On Bayesian Networks and Partial Orders

The essence of the Bayesian network model is largely embodied by its structural component: a directed acyclic graph (DAG). A DAG encodes assertions of conditional independence, whereas the remaining model parameters specify the actual local conditional distributions. The DAG plays an important role, for instance, in causal discovery and inference, where the DAG is interpreted as a representation of direct causes; that is, an arc uv from node u to node v asserts that the events associated with u are direct causes of the events associated with v. Given a DAG it is often trivial to fit the parameters of the local conditional distributions to a data set. On the contrary, learning the (postulated, true) DAG from data is very challenging both statistically and computationally.