How BBNs deal with evidence

In this section we look at the way that evidence is transmitted in BBNs. We consider two types of evidence:

• Hard evidence (instantiation) for a node X is evidence that the state of X is definitely a particular value. For example, suppose X represents the result of a particular match for a football team {win, lose, draw}. Then an example of hard evidence would be knowledge that the match is definitely won. In this case we also say X is instantiated as the value 'win'.

• Soft evidence for a node X is any evidence that enables us to update the prior probability values for the states of X. For example, if we know that the team is winning the match 3-0 at half-time, then the probability of win would be quite high, while the probabilities of both lose and draw would be quite low (compared with ignorance prior values).

We distinguish three types of connection in a BBN:

In a serial connection we will see that any evidence entered at the beginning of the connection can be transmitted along the directed path providing that no intermediate node on the path is instantiated (which thereby blocks further transmission).

In a diverging connection we will see that evidence can be transmitted between two child nodes of the same parent providing that the parent is not instantiated.

In a converging connection we will see that evidence can only be transmitted between two parents when the child (converging) node has received some evidence (which can be soft or hard).

The rules for transmitting evidence for serial, diverging and converging connections are sufficient for us to describe a completely general procedure for determining whether any two nodes of a BBN are dependent or not. This is the formal notion of d-separation. This notion is crucial for understanding how the algorithms for probability propagation in BBNs actually work.