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Subjective confidence reflects representation of Bayesian probability in cortex

Nature Human Behaviour volume 6, pages 294–305 (2022)Cite this article

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A Publisher Correction to this article was published on 09 March 2022

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Abstract

What gives rise to the human sense of confidence? Here we tested the Bayesian hypothesis that confidence is based on a probability distribution represented in neural population activity. We implemented several computational models of confidence and tested their predictions using psychophysics and functional magnetic resonance imaging. Using a generative model-based decoding technique, we extracted probability distributions from neural population activity in human visual cortex. We found that subjective confidence tracks the shape of the decoded distribution. That is, when sensory evidence was more precise, as indicated by the decoded distribution, observers reported higher levels of confidence. We furthermore found that neural activity in the insula, anterior cingulate and prefrontal cortex was linked to both the shape of the decoded distribution and reported confidence, in ways consistent with the Bayesian model. Altogether, our findings support recent statistical theories of confidence and suggest that probabilistic information guides the computation of one’s sense of confidence.

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Fig. 1: Overview of sources of noise and three observer models.
Fig. 2: Ideal observer predictions.
Fig. 3: Reported confidence, behavioural variability and decoded sensory uncertainty.
Fig. 4: Activity in dAI, dACC and left rlPFC over time.

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Data availability

The preprocessed behavioural and fMRI data for individual participants, as well as unthresholded statistical maps from the whole-brain univariate analysis, can be downloaded from https://doi.org/10.34973/983b-a047. To protect participant privacy, the raw data are available from the corresponding author upon request. Source data are provided with this paper.

Code availability

All custom code is available from the corresponding author upon request. Custom code for the probabilistic decoding technique can also be found at https://github.com/jeheelab/.

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Acknowledgements

We thank A. Sanfey and R. Cools for helpful discussions, C. Beckmann for advice on statistical analyses and P. Gaalman for MRI support. This work was supported by European Research Council Starting Grant No. 677601 (to J.F.M.J.). The funder had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

Authors and Affiliations

  1. Donders Institute for Brain, Cognition and Behavior, Radboud University, Nijmegen, the Netherlands

    Laura S. Geurts, James R. H. Cooke, Ruben S. van Bergen & Janneke F. M. Jehee

  2. Zuckerman Mind Brain Behavior Institute, Columbia University, New York, NY, USA

    Ruben S. van Bergen

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  1. Laura S. Geurts
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  3. Ruben S. van Bergen
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  4. Janneke F. M. Jehee
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Contributions

L.S.G., R.S.v.B. and J.F.M.J. conceived and designed the experiments. L.S.G. collected the data. L.S.G. analysed the data, with help from J.F.M.J. L.S.G. and J.R.H.C. constructed the ideal observer models, with help from J.F.M.J. L.S.G., J.R.H.C., R.S.v.B. and J.F.M.J. wrote the manuscript.

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Correspondence to Janneke F. M. Jehee.

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Nature Human Behaviour thanks Dan Bang, Pascal Mamassian and Peter Murphy for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Trial structure.

Each trial started with the presentation of an oriented grating (1500 ms) followed by a 6000-ms fixation interval and two 4500-ms response intervals, during which the participant first reported the orientation of the previously seen stimulus by rotating a bar, and then indicated their level of confidence in this judgment on a continuous scale. Trials were separated by a 1500-ms intertrial interval. Stimulus, response bar and confidence scale are not drawn to their true scale and contrast.

Extended Data Fig. 2 Orientation and uncertainty decoding performance.

The orientation of the presented stimulus, and associated uncertainty, decoded from activity patterns in areas V1-V3. (a) Orientation decoding performance was quantified by means of the circular equivalent of the Pearson correlation coefficient between presented and decoded orientations. Correlation coefficients were computed for each subject individually and then averaged across subjects (N = 32). Presented and decoded orientations were significantly correlated (z = 83.58, p < 0.001, r = 0.60, 95% CI = [0.58, 0.61]). (b-d) To assess the degree to which the decoder captured uncertainty contained in neural population activity, we compared decoded uncertainty to behavioral variability, the rationale being that a more precise representation in cortex should also result in more precise behavioral estimates (see also10). (b) Corroborating our approach, we found that decoded uncertainty was greater for oblique compared to cardinal orientation stimuli (correlation distance-to-cardinal and decoded uncertainty: z = 2.95, p = 0.002, ρ = 0.025, 95% CI = [0.0083 0.041]). This finding was paralleled by the imprecision in observer behaviour (correlation distance-to-cardinal and behavioral variability: t(287) = 13.60, p < 0.001, r = 0.63, 95% CI = [0.55, 0.69]). (c-d) In addition, behavioral orientation responses were more precise when the decoded probability distributions indicated greater certainty in cortex, (c) both across orientation stimuli (correlation decoded uncertainty and behavioral variability: t(287) = 2.30, p = 0.011, r = 0.13, 95% CI = [0.019, 0.25]), and (d) when controlling for orientation (t(286) = 1.68, p = 0.047, r = 0.099, 95% CI=[−0.017, 0.21]). Altogether, this further underscores the validity of the decoding approach and shows that decoded uncertainty reliably characterizes the degree of imprecision in cortical representations of the stimulus (see10,18 for further proof of this approach). Note that these are partial residual plots, which is why the data is centered around 0. Error bars (a-b) represent ± 1 s.e.m. (c-d) Shades of red indicate ten equal-size bins of increasing decoded uncertainty, dots represent individual observers (N = 32).

Extended Data Fig. 3 Oblique effect in reported confidence and decoded uncertainty.

Effect of stimulus orientation on reported confidence (a) and decoded uncertainty (b). Each participant’s data were first binned based on the absolute distance between presented stimulus orientation and the nearest cardinal axis (equal-width bins), and then averaged across trials and finally across subjects (error bars represent ± 1 s.e.m). Dashed lines indicate best-fitting function (least-squares; quadratic for confidence, linear for decoded uncertainty). Functions were fitted on the trial-by-trial data for each participant, and averaged across participants.

Extended Data Fig. 4 Relationship between decoded uncertainty and reported confidence across different numbers of voxels.

Correlation coefficients between decoded uncertainty and reported confidence as a function of the number of voxels included in the ROI, both across all orientations (a) and after removing the effect of stimulus orientation (b). Voxels within V1-V3 were ranked and selected for multivariate analysis based on their response to the visual localizer stimulus (see Methods), using a lenient statistical threshold of p < 0.01, uncorrected. The results proved reasonably robust to variations in the number of voxels selected for analysis. Dark red line indicates group average correlation coefficients, error bars denote ± 1 s.e.m.

Extended Data Fig. 5 No effects of overall BOLD or eyetracking measures on confidence.

Reported confidence is not significantly correlated with the mean BOLD response to the stimulus in areas V1-V3 (z = 0.73, p = 0.47, ρ = 0.0062, 95% CI=[−0.010, 0.023]; equivalence test: z=−0.094, p<0.001), nor with mean eye position (mean absolute distance to screen center; z=−1.38, p=0.17, ρ = −0.012, 95% CI=[−0.030, 0.0051]; equivalence test: z=−0.088, p<0.001), eye blinks (z=0.99, p=0.32, ρ = 0.0087, 95% CI=[−0.0086, 0.026]; equivalence test: z=−0.11, p<0.001), or the number of breaks from fixation during stimulus presentation (z=0.57, p=0.57, ρ = 0.0050, 95% CI=[−0.012, 0.022]; equivalence test: z=−0.11, p < 0.001), suggesting that participants did not rely on heuristics in terms of eye position (‘did I look at the stimulus?’) or eye blinks (‘were my eyes closed?’) for reporting confidence. It furthermore rules out simple heuristic explanations in terms of attentional effort (‘my mind was elsewhere’, ‘I didn’t really try that hard’), as the mean BOLD response to the stimulus tends to increase with attention in these areas73. Shaded blue represents ± 1 s.e.m. Gray dots denote individual observers (N = 32).

Extended Data Fig. 6 Effects of decoded uncertainty and reported confidence on the BOLD response in precuneus, supplementary motor area, dorsal perigenual anterior cingulate cortex, ventral posterior cingulate cortex, dorsal posterior cingulate cortex, and stimulus-driven voxels in V1-V3.

Group-average correlation coefficients for the relationship between decoded uncertainty and BOLD contrast, and reported confidence and BOLD contrast, in six ROIs. (a) In precuneus, the effects of both decoded sensory uncertainty and reported confidence on BOLD peaked around the same time, i.e. during the second half of the response window. This finding is consistent with previous work suggesting that precuneus may represent uncertainty in memory but not in perception74,75,76. (b) In supplementary motor area, both decoded uncertainty and reported confidence modulated cortical activity relatively early in the response window, while the effects of confidence lingered until after observers gave their response. (c-d) In dorsal perigenual anterior cingulate cortex and ventral posterior cingulate cortex, decoded uncertainty had a moderate effect on the BOLD response. Reported confidence modulated cortical activity during as well as shortly after the response window. (e) In dorsal posterior cingulate cortex, the modulatory effect of both decoded uncertainty and reported confidence on the cortical response was largest around the onset of the response window. (f) Stimulus-driven voxels in early visual cortex were modulated by both decoded uncertainty and reported confidence, most notably during the first portion of the response interval. Given the timing of the effect (and taking into account the hemodynamic delay), this likely does not reflect uncertainty in the sensory representation per se, but is consistent with anticipatory processes or working memory-related signals potentially influenced by the imprecision in the cortical stimulus representation77,78,79. Please note there is no net effect of uncertainty on the overall (univariate) BOLD response during the decoding window (stimulus presentation; dashed lines). (a-f) Horizontal lines indicate statistical significance (p < 0.05, FWER-controlled). Error bars represent ± 1 s.e.m. Dark gray area marks stimulus presentation window, light gray area marks response window.

Extended Data Fig. 7 Effects of decoded uncertainty and reported confidence on the BOLD response in dAI, dACC and rlPFC, after accounting for trial-by-trial fluctuations in behavioral response times.

Behavioral response time effects were linearly regressed out from decoded uncertainty and reported confidence, prior to computing the Spearman correlation coefficient between decoded uncertainty (reported confidence) and the BOLD response at different moments in time after stimulus presentation. The remaining analysis steps are identical to those in the main text. Removing the effect of behavioral response time did not qualitatively change the pattern of results in any of these ROIs. Horizontal lines indicate statistical significance (p < 0.05, FWER-controlled). Dark gray area marks stimulus presentation window, light gray area denotes response window. Error bars represent ± 1 s.e.m.

Extended Data Fig. 8 Effects of decoded uncertainty (or reported confidence) on the BOLD response in dAI, dACC and rlPFC, after controlling for confidence (or decoded uncertainty).

Reported confidence (or decoded uncertainty) was linearly regressed on both decoded uncertainty (or reported confidence) and the BOLD response at different moments in time after stimulus presentation. The residuals of these fits were then used to compute the group-averaged correlation coefficient between cortical response amplitude and decoded uncertainty (red) or reported confidence (blue). For all ROIs, the results are qualitatively similar to the main results reported in Fig. 4 in the main text. Horizontal lines indicate statistical significance (p < 0.05, FWER-controlled). Dark gray area marks stimulus presentation window, light gray area denotes response window. Error bars represent ± 1 s.e.m.

Extended Data Fig. 9 Activity in dAI, dACC, and left rlPFC mediates the relationship between decoded uncertainty and reported confidence.

To assess the degree to which the cortical activity in these regions mediates the observed relationship between decoded uncertainty and reported confidence, we performed the following analysis. We first modeled both uncertainty and confidence as a function of the overall BOLD signal in a given ROI at each timepoint, and then used the residuals of these fits to compute the Spearman correlation coefficient between decoded uncertainty and reported confidence when controlled for the BOLD signal. From the resulting correlation coefficient, we subtracted the (baseline) correlation coefficient that was obtained while we did not control for the BOLD signal (see Fig. 3c). We observed a significant net effect at various moments in time, which indicates that there was a reliable reduction in the strength of the inverse (negative) correlation coefficient between uncertainty and confidence when we controlled for BOLD intensity. This suggests that the level of cortical activity in these windows (partially) mediates the relationship between decoded uncertainty and reported confidence. Horizontal lines indicate statistical significance (p < 0.05, FWER-controlled). Dark gray area marks stimulus presentation window, light gray area denotes response window. Dashed lines indicate the decoding window used in the main analyses (Fig. 3b-c and Extended Data Fig. 2). Error bars represent ± 1 s.e.m.

Extended Data Fig. 10 Decoding results over time.

Does reported confidence similarly reflect imprecision in the cortical representation when the orientation is held in visual working memory? To address this question, the analyses of Fig. 3b-c and Extended Data Fig. 2 were repeated over time, using a sliding window of size 3 s (2 TRs). We focused on successive intervals from 1.5 s before to 13.5 s after stimulus onset (which roughly corresponds to the onset of the response window after accounting for hemodynamic delay). Benchmark tests verified that the decoded probability distributions reliably predict the orientation of the presented stimulus (a), and variability in the observer’s behavioral estimates (b-c) over extended periods of time. Having established that the decoded distributions meaningfully reflect the degree of imprecision in the cortical representation, we next investigated the extent to which decoded uncertainty predicts reported confidence during the retention interval. We found a reliable negative relationship between decoded uncertainty and reported confidence that held up well into the delay period (d). This is consistent with an imprecise working memory trace in V1-V3 that influences subjective confidence. Please note, however, that our design does not warrant strong conclusions regarding the nature of this representation: due to fMRI’s low temporal resolution, it is difficult to say whether these signals are purely perceptual or working memory-related (see e.g.47, for similar rationale), and later TRs could simply reflect the visual presentation of the response bar, rather than memory-based signals. (a-d) Data are centered to the middle of the analysis window (of size 2 TRs). Horizontal lines indicate statistical significance (p < 0.05, FWER-controlled). Dark gray area marks stimulus presentation window, light gray area denotes response window. Dashed lines indicate the decoding window used for the main analyses (i.e., Fig. 3b,c and Extended Data Fig. 2). Shaded regions represent ± 1 s.e.m. (standard errors in (a) are too small to be visible).

Supplementary information

Supplementary Information

Supplementary Table 1.

Reporting Summary.

Supplementary Data

Three-dimensional visualization of downstream clusters significantly modulated by uncertainty decoded from visual cortex (P < 0.05, FWER-controlled; also see Fig. 4).

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Geurts, L.S., Cooke, J.R.H., van Bergen, R.S. et al. Subjective confidence reflects representation of Bayesian probability in cortex. Nat Hum Behav 6, 294–305 (2022). https://doi.org/10.1038/s41562-021-01247-w

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