  One approach to monitoring a dynamic system relies on decomposition of the
system into weakly interacting subsystems. An earlier paper introduced a notion
of weak interaction called separability, and showed that it leads to exact
propagation of marginals for prediction. This paper addresses two questions
left open by the earlier paper: can we define a notion of approximate
separability that occurs naturally in practice, and do separability and
approximate separability lead to accurate monitoring? The answer to both
questions is afirmative. The paper also analyzes the structure of approximately
separable decompositions, and provides some explanation as to why these models
perform well.
