Bootstrapped Amplitude Difference in CIT & EFT

• The paper shows that BAD, a participant-level bootstrap test on the P300 amplitude difference, achieves 73.5% accuracy with high specificity but low sensitivity in deception detection.
• BAD is defined as a resampling-based statistical procedure used in EEG-based CIT to compare probe and irrelevant stimuli P300 responses for individual guilt classification.
• The study highlights that while BAD serves as a robust amplitude-difference baseline in CIT, deep learning methods with data augmentation markedly enhance detection performance under low stimulus heterogeneity.

Searching arXiv for the cited BAD-related papers to ground the article in current preprints. Bootstrapped Amplitude Difference (BAD) is, in EEG-based deception detection, a statistical procedure used within the concealed information test (CIT) to determine at the individual level whether the P300 amplitude elicited by a probe stimulus is significantly greater than the amplitude elicited by irrelevant stimuli, indicating recognition of concealed information, i.e. guilt (Kim et al., 2 Sep 2025). In current arXiv usage, the acronym also appears in a separate high-energy-theory context, where a “BAD approach” refers to identifying the difference in the basis of bootstrapped amplitudes allowed in competing effective field theories; the two meanings are terminologically identical but methodologically unrelated (Gröber et al., 2 Sep 2025).

1. Definition within the concealed information test

In the CIT, EEG is used for forensic deception detection by exploiting the P300 event-related potential (ERP) component. The paradigm distinguishes crime-related probe stimuli (PR), irrelevant stimuli (IR), and target stimuli (TR). The operative assumption of BAD is that recognition and salience elevate the P300 response to the probe relative to irrelevant items, and that this elevation can be quantified statistically for each participant (Kim et al., 2 Sep 2025).

Within this framework, BAD is traditionally the most common statistical tool. Its role is narrow but central: it does not attempt to model the full multichannel spatiotemporal EEG response, but instead tests whether the probe-minus-irrelevant P300 difference is sufficiently positive under bootstrap resampling. In laboratory conditions with high heterogeneity, the probe elicits a strong orienting response and BAD performs well. Under realistic investigative conditions, however, the distinction between probe and irrelevant items can become compressed when both are familiar or meaningful, which directly affects the probe-versus-irrelevant contrast on which BAD depends (Kim et al., 2 Sep 2025).

A common misunderstanding is to treat BAD as a general deception classifier. In the CIT literature summarized here, BAD is specifically a participant-level bootstrap test on a P300 amplitude difference, not a broad feature-learning framework. This distinction matters because later comparisons with machine learning and deep learning are comparisons against a highly structured amplitude-based baseline rather than against a generic statistical classifier (Kim et al., 2 Sep 2025).

2. Signal extraction, amplitude estimation, and bootstrap decision rule

The implementation described in the 2025 study follows a fixed workflow. EEG is recorded at 30 scalp sites during presentation of TR, PR, and IR stimuli, and the P300 is typically measured at the Pz electrode because this location shows the strongest response. Trials with artifacts exceeding $\pm 75\,\mu V$ are excluded, and the number of segments per condition is balanced by selecting those closest to the mean amplitude. Fifty-six valid segments per stimulus type are obtained for PR, TR, and IR (Kim et al., 2 Sep 2025).

P300 amplitude is computed on each epoch by a peak-to-peak method. The epoch is smoothed with a 100 ms window, the maximum amplitude is identified within the 350–800 ms post-stimulus window, and the minimum is then identified between that maximum and 1500 ms. The resulting amplitude is

$$\text{P300 Amplitude} = \text{max}_{350\text{–}800\text{ms}}(ERP) - \text{min}_{[\text{max time}],1500\text{ms}}(ERP).$$

The bootstrap stage resamples, with replacement, 46 PR trials and 46 IR trials for each participant, averages each set to create bootstrapped ERP waveforms, and computes the amplitude difference

$\Delta_{P300} = P300_{PR} - P300_{IR}.$

This procedure is repeated for 1,000 bootstraps to obtain a distribution of $\Delta_{P300}$. The guilt classification rule is then based on a one-sided criterion: if the lower bound of the 90% confidence interval for $\Delta_{P300}$ is greater than zero, the participant is classified as guilty; otherwise, innocent (Kim et al., 2 Sep 2025).

Methodologically, BAD is therefore a resampling-based significance test on a single derived ERP contrast. Its interpretive strength is that it yields an individual-level decision rule. Its structural limitation is that all inferential weight is placed on the separability of probe and irrelevant P300 amplitudes within the same participant.

3. Low stimulus heterogeneity as the critical failure mode

The principal limitation identified for BAD arises under low stimulus heterogeneity. This term refers to situations in which all stimuli, including both PR and IR, are familiar or meaningful, which more closely resembles realistic investigative conditions than classic high-heterogeneity laboratory paradigms (Kim et al., 2 Sep 2025).

To simulate such conditions, the study designed a realistic mock-crime setup in which participants were familiarized with all CIT stimuli except the target stimulus. In this setting, both PR and IR were highly familiar. The reported consequence was that probe and irrelevant P300 amplitudes became small or overlapping. Although the P300 difference between PR and IR in guilty individuals remained statistically significant at the group level, it was insufficiently robust for participant-level bootstrapping (Kim et al., 2 Sep 2025).

The empirical result was that BAD achieved 73.5% accuracy, with 50% sensitivity and 97% specificity. The profile is therefore asymmetric: BAD rarely misclassified innocent participants as guilty, but it failed to identify many guilty participants. The study interprets this pattern as a direct consequence of BAD’s reliance on a large within-participant difference between PR and IR, a reliance that is undermined when familiarity reduces the difference in neural response (Kim et al., 2 Sep 2025).

This has immediate forensic significance. In realistic settings, suspects may already be familiar with many key items. Under those conditions, BAD’s high specificity does not compensate for its low sensitivity, because the principal operational error becomes the non-detection of guilty individuals.

4. BAD relative to machine learning and deep learning baselines

The same study evaluated BAD against ML and deep learning (DL) methods under the same low-heterogeneity CIT condition. The ML pipeline used handcrafted features spanning multiple domains: P300 and N200 amplitudes in the time domain, ratio of power spectral density and differential entropy in the frequency domain, and global clustering coefficient and small-worldness in the network domain. These features were computed for all 30 electrodes and all three stimulus types, then reduced via Fisher score ranking. The tested algorithms were Support Vector Machine, Linear Discriminant Analysis, k-Nearest Neighbor, and Random Forest (Kim et al., 2 Sep 2025).

The DL comparison used ShallowNet and EEGNet. Entire multi-channel ERP segments from all three stimuli served as input, with no manual feature engineering. The models were trained in a subject-independent setting, meaning training and testing were conducted on different participants (Kim et al., 2 Sep 2025).

Method	Accuracy	Sensitivity / Specificity
BAD	73.5%	50.0% / 97.0%
LDA	75.0%	73.33% / 76.67%
ShallowNet with augmentation	80.0%	80.0% / 80.0%
EEGNet with augmentation	86.67%	76.67% / 97.0%

The comparison is significant because ML only marginally outperformed BAD, while DL—especially EEGNet—substantially improved performance. The study attributes the limited ML gain to continued dependence on handcrafted features that do not capture subtle waveform differences. By contrast, DL methods could significantly improve the accuracy of deception detection under challenging conditions of low stimulus heterogeneity by effectively capturing subtle cognitive responses not accessible through handcrafted features (Kim et al., 2 Sep 2025).

5. Data augmentation, subject independence, and the status of BAD as a baseline

A key component of the reported DL improvement was a data augmentation approach applied during training. For each participant, 90% of trials were actual and 10% were randomly sampled from other participants, increasing training data size 45-fold. No test or validation participant data were included in the training set, explicitly to avoid data leakage (Kim et al., 2 Sep 2025).

With this augmentation, ShallowNet improved from 76.67% to 80%, and EEGNet improved from 81.67% to 86.67%. EEGNet thereby exceeded BAD while maintaining the same reported specificity level of 97% and markedly improving sensitivity relative to BAD’s 50% (Kim et al., 2 Sep 2025).

In this comparative setting, BAD remains foundational rather than obsolete. It serves as the traditional benchmark for P300-based CIT, and its failure mode under low stimulus heterogeneity clarifies why a transition toward data-driven analysis is being pursued. The study frames this transition explicitly as a move beyond handcrafted features. A plausible implication is that BAD is best understood as a constrained amplitude-difference test whose validity is strongest when the experimental design preserves strong salience contrasts, whereas subject-independent DL models aim to learn distributed spatiotemporal signatures that survive when those contrasts are weak (Kim et al., 2 Sep 2025).

The paper also states that, to the best of its authors’ knowledge, it is the first study that employed DL approaches for subject-independent deception classification using the CIT paradigm (Kim et al., 2 Sep 2025). In that context, BAD functions as the canonical comparator for assessing whether newer methods improve practical forensic deployment.

6. Distinct usage in bootstrapped on-shell amplitudes

In a separate arXiv literature on scattering amplitudes, “BAD approach” has a different meaning. There it generally refers to identifying the difference in the basis of bootstrapped amplitudes allowed in competing effective field theories such as the Standard Model Effective Field Theory (SMEFT) and the Higgs Effective Field Theory (HEFT) (Gröber et al., 2 Sep 2025).

That usage arises in work on gluon-fusion double and triple Higgs production using bootstrapped on-shell amplitudes. The amplitude is built directly from on-shell principles, with non-factorizable contact terms and factorizable terms obtained by recursively gluing lower-point on-shell amplitudes. In that setting, the BAD philosophy is to determine whether a kinematic structure is present in one EFT description but absent in the other at a given order (Gröber et al., 2 Sep 2025).

The 2025 multi-Higgs study reports that, up to the orders considered, all on-shell amplitude structures found up to five points can be generated in both SMEFT and HEFT, though at different EFT orders. It therefore finds no fundamentally unique kinematic structure in HEFT, not also in SMEFT, for double or triple Higgs production at the accessible orders discussed. The exception highlighted is a new five-point $++$ structure, $c_{gghhh}^{++,(2)}$, which appears only at dimension-12 in SMEFT or $N^3LO$ in HEFT (Gröber et al., 2 Sep 2025).

Because this second usage is entirely unrelated to EEG deception detection, acronym conflation is a genuine risk in interdisciplinary reading. In contemporary arXiv practice, “Bootstrapped Amplitude Difference (BAD)” thus denotes either a participant-level bootstrap statistic for P300-based CIT or, in an unrelated amplitude-bootstrap context, a way of characterizing differences between EFT-generated on-shell structures. The meanings coincide only in abbreviation, not in formalism, data type, or inferential objective.