Structural Controllability and Observability in Influence Diagrams
  Influence diagram is a graphical representation of belief networks with
uncertainty. This article studies the structural properties of a probabilistic
model in an influence diagram. In particular, structural controllability
theorems and structural observability theorems are developed and algorithms are
formulated. Controllability and observability are fundamental concepts in
dynamic systems (Luenberger 1979). Controllability corresponds to the ability
to control a system while observability analyzes the inferability of its
variables. Both properties can be determined by the ranks of the system
matrices. Structural controllability and observability, on the other hand,
analyze the property of a system with its structure only, without the specific
knowledge of the values of its elements (tin 1974, Shields and Pearson 1976).
The structural analysis explores the connection between the structure of a
model and the functional dependence among its elements. It is useful in
comprehending problem and formulating solution by challenging the underlying
intuitions and detecting inconsistency in a model. This type of qualitative
reasoning can sometimes provide insight even when there is insufficient
numerical information in a model.
