Sugihara et al. have a really interesting paper in Science, on detection of causality in nonlinear dynamic systems. It’s paywalled, so here’s an excerpt with some comments.
Abstract: Identifying causal networks is important for effective policy and management recommendations on climate, epidemiology, financial regulation, and much else. We introduce a method, based on nonlinear state space reconstruction, that can distinguish causality from correlation. It extends to nonseparable weakly connected dynamic systems (cases not covered by the current Granger causality paradigm). The approach is illustrated both by simple models (where, in contrast to the real world, we know the underlying equations/relations and so can check the validity of our method) and by application to real ecological systems, including the controversial sardine-anchovy-temperature problem.
Identifying causality in complex systems can be difficult. Contradictions arise in many scientific contexts where variables are positively coupled at some times but at other times appear unrelated or even negatively coupled depending on system state.
Although correlation is neither necessary nor sufficient to establish causation, it remains deeply ingrained in our heuristic thinking. … the use of correlation to infer causation is risky, especially as we come to recognize that nonlinear dynamics are ubiquitous. Continue reading “Causality in nonlinear systems”