Sugihara, May, Ye, Hsieh, Deyle, Fogarty, and Munch published what I consider to be a pretty interesting paper in *Science* called “Detecting causality in complex ecosystems”, linked:

- http://dx.doi.org/10.1126/science.1227079
- http://www.uvm.edu/~cdanfort/csc-reading-group/sugihara-causality-science-2012.pdf

Professor Andrew Gelman of Columbia seemed unimpressed by the article, and I wondered why. Alas comments there are closed, so I’m soliciting discussion here. In particular, Sugihara, *et al* have extended the ideas of Granger causality which relies upon relative predictability of two time series in order to give a measure of causality. (There is another survey here.) Now, I know there’s been Bayesian work done in this area, and I would like to see if these things could be done using a more Bayesian framework. In particular, predictive distributions are, in some sense, more fundamental than even Bayesian posteriors, as long as dependence can be dealt with properly. (The subject here is time series here, after all.)

Sugihara, *et al* offer an algorithm called *convergent cross-mapping* (“CCM”) which, ironically, was motivated by the desire to fix problems Granger causation has with “less stochastic” systems. Some Granger tests, totally frequentist, don’t work well with nonlinear system models, and CCM might help.

So, it seems to be an intriguing idea, worth Bayesian consideration, and I’m disappointed that Professor Gelman doesn’t see that.

There are related references regarding dynamical systems and Taken’s Embedding Theorem at:

- http://eprints.ma.man.ac.uk/175/01/covered/MIMS_ep2006_26.pdf
- http://homepages.warwick.ac.uk/~masdh/re/takens.pdf
- http://users.ece.gatech.edu/~crozell/pubs/yapTSP2011.pdf

and supplementary material at Sugihara, *et al* supplement (possible paywall).

*Update*, 2016-07-24

Berner, *et al* do “Stochastic parameterization”, and this is related to the work by Ye, Beamish, Munch, Perrettia, and colleagues on model-free forecasting.

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