Unlike a standard node in a Bayesian network, a temporal node may require more than one distribution. To understand why, it is useful to unroll a dynamic Bayesian network, and look at the equivalent Bayesian network.
A dynamic Bayesian network
The dynamic Bayesian network above unrolled for 5 time steps
The distributions required for the dynamic Bayesian network are shown below.
| Node | Distribution | Why? |
|---|---|---|
| A | P(A[0]) | At time 0, node A has no incoming links |
| A | P(A[0]|A[-1]) | At time 1, node A has a single incoming link from A at time 0 |
| A | P(A[0]|A[-2], A[-1]) | At time 2 or more, A has two incoming links from A at time-1, and A at time-2 |
| B | P(B[0]|A[0]) | At any time, B has a single incoming link from A at the same time |
