Structural Relationships and Independence
The basic independence assumption (simplified version):
- two nodes X and Y are probabilistically independent conditioned on E if every undirected path from X to Y is d-separated by E
- every undirected path from X to Y is blocked by E
- if there is a node Z for which one of three conditions hold
- Z is in E and Z has one incoming arrow on the path and one outgoing arrow
- Z is in E and both arrows lead out of Z
- neither Z nor any descendent of Z is in E, and both arrows lead into Z