Closer investigation of Figures 2 and 3 reveals--apart from the general finding of lower frequencies in frontal and higher in parietal derivations--a finer structure of local maxima. Pursuit of the question, whether it is a property of analyzed EEG or rather an artifact of the analysis method, provoked investigation of statistical properties of MP decomposition as related to the structure of the dictionary. These considerations, which finally led to introduction of stochastic dictionaries, are presented in this chapter.