When using impliedConditionalIndependencies() with the DAG
A ~ W1,
Y ~ W3,
W2 ~ W1 + W3,
W4 ~ W2
several independences are not returned by impliedConditionalIndependencies()
such as A II Y | W3; A II W3 | Y; A II W3 | W1, W2; W1 II Y | A
See section 5.1, top of p, 85 of Fundamentals of Causal Inference by Babette A. Brumback.
When using impliedConditionalIndependencies() with the DAG A ~ W1, Y ~ W3, W2 ~ W1 + W3, W4 ~ W2 several independences are not returned by impliedConditionalIndependencies() such as A II Y | W3; A II W3 | Y; A II W3 | W1, W2; W1 II Y | A See section 5.1, top of p, 85 of Fundamentals of Causal Inference by Babette A. Brumback.