Matrix-based Bayesian Network for efficient memory storage and flexible inference

For real-world civil infrastructure systems that consist of a large number of functionally and statistically dependent components, such as transportation systems or water distribution networks, the Bayesian Network (BN) can be a powerful tool for probabilistic inference. In a BN, the statistical relationship between multiple random variables (r.v.’s) is modeled through a directed acyclic graph. The complexity of inference in the BN depends not only on the number of r.v.’s, but also the graphical structure. As a consequence, the application of standard BN techniques may become infeasible even with a moderate number of r.v.’s as the size of an event set exponentially increases with the number of r.v.’s. Moreover, when the exhaustive set that is required for full quantification of a discrete BN node becomes intractably large, only approximate inference algorithms are feasible, which do not require the full (explicit) description of all BN nodes. We address both issues in discrete BNs by proposing a matrix-based Bayesian Network (MBN) that facilitates efficient modeling of joint probability mass functions and flexible inference. The MBN is developed for exact as well as approximate BN inference. The efficiency and applicability of the MBN are demonstrated by numerical examples. The supporting source code and data are available for download at https://github.com/jieunbyun/GitHub-MBN-code.