## 2 Materials and Methods
### Architectures and Related Methods  
In this study, the wide-spread deterministic architectures were used: EEGNetV4 [22] and Shallow ConvNet [23], with hyperparameters, such as dropout, defined in the respective papers. These architectures were converted to Bayesian algorithms by imposing prior distribution over the weights. In other words, we assumed that each weight of the network is a stochastic variable. Its probability distribution a priori is defined explicitly. Our goal was to obtain a posterior distribution of each parameter after observing the training data; for neural networks, the posterior distribution is intractable. It is possible to obtain samples from the posterior distribution using various Markov Chain Monte Carlo (MCMC) techniques. These methods construct a Markov chain of weight samples that converges to a posterior distribution of model weights. Until recently, Markov Chain Monte Carlo (MCMC) methods were widely used in Bayesian inference due to their ability to approximate complex posterior distributions. However, their drawback was the requirement for a large number of iterations to achieve convergence, which made them computationally expensive and time-consuming. Additionally, MCMC methods needed to evaluate the likelihood function over the entire batch of data at each iteration, which further added to the computational burden, especially for large datasets. To address these limitations, Variational Inference (VI) techniques gained popularity within the Bayesian community. VI offered a faster alternative by approximating the posterior distribution with a more tractable family of parameterized distributions. This approach made it computationally efficient and enabled quicker convergence. Nonetheless, a major concern with VI was that it only provided samples from an approximate posterior, potentially leading to biased estimates compared to the true posterior distribution. Furthermore, VI required selecting an appropriate approximation family, such as Gaussian distributions, which might not capture the complexities of the true posterior distribution accurately. This choice of approximation family often necessitated intensive tuning efforts and expertise, making it less approachable for less experienced practitioners. Fortunately, recent advancements in the field of Bayesian machine learning introduced a new family of stochastic gradient MCMC techniques. These methods cleverly combine the strengths of both MCMC and stochastic gradient optimization, allowing for efficient sampling from the true posterior distribution at significantly reduced computational costs. By leveraging the idea of stochastic gradients, these new techniques achieve faster convergence by using mini-batches of data instead of evaluating the likelihood function over the entire dataset. This results in a dramatic reduction in computational time while still providing high-quality posterior samples. Moreover, unlike Variational Inference, these stochastic gradient MCMC methods generate samples directly from the true posterior distribution, thereby eliminating any potential bias introduced by approximation. This crucial advantage has made them increasingly popular for Bayesian inference tasks, as they can provide more accurate uncertainty estimates and improved predictions. Modern MCMC methods utilize the gradient of the log-likelihood function, equivalent to the loss function of deterministic models. For users, the process is similar to standard optimization of a neural network's loss function, with a log-likelihood replacing the loss function, a log-prior probability density replacing the weight's regularization constraint, and an MCMC sampler replacing the optimizer. The main difference is the need to collect multiple weight samples after the Markov chain converges instead of a single set of weights in standard optimization. To obtain predictions of BNN, we used the Monte Carlo approach. For this purpose, we collected 120 weight samples from the posterior distribution and used them to construct an ensemble of 120 networks.