On 2017 Oct 26, Patrick Stokes commented:

Our arXiv response can now be found here: http://arxiv.org/abs/1709.10248

On 2017 Sep 29, Patrick Stokes commented:

Dear Dr. Marinazzo,

Thank you for the comments posted here as well as those on arXiv.

The main points of our work were to 1) characterize statistical properties of the traditional computation of conditional Granger-Geweke (GG) causality, and 2) to analyze how the dynamics of the system are represented in the GG-causality measure.

We acknowledge that you, as well as Drs. Barnett, Barrett, and Seth, are correct that a state-space approach using a single model fit addresses the problems with bias and variance in conditional GG-causality estimates, employing either the spectral factorization in the frequency-domain or the DARE solution in the time-domain. Your simulation study posted on arXiv illustrates this clearly. Unfortunately, as you suggest in your arXiv article, many investigators are still using separate model fits. We hope our article raises awareness of the problems with doing so, particularly in frequency-domain analyses, which again can be avoided by using appropriate state-space methods under a single model fit.

However, our second point about how dynamics are represented in GG-causality seems far more problematic, and is not resolved by the single-model computation, as it is an intrinsic property of GG-causality In most neuroscience studies, the objective is to identify and/or characterize the mechanism of some observed effect. As we have shown, the dynamics of the effect nodes are absent in GG-causality. Oscillations play an important role in systems neuroscience, and interpretation of causality measures appears particularly problematic in systems with strong frequency-dependent structure. Studies of oscillatory phenomena are invariably geared towards understanding the factors that contribute to oscillations observed at specific frequencies. Ignoring these observed dynamics is simply not compatible with the goal of understanding them.

We focused our paper on analyzing GG-causality. Although we also expressed concerns about other related methods, we did not intend to dismiss efforts to develop improved methods for analyzing directed dynamical influences. To the contrary, we believe that such methods will be essential for gaining meaningful insights from modern neuroscience data. As we try to emphasize in our paper, a crucial priority will be to ensure that the models and derived quantities correspond appropriately to the scientific questions being considered. Developing such methods will require a closer partnership between neuroscientists and quantitative scientists going forward. In the meantime, as we suggest in our paper, a good starting point would be for analysts to pay more attention to the underlying models, the dynamics they represent, and the overall modeling process, all of which form the foundations for subsequent inferences on directed influences.

We have submitted to arXiv a more detailed response to the arXiv posts from your group, and from Drs. Barnett, Barrett, and Seth. It will post in the next few days.

We thank you again for your commentary and the insightful dialogue.

Sincerely,

Patrick A. Stokes and Patrick L. Purdon

On 2017 Sep 12, Daniele Marinazzo commented:

Dear authors

thanks a lot for this paper, that has collected quite some attention.

I agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical unfortunate use of the name “causality”, as nicely described in previous literature).

On the other hand I think that the paper uses a formulation of Granger causality which is outdated (albeit still used), and in doing so it dismisses the measure based on a suboptimal use of it.

In order to provide a more balanced view, we replicated their simulations used the updated State Space implementation, proposed already some years ago, in which the pitfalls are mitigated or directly solved.

You can find the report here https://arxiv.org/abs/1708.06990

Another reply has been also posted, addressing more fundamental issues https://arxiv.org/abs/1708.08001

Best regards

On 2017 Sep 12, Daniele Marinazzo commented:

Dear authors

thanks a lot for this paper, that has collected quite some attention.

I agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical unfortunate use of the name “causality”, as nicely described in previous literature).

On the other hand I think that the paper uses a formulation of Granger causality which is outdated (albeit still used), and in doing so it dismisses the measure based on a suboptimal use of it.

In order to provide a more balanced view, we replicated their simulations used the updated State Space implementation, proposed already some years ago, in which the pitfalls are mitigated or directly solved.

You can find the report here https://arxiv.org/abs/1708.06990

Another reply has been also posted, addressing more fundamental issues https://arxiv.org/abs/1708.08001

Best regards