Computing probabilities for probabilistic influence diagrams

Probabilistic influence diagrams are a useful stochastic modeling tool. To efficiently calculate probabilities of interest relative to a probabilistic influence diagram it will be helpful to use an associated decomposable directed graph. We first explore and discuss some graph-theoretic and conditional independence properties of decomposable probabilistic influence diagrams. These properties are helpful in providing an efficient algorithm for obtaining a posterior decomposable probabilistic influence diagram given the state of one or more observed nodes. The connection between Shachter's sequential creation of conditionally barren nodes concept and Lauritzen and Spiegelhalter's moralization and triangulation algorithm for calculating probabilities relative to a probabilistic influence diagram is made explicit. We also discuss how to use wisely the concepts of sequential creation of conditionally barren nodes and merging nodes together with the graph-theoretic properties of decomposable directed graphs to compute probabilities relative to probabilistic influence diagrams.