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 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. The structural analysis explores the connection between the structure of a model and the functional dependence among its elements.