Serial Connection

Suppose we have some evidence that a signal failure has occurred (A). Then clearly this knowledge increases our belief that the train is delayed (B), which in turn increases our belief that Norman is late (C). Thus evidence about A is transmitted through B to C. In general any evidence about A will be transmitted through B to C as shown in the following animation:


However, now suppose that we know the true status of B; for example, suppose we know that the train is delayed (that is, we have hard evidence for B). In this case any knowledge about A is irrelevant to C because our knowledge of B essentially 'overwrites it'; any new information about the likelihood of a signal failure (A) is not going to change our belief about Norman being late once we know that the train is delayed. In other words the evidence from A cannot be transmitted to C because B blocks the channel as shown in the following animation

In summary, in a serial connection evidence can be transmitted from A to C unless B is instantiated. Formally we say that A and C are d-separated given B.