Confidence of probabilistic predictions modulates the cortical response to pain

Abstract

Pain typically evolves over time, and the brain needs to learn this temporal evolution to predict how pain is likely to change in the future and orient behavior. This process is termed temporal statistical learning (TSL). Recently, it has been shown that TSL for pain sequences can be achieved using optimal Bayesian inference, which is encoded in somatosensory processing regions. Here, we investigate whether the confidence of these probabilistic predictions modulates the EEG response to noxious stimuli, using a TSL task. Confidence measures the uncertainty about the probabilistic prediction, irrespective of its actual outcome. Bayesian models dictate that the confidence about probabilistic predictions should be integrated with incoming inputs and weight learning, such that it modulates the early components of the EEG responses to noxious stimuli, and this should be captured by a negative correlation: when confidence is higher, the early neural responses are smaller as the brain relies more on expectations/predictions and less on sensory inputs (and vice versa). We show that participants were able to predict the sequence transition probabilities using Bayesian inference, with some forgetting. Then, we find that the confidence of these probabilistic predictions was negatively associated with the amplitude of the N2 and P2 components of the vertex potential: the more confident were participants about their predictions, the smaller the vertex potential. These results confirm key predictions of a Bayesian learning model and clarify the functional significance of the early EEG responses to nociceptive stimuli, as being implicated in confidence-weighted statistical learning.

Keywords: EEG; confidence; nociception; pain; temporal statistical learning.

Fig. 1.

Temporal statistical learning experiment. (A) Examples of sequences of stimuli of intensities I ₁ and I ₂ that are applied to the participants’ forearm. Each sequence has different generative statistics (a majority of I ₂ or I ₁, more alternations or repetitions, etc.) and the interstimulus interval (ISI) is set to 3 s. (B) Behavioral questions asked to the participants every 15 ± 3 stimuli in the sequences to evaluate their stimulus probability estimates and confidence estimates in these predictions. The sequences are paused for a maximum of 8 s per question. (C) Markovian generative process of the sequences of stimuli whose intensities are I ₁ and I ₂. (D) Transition probability matrix in which the five generative pairs of transition probabilities (TPs) employed are indicated with bold numbers. One example of a sequence generated with each of these five TPs is shown in (A).

Fig. 2.

Participants identify the generative sequence statistics. (A) True and rated probabilities to receive a stimulus of intensity I ₁ are correlated subject-wise (N = 31 subjects). The mean correlation across participants is 0.454 (t ₃₀ = 13.603, P <  10⁻⁵, Cohen’s d = 2.443), indicating that participants identify the trends within the sequences. The dotted line indicates identity; plain line, linear fit averaged across participants; and blue squares, mean rated probabilities. (B) Participants also accurately identify the trends in the transitions from I ₁. The grand mean correlation between generative and estimated p(I ₁|I ₁) is 0.549 (t ₃₀ = 14.007, P <  10⁻⁵, Cohen’s d = 2.516). (C) Similar to (B) for the transitions from I ₂. The grand mean correlation between generative and estimated p(I ₁|I ₂) is 0.489 (t ₃₀ = 11.585, P <  10⁻⁵, Cohen’s d = 2.443). (D) Confidence estimates are quadratically related to the probability estimates (mean coefficient of determination of the quadratic fits: R ² = 0.47). Plain colored lines indicate individual quadratic fits, and the thick plain black line indicates quadratic fit averaged across participants.

Fig. 3.

Model comparison. Six different models are considered to explain the subjective reports (N = 31 participants): Bayesian learners inferring the alternation frequency (AF), the item frequency (IF) or the transition probabilities (TPs), and delta rule, or Rescorla–Wagner (RW) models, inferring the same sequence statistics (AF, IF, and TP). (A) Bayesian model comparison shows that the participants’ reports are best approximated by a Bayesian model learning the TPs (the exceedance probability of this model—i.e., the probability for this model to be more frequent than the others in the population—is ϕ = 0.974). Colored bars: model probabilities; horizontal gray line: prior (uniform) probability. (B) Bayesian model averaging reveals that the participants’ integration of observations is best approximated with a time constant ω of 8 stimuli. Horizontal line: uniform prior probability; shaded area: SEM across participants; plain dot: curve maximum. The inset illustrates the exponentially decreasing weights that are used to count the number of past stimuli when n stimuli have been delivered, with a time constant ω of 8. (C) Individual model probabilities (reflecting the similarity between estimated and modeled probabilities) indicate that most subjective reports are best approximated by the Bayesian model learning the TPs and to a lesser extent by the Bayesian model learning the IFs, but not much by RW models.

Fig. 4.

Quality of fit of the best model for the ratings. Subjective estimates of stimulus probability and confidence are highly correlated with Bayes-optimal values obtained from a model learning the TPs with an integration time constant of 8 stimuli (N = 31 participants). (A) Scatter plot of estimated and modeled stimulus probabilities, with one color per participant. The grand mean correlation is 0.659 (t ₃₀ = 24.398, P <  10⁻⁵, Cohen’s d = 4.382). Dotted line: identity; plain colored lines: individual linear fits; thick plain black line: linear fit averaged across participants. (B) Scatter plot of estimated and modeled confidence, with the same color code as in (A). The grand mean correlation is 0.285 (t ₃₀ = 9.293, P <  10⁻⁵, Cohen’s d = 1.669). (C) The accuracy of probability and confidence estimates are positively correlated across participants (Pearson correlation: 0.493, P = 0.005). Each accuracy was computed as the correlation coefficient between the subjective reports and the corresponding modeled quantities across trials. (D) Bayesian confidence is quadratically related to Bayesian probability estimates (mean coefficient of determination of the quadratic fits: R ² = 0.59). Plain colored lines: quadratic fits obtained using the sequences of each participant; thick plain black line: quadratic fit averaged across participants’ sequences.

Fig. 5.

EEG correlates of Bayesian confidence. (A) EEG responses averaged over trials, blocks, and participants, for low (L e f t) and high (R i g h t) stimulation intensities. Global field power (GFP) time courses are shown in gray, with shaded SD across participants (N = 31). Labels of depicted electrodes, whose positions are shown in the topoplot at the center: C3, Cz, FCz, CPz, and C4. (B) Encoding of residual confidence in the EEG responses—t-statistics for the regression coefficients associated with model confidence. Confidence is obtained from the model which best explains the participants’ behavior: a Bayesian model learning the TPs with an integration time constant of 8 stimuli. The shaded horizontal areas centered around 0 indicate the nonsignificant regions for P <  0.05, two-tailed. Red bars at the bottom of the plots show intervals where the regression coefficients are significantly different from 0 after false discovery rate (FDR) correction of the significance levels. Topographies of the largest effects are indicated.

Fig. 6.

EEG correlates of Bayesian prediction error (BPE). Encoding of BPE in the EEG responses, similar to Fig. 5B —t-statistics for the regression coefficients associated with BPE. BPE is obtained from the model which best explains the participants’ behavior: a Bayesian model learning the TPs with a time constant of 8 stimuli. The shaded horizontal areas centered around 0 indicate the nonsignificant regions for P <  0.05, two-tailed. No time interval was deemed significant after false discovery rate (FDR) correction of the significance levels.