Using the structure of d-connecting paths as a qualitative measure of the strength of dependence

Abstract

Pearls concept OF a d - connecting path IS one OF the foundations OF the modern theory OF graphical models : the absence OF a d - connecting path IN a DAG indicates that conditional independence will hold IN ANY distribution factorising according TO that graph. IN this paper we show that IN singly - connected Gaussian DAGs it IS possible TO USE the form OF a d - connection 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.