This paper is concerned with a study of hypoglycemia under natural occurrence conditions at night time. Five adolescents with type 1 diabetes (T1D) participated in the experiments. Patients' blood glucose profiles were interpolated to estimate the intermediate values. The proposed system used spectral moments of electroencephalogram (EEG) signals from central and occipital areas as features for detecting hypoglycemia. We found that hypoglycemia could be detected non-invasively using EEG spectral moments. During hypoglycemic episodes, theta moments increased significantly (P<0.005) whereas beta moments decreased significantly (P<0.001). Based on the optimal network architecture associated with the highest log evidence, the proposed optimal Bayesian neural network resulted in a sensitivity of 82% and a specificity of 52%. In addition, the estimated blood glucose profiles showed a significant correlation (P<1e-6) with interpolated blood glucose values in the test set.