural responses (see Appendix 2); and is based on the assumptions of the model. By examining these two estimates, we avoid relying on the same set of assumptions throughout the analysis. As reported in the Results section, the estimate of the single-sample inference error from the cluster representation was significantly correlated with the single-sample inference error estimated from the computational model of confidence ratings (t(19) = 5.12, p < 0.001), and this correlation was significantly greater than the error estimated from the model of perceptual decisions alone (t(19) = 2.62, p = 0.017). This correlation between these estimates suggests that they do tap into the suboptimal inference of the observer.

Appendix 8—figure 1

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Appendix 8—figure 1b shows the correlation of these estimates of the inference error and different variables related to the stimulus presentation and behaviour, averaged across subjects. We also examined the average absolute effect size of the within subject difference between different variables dividing trials by Noise Min and Noise Max epochs is shown in Appendix 8—figure 1c. There was a larger effect on confidence inference error (d = 0.06) than perceptual inference error (d = 0.02), from the model estimate. There were some effects on stimulus variables: a small effect of condition (More vs Less, d = 0.03), a large effect on sample position in the sequence (Noise Min epochs tended to correspond to earlier samples, d = 0.2), and an effect on decision update (Noise Min epochs tended to correspond to smaller momentary decision updates, d = 0.08). The effects on behaviour were largest for confidence accuracy (d = 0.06), with limited effect on perceptual accuracy (d = 0.02) and confidence rating (Noise Min epochs were somewhat more associated with high confidence ratings, d = 0.03).

Regions of interest were selected based on the previous literature. Specifically, Herding et al., 2019 found subjective evidence to modulate activity in the superior parietal cortex; Gherman and Philiastides, 2018 found correlates of confidence encoding in the ventro-medial prefrontal cortex (overlapping with the MindBoggle orbitofrontal cortex coordinates), whilst Graziano et al., 2015 examined ROIs in the anterior cingulate cortex, orbitofrontal cortex, temporal lobe, posterior parietal cortex, and occipital cortex. We chose to use ROIs defined by MindBoggle (Klein et al., 2017) that corresponded to similar regions: lateral occipital cortex, superior parietal cortex, orbitofrontal cortex (combining medial and lateral partitions), rostral middle frontal cortex, and initially the anterior cingulate cortex (combining rostral and caudal partitions; Appendix 9—figure 1b). These regions do not necessarily map on to regions of the greatest current density (Appendix 9—figure 1a shows the current density over time for the Noise Min epochs). The results of the anterior cingulate cortex were similar to the neighbouring orbitofrontal region, so we decided not to present this in the manuscript for simplicity. We show the results in Appendix 9—figure 1c, for left and right hemispheres separately (statistical analyses were performed on the average).

Appendix 9—figure 1

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The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Human subjects: Participants provided written informed consent prior to commencing the experiment. Ethical approval was granted by the INSERM ethics committee (ID RCB: 2017-A01778-45 Protocol C15-98).

© 2021, Balsdon et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.