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Research ArticleNew Research, Cognition and Behavior

Single-Trial Event-Related Potential Correlates of Belief Updating

Daniel Bennett, Carsten Murawski and Stefan Bode
eNeuro 28 September 2015, 2 (5) ENEURO.0076-15.2015; https://doi.org/10.1523/ENEURO.0076-15.2015
Daniel Bennett
1Melbourne School of Psychological Sciences, The University of Melbourne, Parkville, Victoria 3010, Australia
2Department of Finance, The University of Melbourne, Parkville, Victoria 3010, Australia
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Carsten Murawski
2Department of Finance, The University of Melbourne, Parkville, Victoria 3010, Australia
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Stefan Bode
1Melbourne School of Psychological Sciences, The University of Melbourne, Parkville, Victoria 3010, Australia
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  • Figure 1.
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    Figure 1.

    A, Following a self-paced button press, a checkerboard stimulus was presented whose contrast changed linearly. The participant could at any time select the contrast displayed on screen by pressing a button with the right index finger. The trial continued until a button was pressed or until stimulus duration exceeded 30 s. Following the participant’s choice, the selected contrast remained on screen for 2 s, after which time the monetary reward associated with the chosen contrast was displayed for 2.5 s. In the event that no button was pressed within 30 s, feedback was a message reminding the participant of the task instructions. B, Two demonstrative examples of stimulus contrast as a function of elapsed time. Example trial 1 (blue) has an initial contrast of 63%, is initially increasing, and has a half-cycle period of 9 s. Example trial 2 (red) has an initial contrast of 39%, is initially decreasing, and has a half-cycle period of 6 s. The checkerboard stimulus phase reversed at a rate of 12 Hz. C, Functional mapping between the contrast difference from target and monetary reward. The mapping was a symmetrical triangular function with a center of 0% contrast difference, a half-width of 15% contrast difference, and a height of 25 cents. As such, the received reward was maximal when the participant responded at the target contrast and decreased linearly with increasing difference of chosen contrast from the target. The reward was 0 for responses at >15% distance. Feedback received was rounded to the nearest whole-cent value.

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    Figure 2.

    Mean accuracy as a function of within-block trial number across participants. Accuracy is presented as the absolute difference of chosen and target contrasts, where lower differences indicate better task performance. Error bars represent the SEM. Note that the number of trials per block varied across blocks and participants, and as a result some participants did not complete >19 trials in any block. This confound limited the interpretability of accuracy data for trial numbers >20, and the final data point of the series therefore represents mean accuracy across trials 19–25 for each participant.

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    Figure 3.

    Computational belief variables as a function of trial number. A, Belief entropy. B, Feedback surprise. C, Belief update size measured as mutual information (see Eq. 14). D, Belief update size measured as Bayesian surprise (see Eq. 15). Note that the number of trials per block varied across blocks and participants, and, as a result, some participants did not complete >19 trials in any block. This confound limited the interpretability of computational belief variables for trial numbers >20, and the final data point of the each series therefore represents a mean across trials 19–25 for each participant. Error bars represent the SEM.

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    Figure 4.

    P3 analysis. A, Median split waveforms for 200–1000 ms following visual presentation of feedback. The P3 regression analysis window is indicated by the gray bar. ERP waveforms were low-pass filtered at 30 Hz for display purposes only. B, Mean voltage topography during the P3 analysis window from 300 to 450 ms following visual presentation of feedback (time = 0). C, Topography of the mean voltage difference between large and small belief update trials across participants during P3 analysis window. A median split was used to divide trials into two bins for each participant, corresponding to large and small belief updates according to model-derived estimates. This median split was for display purposes only and was not used in the main regression analysis, which was based on single-trial amplitudes.

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    Figure 5.

    Stimulus-preceding negativity analysis. A, Median split waveforms for 0–1500 ms prior to the visual presentation of feedback. The SPN regression analysis window from 0 to 500 ms preceding feedback is indicated by the gray bar. ERP waveforms were low-pass filtered at 30 Hz for display purposes only. B, Mean voltage topography during SPN analysis window from 0 to 500 ms prior to visual presentation of feedback (time = 0). C, Topography of the mean voltage difference between high and low uncertainty trials across participants during the SPN analysis window. A median split was used to divide trials into two bins for each participant, corresponding to high and low belief uncertainty according to model-derived estimates. This median split was for display purposes only and was not used in the main regression analysis, which was based on single-trial amplitudes.

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    Table 1.

    Summary of statistical analyses

    Data structureType of testObserved power
    aNormally distributedSingle-sample t test1.0
    bModel likelihoodsBICNot applicable
    cNormally distributedSingle-sample t test1.0
    dNormally distributedSingle-sample t test0.54
    eNormally distributedSingle-sample t test0.65
    fNormally distributedSingle-sample t test0.06
    gNormally distributedSingle-sample t test1.0
    hNormally distributedPearson correlation0.99
    iNormally distributedSingle-sample t test0.95
    jNormally distributedSingle-sample t test1.0
    kNormally distributedRepeated-measures ANOVA0.77
    lNormally distributedRepeated-measures ANOVA0.08
    mNormally distributedRepeated-measures ANOVA0.13
    nNormally distributedSingle-sample t test0.31
    oNormally distributedSingle-sample t test0.97
    pNormally distributedSingle-sample t test0.98
    qNormally distributedSingle-sample t test1.0
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    Table 2.

    Summary of behavioral model fits for 4417 choices by 16 participants

    ModelParameters per participantParametersBelief distributionLog-likelihoodBICN best fit
    Unbiased updating1σYes−201904051511
    Win-stay/lose-shift1σNo−20350408345
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    Table 3.

    Correlation matrix for predictors in P3 regression analysis

    RewardBelief update size (I)Belief update size (IKL )
    Reward1
    Belief update size (I)0.22 (0.19)1
    Belief update size (IKL )−0.24 (0.12)0.64 (0.16)1
    Surprise0.45 (0.21)0.22 (0.12)0.05 (.14)
    • Data are presented as mean Spearman coefficient across participants (SD).

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Single-Trial Event-Related Potential Correlates of Belief Updating
Daniel Bennett, Carsten Murawski, Stefan Bode
eNeuro 28 September 2015, 2 (5) ENEURO.0076-15.2015; DOI: 10.1523/ENEURO.0076-15.2015

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Single-Trial Event-Related Potential Correlates of Belief Updating
Daniel Bennett, Carsten Murawski, Stefan Bode
eNeuro 28 September 2015, 2 (5) ENEURO.0076-15.2015; DOI: 10.1523/ENEURO.0076-15.2015
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Keywords

  • belief updating
  • computational modeling
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  • single-trial
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  • RE: Single-Trial Event-Related Potential Correlates of Belief Updating
    Bruno Kopp, Antonio Kolossa and Tim Fingscheidt
    Published on: 27 October 2015
  • Published on: (27 October 2015)
    Page navigation anchor for RE: Single-Trial Event-Related Potential Correlates of Belief Updating
    RE: Single-Trial Event-Related Potential Correlates of Belief Updating
    • Bruno Kopp, Neuropsychologist, Hannover Medical School
    • Other Contributors:
      • Antonio Kolossa
      • Tim Fingscheidt
    Progress in understanding the neural bases of cognition requires computational frameworks. Bennett et al. provide an important example for Bayesian belief updating (BBU). They describe BBU as the transformation of prior beliefs into posterior beliefs after new information is observed, and they report that BBU is encoded in anterior P3 (P3a) amplitude variability. Bennett et al. describe their P3a finding as if it was novel, citing two previous publications as formulating the hypothesis that P3 amplitude reflects a BBU mechanism (Kopp, 2008; Mars et al., 2008). Kopp (2008) provides theoretical arguments. Mars et al. (2008) found that predictive surprise was encoded in the parietal P3b, leading these authors to speculate that the P3a may encode BBU, but they left their speculation unexamined. Bennett et al. shortly mention another recently published study: ’The observed results are broadly consistent with recent research investigating Bayesian single-trial properties of the P3 in a prediction task without reinforcement (Kolossa et al., 2015).’ (p. 12). However, they do not provide detailed descriptions of the reported findings: This study evidently showed that P3a amplitude variability can be best accounted for by BBU, that P3b amplitude variability can be best accounted for by predictive surprise (see also Kolossa et al., 2013), and that posterior slow wave amplitude variability can be best accounted for by Bayesian prediction updating. Our previous work was inadequately cited...Show More
    Progress in understanding the neural bases of cognition requires computational frameworks. Bennett et al. provide an important example for Bayesian belief updating (BBU). They describe BBU as the transformation of prior beliefs into posterior beliefs after new information is observed, and they report that BBU is encoded in anterior P3 (P3a) amplitude variability. Bennett et al. describe their P3a finding as if it was novel, citing two previous publications as formulating the hypothesis that P3 amplitude reflects a BBU mechanism (Kopp, 2008; Mars et al., 2008). Kopp (2008) provides theoretical arguments. Mars et al. (2008) found that predictive surprise was encoded in the parietal P3b, leading these authors to speculate that the P3a may encode BBU, but they left their speculation unexamined. Bennett et al. shortly mention another recently published study: ’The observed results are broadly consistent with recent research investigating Bayesian single-trial properties of the P3 in a prediction task without reinforcement (Kolossa et al., 2015).’ (p. 12). However, they do not provide detailed descriptions of the reported findings: This study evidently showed that P3a amplitude variability can be best accounted for by BBU, that P3b amplitude variability can be best accounted for by predictive surprise (see also Kolossa et al., 2013), and that posterior slow wave amplitude variability can be best accounted for by Bayesian prediction updating. Our previous work was inadequately cited by Bennett et al., leaving the unjustified impression that their “P3a encodes BBU” finding represents a first-time scientific discovery through neglecting our study’s veritable impact.Show Less
    Competing Interests: None declared.

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