## 4 Discussion
Concerning the two other studies that dealt with uncertainty estimation, [PERSON] et al. [12] used a similar threshold method with entropy as the uncertainty measure. However, they used that method for a different task, namely, classification with rejection. The purpose of the classification task with rejection is to reject all data with high uncertainty, i.e., where the classifier can make random predictions. It is quite closely related to the OOD data detection problem, but there are some differences. In an OOD data detection problem, one states if the sample is from a known data distribution or not, whereas in classification with a rejection problem, one needs to assign a class label to a sample if it is from the data distribution. [PERSON] et al. [11] also studied uncertainty estimation, but they focused on its reduction. Moreover, they used a dropout for making predictions on a test set as a Bayesian feature of architecture, which is a very restricted case of the Bayesian deep learning framework. This may raise the question of the perspectives of BNN-based OOD detection methods in BCIs, especially in online (real-time) experiments. With our hardware, it took a couple of hours to train a BNN, whereas the training of the deterministic ensemble of the same size requires less than an hour. The amounts of time consumed for the experiments' conduction are presented in Table 2. One may refer to the variational inference methods as the faster ones, but we expect that they provide a less accurate approximation. We state that mainly relying on two arguments: firstly, the family of known distributions to approximate the posterior is quite sparse; secondly, the obtained approximations of the posterior can significantly differ from a real one [38]. Interestingly, the Bayesian algorithms made from EEGNet were trained faster than the deterministic ones. It happens because we had to start training each new instance of the ensemble from randomly initialized weights, while for the Bayesian model, we just continued the same Markov chain to collect new samples of the weights. The intractability of the integrals in [PERSON] theorem, complex approximations, and a bulky mathematical apparatus come as a hindrance to the possible successful usage of these methods in online experiments, mainly because of higher time complexity, which \begin{table}
\begin{tabular}{c c} \hline \hline
**Experiment** & **Time (HH:MM:SS)** \\ \hline Training for OOD detection (Bayesian EEGNet) & 01:19:52 \\ Training for OOD detection (Bayesian Shallow ConvNet) & 00:30:02 \\ Training for OOD detection (Ensemble of EEGNets) & 01:57:54 \\ Training for OOD detection (Ensemble of Shallow ConvNets) & 00:19:22 \\ Training on 4 classes (Bayesian EEGNet) & 02:31:02 \\ Training on 4 classes (Bayesian Shallow ConvNet) & 00:54:19 \\ Training on 4 classes (Ensemble of EEGNets) & 03:46:32 \\ Training on 4 classes (Ensemble of Shallow ConvNets) & 00:35:00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Time consumed by classifier training for different experiments. comes as a consequence of the architectural drawbacks. The problem of time complexity can be solved by using more modern GPUs. The complex math also may be the cause of the higher entry-level, which can affect the spreading of the BNN-based methods negatively. This might be overcome by a significant increase in the quality of classification or OOD detection quality when few learning data are available. Irrespective of the opportunities to improve the OOD detection method we suggested here, we would like to emphasize that OOD detection methods are no less important for BCIs than for other applications. Other ways to address the OOD challenge in BCIs could develop more specific novel methods or adapt existing ones from other areas of science, for example, distance-based [39] or density-based [40].