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An automated diagnosis procedure based on a statistical machine learning methodology using electroencephalograph (EEG) data is proposed for diagnosis of psychiatric illness. First, a large collection of candidate features, mostly consisting of various statistical quantities, are calculated from the subject's EEG. This large set of candidate features is then reduced into a much smaller set of most relevant features using a feature selection procedure. The selected features are then used to evaluate the class likelihoods, through the use of a mixture of factor analysis (MFA) statistical model. In a training set of 207 subjects, including 64 subjects with major depressive disorder (MDD), 40 subjects with chronic schizophrenia, 12 subjects with bipolar depression and 91 normal or healthy subjects, the average correct diagnosis rate attained using the proposed method is over 85%, as determined by various cross-validation experiments. The promise is that, with further development, the proposed methodology could serve as a valuable adjunctive tool for the medical practitioner.