Non-Gaussian modeling of sleep EEG based on a skewed scale mixture structure and its application to sleep stage analysis

Electroencephalograms (EEGs) are widely used to evaluate sleep. Changes in the shape of EEG amplitude distributions serve as useful indicators to characterize sleep stages. However, existing models lack the representational power to comprehensively capture the non-Gaussian characteristics of EEGs. To address this limitation, we propose a novel skew-scale mixture model based on a skewed scale mixture structure. This model treats EEG amplitudes as random variables following a multivariate Gaussian distribution, whose mean vector and covariance matrix are weighted by scale and skewness parameters. These parameters are estimated using marginal likelihood maximization and used as features to quantify non-Gaussian characteristics such as tail weight and lateral asymmetry. The proposed model was validated through simulations and applied to EEG data from the Montreal Archive of Sleep Studies (MASS) dataset, which includes five sleep stages: wakefulness, REM, N1, N2, and N3. Compared to conventional probabilistic models (e.g., Gaussian and scale mixture models), the proposed model demonstrated superior ability to represent non-Gaussian characteristics, as evaluated by Bayesian Information Criterion (BIC) scores. Moreover, extracted features showed significant variation across sleep stages, reflecting stage-specific EEG characteristics such as slow waves and spindles. The proposed skew-scale mixture model provides a unified framework for comprehensively representing the non-Gaussian characteristics of sleep EEGs, including lateral asymmetry. This model offers the potential for applications such as improved classification accuracy and enhanced detection of characteristic waveforms, laying a foundation for future developments in automated sleep stage classification. • The stochastic model that unifies the representation of non-Gaussianity in sleep EEG. • Model parameters are estimated with high accuracy by maximum likelihood estimation. • High validity for multi-channel EEG in multiple sleep stages. • Significant change in non-Gaussian characteristics with change in sleep stage.