Figure5: Detectedcausal pathsof the spreadof Covid-19amongthe federalGermanstates, including causes among the restriction measures taken by each federal state. Each colour (in arrows and policies) indicates causes of one state (see top legend). The four subfigures correspond to the four combinations of threshold 1 and 2 that we tested. A distribution P is faithful to a directed acyclic graph (DAG) G if no conditionalindependence relationsotherthanthe onesentailed by the Markov property are present. Let G be a causal graph with vertex setV and P be a probability distribution over the vertices inV generated by the causal structure represented by G. G and P satisfy the Causal Markov Condition if and only if for every W in V, W is independent of V\(Descendants(W) Parents(W)) given Parents(W).

W in V, W is independent of V\ ( Descendants(W) Parents( W)) given Parents (W) . As expected we see that the number of detected causes by Granger is multiple times more than those of SyPI; in most cases Granger detects as causes all the candidate states. On the other hand, SyPI does not suffer from such problems even when there are latent confounders. Finally, in the third column, we report the detected distant causes. Strict thresholds (the default of SyPI method) are used for the analysis.