Comments on 'Is partial coherence a viable technique for identifying generators of neural oscillations?': Why the term 'Gersch Causality' is inappropriate: common neural structure inference pitfalls.

To aid prospective neural connectivity inference analysts and hoping to preclude misconception spread, we exploit the didatic value of some of the issues raised by Albo et al. (Biol Cybern 90: 318-326, 2004) who claim that signal-to-noise ratio (SNR) values can lead to mistakes in structural inference when using partial coherence in connection to Gersch's 1970 method for spotting signal sources (Gersch in Math Biosci 14: 177- 196, 1972). We show theoretically that Gersch's method is able only to spot which measurement of some common underlying factor has the least amount of additive noise and that this has nothing to do with any reasonable notion of 'causality' as suggested by Albo et al. (Biol Cybern 90: 318-326, 2004). We also show that despite the inherent structural ambiguity of the model used by Albo et al. (Biol Cybern 90: 318-326, 2004) to back their claim, its data can nonetheless furnish the correct time precedence hierarchy between the activities in its measured structures, both when simple (correlation) and more sophisticated methods are used (partial directed coherence) (Baccala and Sameshima in Biol Cybern 84:463-474, 2001a) in a true depiction of time series causality.