In reading Detecting Causality in Complex Ecosystems I came across the following passage:

Our alternative approach [...] tests for causation by measuring the extent to which the historical record of Y values can reliably estimate states of X. This happens only if X is causally influencing Y.

Can someone explain, perhaps through examples, why the test might work in "reverse": using values of Y to predict X in order to determine whether X causes Y.

  • $\begingroup$ In a simpler context - if, every time you are in state A, you note that it was immediately preceded by state B, you might suspect that B -> A. However, the converse is not true; if, every time you are in state B, it is followed by A, it could just be that any time you are in any state other than A, say, C, D, or E, you transition to A, so it would be harder to infer that being in state B specifically is what "caused" A. $\endgroup$ – jbowman Mar 22 at 0:40
  • $\begingroup$ It doesn't matter which direction you do the prediction. However, this "test for causation" assumes no confounders, which is unrealistic. $\endgroup$ – Neil G Mar 22 at 5:15

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