  This paper considers the problem of invoking auxiliary, unobservable
variables to facilitate the structuring of causal tree models for a given set
of continuous variables. Paralleling the treatment of bi-valued variables in
[Pearl 1986], we show that if a collection of coupled variables are governed by
a joint normal distribution and a tree-structured representation exists, then
both the topology and all internal relationships of the tree can be uncovered
by observing pairwise dependencies among the observed variables (i.e., the
leaves of the tree). Furthermore, the conditions for normally distributed
variables are less restrictive than those governing bi-valued variables. The
result extends the applications of causal tree models which were found useful
in evidential reasoning tasks.
