- The network represents a set of conditional independence assertions.
- Each node is asserted to be conditionally independent of its nondescendants, given its immediate predecessors.
- It forms a directed acyclic graph.
- In general, \[P(y_1, \ldots, y_n) = \prod_{i=1}^{n} P(y_i \,|\, Parents(Y_i)) \] where $Parents(Y_i)$ denotes immediate predecessors of $Y_i$ in graph
- Joint distribution is fully defined by graph, plus the $P(y_i\,|\,Parents(Y_i))$.