Hierarchical Bayesian Networks: A Probabilistic Reasoning Model for Structured Domains

Bayesian Networks are being used extensively for reasoning under uncertainty. Inference mechanisms for Bayesian Networks are compromised by the fact that they can only deal with propositional domains. In this work, we introduce an extension of that formalism, Hierarchical Bayesian Networks, that can represent additional information about the structure of the domains of variables. Hierarchical Bayesian Networks are similar to Bayesian Networks, in that they represent probabilistic dependencies between variables as a directed acyclic graph, where each node of the graph corresponds to a random variable and is quantified by the conditional probability of that variable given the values of its parents in the graph. What extends the expressive power of Hierarchical Bayesian Networks is that a node may correspond to an aggregation of simpler types. A component of one node may itself represent a composite structure; this allows the representation of complex hierarchical domains. Furthermore, probabilistic dependencies can be expressed at any level, between nodes that are contained in the same structure.