Constructing the Maximal Prime Decomposition of Bayesian networks

The maximal prime decomposition (MPD) of a Bayesian network is a hierarchical structure, which represents conditional independency information. The MPD representation has shown to facilitate probabilistic inference in uncertainty management. One method for building the MPD involves applying the moralization and triangulation procedures to the given Bayesian network. An alternative method constructs the MPD using certain independencies encoded in a Bayesian network. In this paper, we analyze these two methods with respect to the construction and representation of the root level in the MPD. Our comparison reveals that the latter method can be seen as only requiring the moralization procedure. A second difference is that the former method represents the root level of the MPD as a jointree, while the later represents it as an acyclic hypergraph. Finally, our investigation of these two different approaches to the construction of the MPD yields the introduction of a new hybrid construction algorithm.