Using the structure of d-connecting paths as a qualitative measure of the strength of dependence
Sanjay Chaudhuri, Thomas S. Richardson · arXiv (Cornell University) · 2002
Pearl's concept of a d-connecting path is one of the foundations of the modern t h e ory of graphical models: the absence of a d-connecting path in a DAG indicates that conditional independence will hold in any distribution factorizing according to that graph. In this paper we show that in singlyconnected Gaussian DAGs it is possible to use the form of a d-connecting path to obtain qualitative information about the strength of conditional dependence. More precisely, the squared partial correlations between two given variables, conditioned on different subsets may be partially ordered by examining the relationship between the d-connecting path and the set of variables conditioned upon.